The value of the functions are:
a. g(-4) + f(-2) = 24
b.. f(1) - g(0) = 1
What is a function?A function can be defined as an expression showing the relationship between two variables.
Given the functions;
f (x) = 3x - 1 g (x) = x² + 1g(-4); substitute the value of x as - 4 in g(x)
g(-4) = (-4)² + 1
g(-4) = 16 + 1
g(-4) = 17
f(-2); substitute the value of x as - 2 in f(x)
f(-2) = 3(-2) - 1
f(-2 = -7
a. g(-4) + f(-2) = 17 -(-7)
g(-4) + f(-2) = = 24
f(1) = 3(1) - 1
f(1) = 2
g(0) = (0)² + 1
g(0) = 1
b. f(1) - g(0) = 2 - 1
f(1) - g(0) = 1
Thus, the value of g(-4) + f(-2) and f(1) - g(0) are 24 and 1 respectively.
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[HELP] For j(x) = [tex]5^x^-^3[/tex], find j of the quantity x plus h end quantity minus j of x all over h period
the quantity x minus 3 end quantity times the quantity 5 to the power of h plus 1 end quantity all over h [tex]\frac{(x-3)(5^2+1)}{h}[/tex]
5 to the power of the quantity x minus 3 end quantity times the quantity 5 to the power of h end quantity all over h [tex]\frac{5^x^-^3(h^h)}{h}[/tex]
5 to the power of the quantity x minus 3 end quantity times the quantity 5 to the power of h plus 1 end quantity all over h [tex]\frac{5^x^-^3(5^h+1)}{h}[/tex]
5 to the power of the quantity x minus 3 end quantity times the quantity 5 to the power of h minus 1 end quantity all over h [tex]\frac{5^x^-^3(5^h-1)}{h}[/tex]
The difference quotient of the function that has been presented to us will turn out to be 5.
How can I calculate the quotient of differences?In this step, we wish to determine the difference quotient for the function that was supplied.
To begin, keep in mind that the difference quotient may be calculated by:
Lim h->0 [tex]\frac{f(x+h)-f(x)}{h}[/tex]
Now, for the purpose of the function, we need this:
Then we will have:
[tex]$$\begin{aligned}&\lim _{h \rightarrow 0} \frac{j(x+h)-j(x)}{h} \\&\lim _{h \rightarrow 0} \frac{5 *(x+h)-3-5 * x+3}{h} \\&\lim _{h \rightarrow 0} \frac{5 x+5 h-3-5 x+3}{h} \\&\lim _{h \rightarrow 0} \frac{5 h}{h}=5\end{aligned}$$[/tex]
j(x) = 5x - 3
Then the following will be true:
Therefore, 5 is the value of the difference quotient for j(x) is %
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Match the imaginary solutions with the correct simplified forms:
Answer:
See the picture below.
Step-by-step explanation:
Answer:
[tex]\sqrt{-63}=3i\sqrt{7}[/tex]
[tex]\sqrt{-156}=2i\sqrt{39}[/tex]
[tex]6\sqrt{-12}=12i\sqrt{3}[/tex]
[tex]-5\sqrt{-75}=-25i\sqrt{3}[/tex]
Step-by-step explanation:
An imaginary number is a non-zero real number multiplied by the imaginary unit [tex]i[/tex].
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Imaginary Number Rule}\end{center}\\\begin{center}$\sqrt{-1}=i$\end{center}\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Radical Rule}\end{center}\\\begin{center}$\sqrt{a \cdot b}=\sqrt{a} \sqrt{b}$\end{center}\end{minipage}}[/tex]
[tex]\begin{aligned}\sqrt{-63} & = \sqrt{9 \cdot -1 \cdot 7}\\& = \sqrt{9}\sqrt{-1}\sqrt{7}\\& = 3i\sqrt{7}\end{aligned}[/tex]
[tex]\begin{aligned}\sqrt{-156} & = \sqrt{4 \cdot -1 \cdot -39}\\& = \sqrt{4} \sqrt{-1} \sqrt{39}\\& = 2i\sqrt{39}\end{aligned}[/tex]
[tex]\begin{aligned}6 \sqrt{-12} & = 6 \sqrt{4 \cdot -1 \cdot -3} \\& = 6 \sqrt{4} \sqrt{-1} \sqrt{3} \\& = 6 \cdot 2 i \sqrt{3} \\& = 12i \sqrt{3}\end{aligned}[/tex]
[tex]\begin{aligned}-5 \sqrt{-75} & = -5 \sqrt{25 \cdot -1 \cdot -3} \\& = -5 \sqrt{25} \sqrt{ -1 } \sqrt{3} \\& = -5 \cdot 5i \sqrt{3} \\& = -25i \sqrt{3}\end{aligned}[/tex]
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The start of an arithmetic sequence is
16, 19, 22, 25, ...
