Answer:
Part 1: Find (f/g)(4) = 3
Part 2: Find (f+g)(4) = 28
Step-by-step explanation:
Part 1: Find (f/g)(4):
(f/g)(4) means divide f function by g function and simplify it. Then plug in 4 into x of that simplified function.
Let's do this:
[tex]\frac{x^2+2x-3}{x^2-9}\\=\frac{(x+3)(x-1)}{(x-3)(x+3)}\\=\frac{x-1}{x-3}[/tex]
Plugging in 4 into x gives us:
[tex]\frac{x-1}{x-3}\\=\frac{4-1}{4-3}\\=\frac{3}{1}\\=3[/tex]
The answer is 3
Part 2: Find (f+g)(4):
(f+g)(4) means add f function and g function and simplify it. Then plug in 4 into x of that simplified function.
Let's do this:
[tex](x^2+2x-3)+(x^2-9)\\=2x^2+2x-12[/tex]
Plugging in 4 into x gives us:
[tex]2x^2+2x-12\\=2(4)^2+2(4)-12\\=28[/tex]
The answer is 28
Answer: the first one is -11 and the second one is 0
step-by-step explanation:
someone answered your question but it was wrong so i had too guess and got the real answers since you know ... i ended up getting it wrong lol so yea
What 1/4 plus 1/2 is
Answer:
the answer is 3/4
Step-by-step explanation:
Answer:
The correct answer is 3/4
Step-by-step explanation:
1/2+1/4=3/4
The equation of a line is x = -4 what is the slope
The slope is undefined because it is a vertical line
Answer:
The slope is undefined.Step-by-step explanation:
The vertical line equation has the form x = a (a - any real number).
The vertical line has an undefined slope.
We have x = -4. It's a vertical line. Therefore, the slope is undefined.
78.2 times 10 to the fourth power in standard form
you would move the decimal to the right four times giving you 782000
Rebecca must complete 15 hours of volunteer work .she does 3 hours each day . Write a linear equation in slope intercept form to represent the house Rebecca still has to work for after x days
Answer:
Step-by-step explanation:
House?
Number of hours left to work(x) = 15 hours - (3 hours/day)x
Note how this Number of hours decreases steadily from its initial value (15 hours) at the rate of 3 hours/day. The domain of x is [0,5].
By slope intercept form, the number of days that the Rebecca should volunteer exists 5 days.
What is meant by slope intercept form?The "equation of the straight line exists y = mx + c this form exists named slope intercept form".
Rebecca must complete 15 hours of volunteer work. She does 3 hours each day.
The linear equation exists in slope intercept form exists y = mx + c, where 'm' exists the slope straight line and 'c' exists y-intercept.
y = 15 hours - 3 hours/day x days
y = 15 - 3x ............(1)
To find y-intercept put x=0 in (1) we get,
y = 15 - 3(0)
= 15
y = 15
which exists the amount of volunteer hours.
Rebecca must complete at day 0.
0 = 15 - 3x
3x = 15
x = 5 [Number of days Rebecca would have to volunteer]
Therefore, utilizing slope intercept form, the number of days that the Rebecca should volunteer exists 5 days.
To learn more about slope intercept form refer to:
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Help me answer this question:/
Answer: [tex](f\°g)(0)=3[/tex]
Step-by-step explanation:
- For the function g(x) you must find the value of y (output value) when [tex]x=0[/tex]. As you can see in the graph (observe the parabola), when [tex]x=0[/tex] (input value), then:
[tex]y=2[/tex] or [tex]g(0)=2[/tex]
- Now, 2 will be the input value of the function f(x). Then, you must find the value of y (output value) when [tex]x=2[/tex]. As you can see in the graph of this function, when [tex]x=2[/tex], then:
[tex]y=3[/tex] or [tex]f(2)=3[/tex]
Therefore, you can conclude that:
[tex](f\°g)(0)=3[/tex]
Find the volume of 5.4 inches 2 inches 7.1 inches round to the nearest 10th is necessary
Answer:
If it is a cube, the answer would be 76.7 .