The rule for the sequence can be written in the
form xn = cn +d, where c and d are
numbers.
a) By first calculating the values of c and d,
work out the rule for the sequence.
b) What is the value of x11?
a) If the [tex]n[/tex]-th term is [tex]x_n = cn+d[/tex], then
[tex]x_1 = c + d = 16[/tex]
[tex]x_2 = 2c + d = 19[/tex]
Eliminating [tex]d[/tex],
[tex](2c+d) - (c+d) = 19-16 \implies c = 3[/tex]
Solving for [tex]d[/tex],
[tex]3 + d = 16 \implies d = 13[/tex]
Then
[tex]\boxed{x_n = 3n + 13}[/tex]
b) When [tex]n=11[/tex], we get
[tex]x_{11} = 3\cdot11 + 13 = \boxed{46}[/tex]
Simplify m7m−4.
please please helpppp
Answer:
[tex]m^8-4[/tex]
Step-by-step explanation:
[tex]Rule: a^b\cdot \:a^c=a^{b+c}\\=m^7m=m^{7+1}\\=m^{7+1}-4\\=m^8-4[/tex]
Beginning with the graph of f(x) = x2, what transformations are needed to form g of x equals one half times the quantity x plus 4 end quantity squared minus 3 question mark
The graph of g(x) is narrower than f(x) and is shifted to the right 4 units and down 3 units.
The graph of g(x) is narrower than f(x) and is shifted to the left 4 units and down 3 units.
The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.
The graph of g(x) is wider than f(x) and is shifted to the right 4 units and down 3 units.
Beginning with the graph of f(x) = x2, The transformations that are needed to form [tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex] is
The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units
This is further explained below.
What is transformations?Generally, A point, a line, or a geometric figure may undergo one of these four distinct transformations in order for the point's, line's, or figure's shape and/or location to be altered.
The shape of the item as it was before the transformation is referred to as the Pre-Image, while the shape and location of the object after the change make up the Image.
In conclusion, The necessary transformations may be found by beginning with the graph of the function f(x) = x2.
[tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex]
The graph of g(x) is bigger than the graph of f(x), and it is displaced 3 units to the left and 3 units down from its original position.
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Answer:
The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.
Step-by-step explanation:
I got it right.
An American dollar is worth about €0.89 in Euro currency. Which is approximately equal to €550 Euros?
(A) $635 U.S. dollars
B $621 U.S. dollars
D
$337 U.S. dollars
$331 U.S. dollars
Question 4
Which operation would produce the correct answer for
Answer:
Step-by-step explanation: Well €550 Euros is equal to $547.42 US dollars in currency. But since this is approximately, (D) should be correct.
Fatima is selling cookies in a bake sale. She packages 20 cookies in 4 minutes. Describe the relationship between the amount of cookies and the time it takes to package them.
Based on the number of cookies that Fatima was able to package in a certain amount of time, the relationship between the cookies and the time it takes to package them is a single cookie is packaged in 12 seconds.
How long does it take to package the cookies?To find the amount of time it takes to package the cookies, the formula is:
= Number of minutes / Number of cookies
= 4 / 20
= 1/5
= 0.20 minutes
When converted to minutes, this is:
= 0.20 x 60 seconds per minute
= 12 seconds
In conclusion, it takes 12 seconds to package a cookie on average.
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If we know the distance of an object from earth, we can determine the size of the object by measuring its parallax. True or false?.
False, If we know the distance of an object from earth, we can determine the size of the object by measuring its parallax.
The size of an object can be calculated by measuring its parallax if we know how far it is from Earth. According to the heliocentric theory of the universe, Earth is the center of the universe, and everything else revolves around it. A planet's speed is unaffected by the location of the planet within its orbit.
What is parallax explain?
Particularly: the angular difference in direction of a celestial body as measured from two places in the earth's orbit. the apparent displacement or the difference in apparent direction of an object as observed from two separate points that are not on a straight line with the object.Learn more about parallax
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What am I doing wrong here? Please help!
Answer:
If there are dotted lines available then use dotted lines for the range where its only greater than or less than, when there is no equals to sign then you use dotted lines
Step-by-step explanation:
Evaluate 2d+32 when d=8.