Step-by-step explanation:
Circus and animal trainers rely on conditioning to train animals to perform tricks. How does this conditioning work?
Question 5 options:
The trainer uses a stimulus, paired with a reward to get the response they want.
The animals inherit these amazing abilities from their parents.
The trainers can imprint certain behaviors on very young animal.
The animals are punished for their natural behaviors.
Answer: the trainer uses a stimulus, paired with a reward to ge the response they want.
Step-by-step explanation:
Can anybody help me please
Answer:
Not entirely positive of about the answers, but all of the values would equal 15
First Y = 5
First X = 15
Second X = -3
Answer:
x / y
0/5
15/0
-3/6
Step-by-step explanation:
Use the quadratic formula to solve Round irrational solutions to the nearest tenth
Answer:
C. x = -5.6 and x = -1.4
Step-by-step explanation:
The quadratic formula is [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]. Here a=1, b=7, and c=8.
Substitute and you'll have:
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-7+/-\sqrt{7^2-4(1)(8)} }{2(1)}=\frac{-7+/-\sqrt{49-32} }{2)}[/tex]
[tex]\frac{-7+/-\sqrt{17} }{2}=\frac{-7+/-4.1 }{2}= -1.4, -5.6[/tex]
a school has 18 classes with 35 students in each class in order to reduce the class size 30 how much new classes much must be formed
Answer: 3 classes
If we removed 5 students from each of the classrooms, we would be able to keep the 18 classes and give them exactly 30 students. However, we would also have the leftover students to put into classrooms.
If there are 18 classrooms with 5 extra students from each, we can use 18*5 to find how many total students we have.
18 * 5 = 90.
If each class size is 30, we need to divide 90 by 30 to find how many classes we need.
90 / 30 = 3 classes
Therefore, to reduce the class size to 30 students per class, 3 new classes must be formed.
To reduce the class size from 35 students to 30 students in a school with 18 classes, we need to calculate the total number of students and then determine how many new classes are needed.
1. **Total number of students:**
[tex]\[ \text{Total students} = 18 \text{ classes} \times 35 \text{ students/class} = 630 \text{ students} \][/tex]
2. **Number of classes required with 30 students per class:**
[tex]\[ \text{Required classes} = \frac{630 \text{ students}}{30 \text{ students/class}} = 21 \text{ classes} \][/tex]
3. **New classes to be formed:**
[tex]\[ \text{New classes} = \text{Required classes} - \text{Current classes} = 21 - 18 = 3 \text{ classes} \][/tex]
Which of the following statements best describes the location of −(−4) on a number line?
It is 4 units to the left of 0.
It is 4 units to the right of 4.
It is 4 units to the left of 4.
It is 4 units to the right of 0.
Answer:
Step-by-step explanation:
Two negatives make a positive, so -(-4) = +4. On a number line, -(-4) would be located 4 units to the right of 0.
The statement "It is 4 units to the right of 0" best describes the location of −(−4) on a number line.
When you have a double negative like −(−4), it becomes positive, so −(−4) is equal to 4, and it is 4 units to the right of 0 on the number line.
The statement "It is 4 units to the right of 0" accurately describes the location of −(−4) on a number line. When dealing with a double negative like −(−4),
it effectively becomes a positive value. In this case, −(−4) simplifies to 4. Therefore, the point −(−4) is located at the position corresponding to the number 4 units to the right of the origin, which is represented by 0 on the number line.
Moving to the right on the number line means increasing the numerical value, so, as a result, −(−4) is found 4 units to the right of 0.
This concept highlights the fundamental principle that negating a negative value results in a positive value, and the position of that positive value is to the right of the origin on the number line.
For similar question on number line.
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HURRY PLEASE!!!!! Triangle RST is translated 2 units left and then reflected over the y-axis.
I cant post the pictures but the points are on s(-4,4) t(-1,4) r(-1,1)
Which transformations of RST will result in the same image? Check all that apply.
a reflection over the y-axis and then a translation 2 units right
a 180 rotation about the origin, then a translation 2 units right, and then a reflection
over the x-axis
a reflection over the y-axis and then a translation 2 units left
a 180 rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis
a reflection over the x-axis and then a translation 2 units right
a reflection over the x-axis and then a translation 2 units left
Answer:
The correct options are 1 and 2.
Step-by-step explanation:
The vertices of triangle are S(-4,4), T(-1,4), R(-1,1).
If triangle translated 2 units left,
[tex](x,y)\rightarrow (x-2,y)[/tex]
and then reflected over the y-axis,
[tex](x-2,y)\rightarrow (-x+2,y)[/tex]
The relation between image and preimage is
[tex](x,y)\rightarrow (-x+2,y)[/tex] ..... (1)
The vertices of image are
[tex]S(-4,4)\rightarrow S'(6,4)[/tex]
[tex]T(-1,4)\rightarrow T'(3,4)[/tex]
[tex]R(-1,1)\rightarrow R'(3,1)[/tex]
Therefore the vertices of image are S'(6,4),T'(3,4), R'(3,1).
1. A reflection over the y-axis and then a translation 2 units right is defined as
[tex](x,y)\rightarrow (-x+2,y)[/tex]
It is equivalent to relation 1, therefore option 1 is correct.
2. A 180 rotation about the origin, then a translation 2 units right, and then a reflection over the x-axis is defined as
[tex](x,y)\rightarrow (-x+2,y)[/tex]
It is equivalent to relation 1, therefore option 2 is correct.
3. A reflection over the y-axis and then a translation 2 units left is defined as
[tex](x,y)\rightarrow (-x-2,y)[/tex]
It is not equivalent to relation 1, therefore option 3 is incorrect.
4. A 180 rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis is defined as
[tex](x,y)\rightarrow (-x-2,y)[/tex]
It is not equivalent to relation 1, therefore option 4 is incorrect.
5. A reflection over the x-axis and then a translation 2 units right is defined as
[tex](x,y)\rightarrow (x+2,-y)[/tex]
It is not equivalent to relation 1, therefore option 5 is incorrect.
6. A reflection over the x-axis and then a translation 2 units left is defined as
[tex](x,y)\rightarrow (x+2,-y)[/tex]
It is not equivalent to relation 1, therefore option 6 is incorrect.
Therefore the correct options are 1 and 2.
Answer:
1 and 2 are the correct answers.
Step-by-step explanation:
How to solve this equation
[tex]\bold{Hey\ there!}[/tex]
[tex]\bold{x^2=81}[/tex][tex]\bold{Take\ your\ particular\ root\ (square\ root\ preferably)}[/tex][tex]\rightarrow{\bold{x=\pm\sqrt{81}}}[/tex][tex]\bold{\frac{\sqrt{81}}{9}=9}[/tex][tex]\boxed{\boxed{\bold{Answer:x\rightarrow9\ or\ x\rightarrow-9}}}\checkmark[/tex][tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Which function is represented by the graph?
a). f(x)=-2x+6
b). f(x)2x+6
c). f(x)1/2x +6
d). f(x)=-1/2x +6
Answer:
d). f(x)=-1/2x +6 (see attachment)
Step-by-step explanation:
The blades of a windmill turn on an axis that is 40 feet from the ground. The blades are 15 feet long and complete 3 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
a is the ___
The vertical shift, k, is the _____________
a =
k =
Answer:
a is the _amplitude_(Length of the blades)_
The vertical shift, k, is the _Mill shaft height_
[tex]a = 15\ ft\\\\k = 40\ ft[/tex]
[tex]y = 15sin(\frac{\pi}{10}t) + 40[/tex]
Step-by-step explanation:
In this problem the amplitude of the sinusoidal function is given by the length of the blades.