Given [tex]2d+32[/tex]
[tex]d=8[/tex]
Put the value of d in the given equation
[tex]2d+32[/tex]
[tex]2(8)+32[/tex]
[tex]16+32[/tex][tex]= 48[/tex]
What we do in Evaluation in math?
The verb "evaluate" is used in mathematics to mean to discover or determine the worth of something. Finding the precise value of an algebraic expression or numerical computation is relevant here as well as financial mathematics.
In mathematics, the terms "evaluate" and "solve" are often used interchangeably. Consider the following basic multiplication problem: "Evaluate the cost of six tomatoes when the tomatoes are purchased at $2 each." The student would multiply 6 by 2 to get the result of $12. The term evaluate might also come before a list of inquiries, as a list of straightforward algebraic equations.
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PLEASE HELP!!!!! please? :D
Answer:
9
Step-by-step explanation:
→ Substitute in the values
2³ +√64 ÷ 8
→ Simplify
8 + 8 ÷ 8
→ Calculate
8 + 1 = 9
Answer:
9
Step-by-step explanation:
2 to the power of 3 is 8
8 + 64 = 72
72 ÷ 8 = 9
Find the value of |-4 + 3| · 8.
-8
56
8
-56
?
The value of expression |-4 + 3| · 8 is 8.
What is Modulus function?
A modulus function is a function which gives the absolute value of numbers or variable.
The expression is given as;
| -4 + 3 | * 8
Now, Solve the expression as;
⇒ | -4 + 3 | * 8
⇒ | - 1 | * 8
⇒ 1 * 8
⇒ 8
Since, Modulus of a negative number gives the positive of that number.
Hence, The value of expression |-4 + 3| · 8 is 8.
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Answer and how to solve this
Answer: Marie ran 4.5 miles on Monday.
Step-by-step explanation: 5.7
+1.2
6.9
What is the price of a perpetuity that has a coupon of $55 per year and a yield to maturity of 2.5%? the price of the perpetuity is $?
The price of the perpetuity is $2200
What is price of the perpetuity?The present value of a perpetuity is determined by simply dividing the amount of the regular cash flows by the discount rate. A growing perpetuity includes a growth rate that increases the cash flows received each period going forward.
Given:
coupon=$55
yield to maturity=2.5%
As, we know price of the perpetuity is determined by dividing the coupon by the yield to maturity.
So,
price=coupon/yield to maturity
price=$55/2.5%
price=$2200
Hence, the price of the perpetuity is $2200
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Add using the number line. -9 +6 Drag and drop the word Sum to the correct value on the number line. -151413121110-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
If we select -9 in the number line, then we need to add 6. Because 6 is positive, we need to move 6 units to the right of -9, it will give:
-9 + 6 = -3
How to add using a number line?
When we have two values A and B and we want to add them using the number line, the first thing we need to do is select one of these two, and locate it on the number line.
Once we did that, the other number will tell us how many units we need to move to the left (if B is negative) or to the right (if B is positive).
In this case the two numbers are -9 and 6.
If we select -9 in the number line, then we need to add 6. Because 6 is positive, we need to move 6 units to the right of -9, it will give:
-9 + 6 = -3
We will get the exact same thing if we first step on the number 6 on the number line, and then move 9 units to the left, we will got -3.
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Find the volume of the solid.
The volume of the solid is
cubic centimeters.
Answer:
27
Step-by-step explanation:
4.5*3*2 = 27
hi,
You just have to multiply the three measures.
So :
2*3*4.5 = 27 cm³
Easy, is it not ?
An 8ft length of 4 inch wide crown molding costs $14. how much will it cost to buy 40ft of crown molding?
It would cost $70 to buy 40 ft of crown molding.
What is cost explain?
Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.8 ft length costs $14
To find the cost of 1 ft length,
Divide through by 8
8ft/8 length costs $14/8
1ft costs $1.75
Now, to find the cost of 40 ft length
1ft costs $1.75
1 ft x 40 would cost $1.75
40 ft would cost $70
Therefore, it would cost $70 to buy 40 ft of crown molding.
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Last week, 3/4 of the students in Mr. Zanker's class went on a field trip. 5/8 of the
students in Mr. Haynes's class went. What is the average fraction of students
in the two classes who went on the field trip?