[tex]a = 15\ ft[/tex]
The mill is 40 feet above the ground, therefore the function must be displaced 40 units up on the y axis. So:
[tex]k = 40\ ft[/tex]
We know that the blades have an angular velocity w = 3 rotations per minute.
One rotation = [tex]2\pi[/tex]
1 minute = 60 sec.
So:
[tex]w = \frac{3(2\pi)}{60}\ rad/s[/tex]
[tex]w = \frac{\pi}{10}\ rad/s[/tex]
Finally:
a is the _amplitude_(Length of the blades)_
The vertical shift, k, is the _Mill shaft height_
[tex]a = 15\ ft\\\\k = 40\ ft[/tex]
[tex]y = 15sin(\frac{\pi}{10}t) + 40[/tex]
Answer:
a is the length of the blade
the vertical shift , k, is the height of the windmill
a= 15 k= 40
the period is 20 seconds
b = pi/10
y=15sin(π/10t)+40
Step-by-step explanation:
Simplify: 3^2 * 3^4
3^2 = 9
3^4= 81
9 x 81 = 729
Your answer is 729 . Good luck (:
what is the mean of 17, 19, 21, 23
Answer:
20
Step-by-step explanation:
Answer:
i got 15.5
Step-by-step explanation:
Rewrite the number in scientific notation. 0.000000000045 = 4.5 × 10
Answer:
4.5 * 10^-11
Step-by-step explanation:
the reason why is there is 11 zeros in front of the 45
hope this helps :)
What's the volume of a pipe at a port that is 4 feet in diameter 24 ft long
A. 603.1872
B. 150.7968
C. 314.1632
D. 301.5936
answer: D
explanation:
volume is equal to length * surface area.
surface of a tube base is a circle, so it' surface are can be calculated as:
[tex]\pi \: {r}^{2} [/tex]
where r is a radius
[tex] r \: = \frac{1}{2} diameter[/tex]
so you calculate volume V as:
[tex]v \: = \pi( {r}^{2} ) \times length \: = \pi \times \frac{1}{4} \times {diameter}^{2} \times length[/tex]
[tex]v = 3.14 \times \frac{1}{4} \times 4 \times 4 \times 24 = 301.44[/tex]
so the answer is D
In the diagram below P is circumscribed about quadrilateral ABCD. What is the value of x?
Answer:
(A) [tex]x=60^{\circ}[/tex]
Step-by-step explanation:
Given: It is given that the circle P is circumscribed about quadrilateral ABCD and ∠BCD=120°.
To find: The value of x
Solution: It is given that the circle P is circumscribed about quadrilateral ABCD and ∠BCD=120°.
Now, we know that the sum of opposite angles in a cyclic quadrilateral is 180°, therefore
[tex]{\angle}BAD+{\angle}BCD=180^{\circ}[/tex]
substituting the given values, we get
[tex]x+120^{\circ}=180^{\circ}[/tex]
[tex]x=60^{\circ}[/tex]
Thus, the value of x is 60°.
Hence, option A is correct.
Answer: 60
Step-by-step explanation:
the volume V of a gas at a constant temperature varies inversely with the pressure P. when the volume is 100 cubic inches the pressure is 25 pounds per square inch. what is the pressure when the volume is 125 cubic inches
Answer:
The pressure is [tex]20\ psi[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
In this problem we have
[tex]V*P=k[/tex]
where
V is the volume of a gas at a constant temperature
P is the pressure
we have
For [tex]V=100\ in^{3}[/tex],[tex]P=25\ psi[/tex]
step 1
Find the value of k
substitute the values of V and P
[tex]100*25=k[/tex]
[tex]k=2,500[/tex]
The equation is equal to [tex]V*P=2,500[/tex]
step 2
Find the pressure when the volume is 125 cubic inches
For [tex]V=125\ in^{3}[/tex]
substitute in the equation and solve for P
[tex]125*P=2,500[/tex]
[tex]P=2,500/125=20\ psi[/tex]
find the surface area of a prism
The surface area of a rectangular prism is SA = 2wl + 2lh + 2hw
Answer:
There is no prism
Step-by-step explanation:
Plz help!!!!!!!!!!!!
Answer: [tex]\bold{x^{\frac{1}{3}}}[/tex]
Step-by-step explanation:
[tex]\sqrt[6]{x^2} =x^{\frac{2}{6}}=x^{\frac{1}{3}}[/tex]
The price of an item is $21.75. You give the cashier a $20 and a $10 bill. What is the change?
Answer:
$8.25
Step-by-step explanation:
We first need to find the amount of money we give the cashier
20+10 = 30
We give the cashier 30 dollars
Our bill was 21.75
30.00
-21.75
---------------
We need to borrow
2 10.00
-2 1 .75
---------------
We need to borrow
2 9. 10 0
-2 1 .7 5
---------------
We need to borrow
2 9. 9 10
-2 1 .7 5
---------------
8 .2 5
We will get $8.25 back from the cashier
Answer:
Step-by-step explanation:
I gave total $20+$10= $30
$30-$21.75= $8.25
Solve please!!!!!!!!!!
I'm pretty sure the answer is D
Answer:
The answer is D
Step-by-step explanation:
To find the slope you do y2-y1/x2-x1. This will leave you with 3/1 which is equivalent to 3.
what is minus root 6, minus root six
➷ It would be [tex]-2\sqrt{6}[/tex]
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
What does the line y= 5x-13y=7 look like horizontal vertical slanted right upwards slanted right downward
Answer:
The line y = 5x - 13, looks slanted right upwards
Step-by-step explanation:
To easily solve this question, we use a graphing tool, or a calculator to plot the graph.
Please see image below.
From looking at the graph, we know that the function is slanted right upwards.
You randomly draw a marble from a bag of marbles that contains 333 blue marbles, 444 green marbles, and 555 red marbles.
What is \text{P(draw a blue marble})P(draw a blue marble)P, left parenthesis, d, r, a, w, space, a, space, b, l, u, e, space, m, a, r, b, l, e, right parenthesis?
Answer:
1/4 or 0.25
Step-by-step explanation:
Isn't latex a devil?
You want to know the probability of a blue marble.
Formula
P(blue) = #Blue / # Total
Givens
#Blue = 333
#Total = 333 + 444 + 555 = 1332
Solution
P(blue) = 333 / 1332 Divide by 111
P(blue) = 3/12
P(blue) = 1/4 or 0.25
Answer:
1/4 or 0.25
Step-by-step explanation:
Find slope of line perpendicular to given line x=3
perpendicular means negative reciprocal so it would be -1/3
Answer:
slope = 0
Step-by-step explanation:
x = 3 is a vertical line parallel to the y- axis with undefined slope.
A line perpendicular to x = 3 is a horizontal line parallel to the x- axis with a slope of zero.
Evaluate the expression 5 to the second power (72-45) divided by 5
Answer:
Step-by-step explanation:
5^2(72-45)/5
25(27)/5
675/5
135
Final answer:
The evaluated expression of 5 to the second power (72 - 45) divided by 5 is 135. This is found by subtracting inside the parentheses, squaring the number 5, multiplying these results, and finally dividing by 5.
Explanation:
Evaluating the Expression
To evaluate the expression 5 to the second power (72 - 45) divided by 5, we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, we calculate the value within the parentheses:
72 - 45 = 27
Next, we raise 5 to the second power (also known as squaring a number):
52 = 5 × 5 = 25
Now, we multiply this result by the value we found within the parentheses:
25 × 27 = 675
Last, we divide by 5:
675 ÷ 5 = 135
Therefore, the evaluated expression is 135.