A. 2/3
B. 11/16
C. 15/32
D. 15/16
The average fraction of students in the two classes who went on the field trip is 11/16
What is the average fraction of students in the two classes who went on the field trip?The given parameters are:
Class 1 = 3/4
Class 2 = 5/8
The average is calculated as
Average = 1/2 * (Class 1 + Class 2)
So, we have
Average = 1/2 * (3/4 + 5/8)
Evaluate
Average = 11/16
Hence, the average fraction of students in the two classes who went on the field trip is 11/16
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Point S is located at -10. Points T and U are each 5 units away from point S. Where are T and U located?
Can someone help me with this please?
since you said please: 127*
The price of a stock steadily decreased by a total of $ 138 over the past13 months. Which expression shows the change in the stock's value?
( dont know this math i'm in 6th grade can anybody help?)
The expression to show the stock's value is -$138 x 13
Given that the price of a stock is steadily decreasing.
Decreasing values are usually represented along with a negative sign.
The decreased price = $138
This means the decrease is of -$138.
Number of months = 13 years
That is $138 is decreased over 13 years.
Then The expression to show the stock's value is -$138 x 13
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ana worked 6 1/2 h on monday, 5 3/4 h on Tuesday and 7 1/6 h on Friday. how many hours did she work these three days.
Arianna buys computer games from an online store. each game she orders costs $22 and shipping for her total is $9. arianna can spend no more than $75. how many computer games can arianna buy?
There are 3 computer games she can brought at $75.
Unitary method
Unitary method is defined as the process of finding the value of a unit and then the value of a required number of units.
Given,
Arianna buys computer games from an online store.
Each game she orders costs $22 and shipping for her total is $9.
Arianna can spend no more than $75.
Here we need to find how many computer games did Arianna Brought.
Let x be the number of computer games she brought.
We know that,
Cost for one game = $22
Shipping cost = $9.
She spent = $75.
So, it can be written as,
=> 22x + 9 = 75
=> 22x = 75 - 9
=> 22x = 66
=> x = 66/22
=> x = 3.
So, she can brought 3 computer games at $75.
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An equilateral triangle is inscribed in a circle of radius 2r. express the area a within the circle but outside the triangle as a function of the length 3x of the side of the triangle.
The expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle is [tex]\frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].
It is given that:-
Radius of circle = 2r
Length of side of equilateral triangle = 3x
We have to find the expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle.
We know that,
Area of circle = [tex]\pi R^2[/tex]
Where R is the radius of the circle.
We have R = 2r
Area of an equilateral triangle = [tex]\frac{\sqrt{3} }{2}a^2[/tex]
Where, a is the length of side of equilateral triangle.
a = 3x
Hence,
Expression = [tex]\pi R^2-\frac{\sqrt{3} }{2}a^2[/tex]
Expression = [tex]\frac{22}{7}*(2r)^2-\frac{\sqrt{3} }{2}*(3x)^2 = \frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].
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In FGH, g = 140 inches, f= 980 inches and to the nearest degree.
Answer:
1204.7 in
Explanation:
15. On the cross-country team, 7th graders
are required to run x number of miles each
morning. 8th graders are required to run 15%
more than the 7th graders. Which expression
represents the number of miles an 8th grader
is required to run?
help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help
Answer:
1. (2x + 1) (x - 4)
2. (3y +2 ) (y + 1)
3. (w - 3) (3w + 5)
4. (4s - 1) (s + 7)
5. (x + 5) (2x - 3)
Step-by-step explanation:
Lots of good articles on factoring quadratics - that is what this is called.
Answer:
1. (2x + 1) (x - 4)
2. (3y +2 ) (y + 1)
3. (w - 3) (3w + 5)
4. (4s - 1) (s + 7)
5. (x + 5) (2x - 3)
Step-by-step explanation:
Without making any calculations, which data set has the smallest standard deviation? 1, 1, 2, 2, 3, 3 1, 3, 5 0, 1, 5, 6, 9, 10 1, 1, 1, 1, 2, 2, 2, 2
Answer: 0
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
One batch of brown paint uses 8 of yellow paint and 3 cups of purple paint Tyler made a large amount of brown paint using 40 cups of yellow paint
Answer:
not sure what you were asking, but its 15 cups of purple paint
Find the value of sin c
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{\sqrt{95}}\\ \end{cases} \\\\\\ c=\sqrt{7^2~~ + ~~(\sqrt{95})^2}\implies c=\sqrt{49+95}\implies c=\sqrt{144}\implies c=12 \\\\[-0.35em] ~\dotfill\\\\ sin(C )=\cfrac{\stackrel{opposite}{\sqrt{95}}}{\underset{hypotenuse}{12}}\implies sin(C)\approx \text{\LARGE 0.81}[/tex]
