Answer: [tex](gof)(-7) =495[/tex]
Step-by-step explanation:
Given the functions f(x) and g(x), to find [tex](gof)(x)[/tex] you need to substitute [tex]x=f(x)=x^2 + 6[/tex] into the function g(x):
[tex](gof)(x) = ( x^2 + 6)+ 8( x^2 + 6)\\\\(gof)(x)=x^2 + 6+ 8x^2 + 48\\\\(gof)(x)=9x^2 + 54[/tex]
Now, to find [tex](gof)(-7)[/tex] you must substitute [tex]x=-7[/tex] into [tex](gof)(x)[/tex], then you get:
[tex](gof)(-7) = 9(-7)^2 + 54\\\\(gof)(-7) =9(49)+54\\\\(gof)(-7) =441+54\\\\(gof)(-7) =495[/tex]
2^x=3^x+1 what are the exact approximate solutions
Answer:
d.
Step-by-step explanation:
The goal of course is to solve for x. Right now there are 2 of them, one on each side of the equals sign, and they are both in exponential positions. We have to get them out of that position. The way we do that is by taking the natural log of both sides. The power rule then says we can move the exponents down in front.
[tex]ln(2^x)=ln(3^{x+1})[/tex] becomes, after following the power rule:
x ln(2) = (x + 1) ln(3). We will distribute on the right side to get
x ln(2) = x ln(3) + 1 ln(3). The goal is to solve for x, so we will get both of them on the same side:
x ln(2) - x ln(3) = ln(3). We can now factor out the common x on the left to get:
x(ln2 - ln3) = ln3. The rule that "undoes" that division is the quotient rule backwards. Before that was a subtraction problem it was a division, so we put it back that way and get:
[tex]x(\frac{ln(2)}{ln(3)})=ln(3)[/tex]. We can factor out the ln from the left to simplify a bit:
[tex]x[ln(\frac{2}{3})]=ln(3)[/tex]. Divide both sides by ln(2/3) to get the x all alone:
[tex]x=\frac{ln(3)}{ln(\frac{2}{3}) }[/tex]
On your calculator, you will find that this is approximately -2.709
The cities D, E, and F lie, in respective order, approximately in a straight line. The distance from city D to city E is 125 miles. The distance from city D to city F is 160 miles. Find the distance from city E to city F
Answer:
35 miles
Step-by-step explanation:
The segment addition theorem tells you ...
DE + EF = DF
125 + EF = 160
EF = 35 . . . . . . . subtract 125
The distance from E to F is about 35 miles.
Help with this question, please ASAP!!
Answer:
the middle set of points
Step-by-step explanation:
A translation < 3, - 4 > means add 3 to the x- coordinate and subtract 4 from the y- coordinate.
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Hence
X(0, - 2) → X'(0 + 3, - 2 - 4) → X'(3, - 6) → X''(3, 6)
Y(1, 4) → Y'(1 + 3, 4 - 4) → Y'(4, 0) → Y''(4, 0)
Z(5, 3) → Z' (5 + 3, 3 - 4) → Z'(8, - 1) → Z''(8, 1 )
You're insecure
Don't know what for
You're turning heads when you walk through the door
Don't need make-up, to cover up
Being the way that you are is enough
Everyone else in the room can see it
Everyone else but you
Baby you light up my world like nobody else
The way that you flip your hair gets me overwhelmed
But when you smile at the ground it ain't hard to tell
You don't know, oh oh
You don't know you're beautiful
If only you saw what I can see
You'll understand why I want you so desperately
Right now I'm looking at you and I can't believe
You don't know, oh oh
You don't know you're beautiful, oh oh
That's what makes you beautiful
Takes these points if you like this song
Answer:
: ) It be gud song.
Step-by-step explanation:
While flying a kite, 400 ft of string was let out. The string ,when pulled tight, formed a 40 angle with the ground .What was the approximate height of the kite
Answer:
257 ft
Step-by-step explanation:
You know based upon soh that sin=opp/hyp
So drawing a right triangle with a hypotenuse of 400 ft and an angle of 40° with the ground, you can see that sin40=x/400
Multiply both sides to find your x value or height which is 257.
please help asap will mark brainliest
Answer:
The fraction is 7/10 and the decimal is 0.7
Step-by-step explanation:
Each incriment represents 1/10, or 0.1.
Answer:
Decimal: 0.7
Fraction: Simplified - 7/10 ; Non-simplified: 70/100
Step-by-step explanation:
There are 9 dashes in-between 0 & 1, meaning that each dash signifies 0.1, and that you are adding 0.1 each time.
The dot is located 7 dashes away from 0. Multiply 7 with 0.1
7 x 0.1 = 0.7
0.7 is your decimal answer.
Change the decimal to a fraction. To do so, move the decimal point to the right two place values and put it over 100. Add 0's if needed.
0.7 = 70/100
As it does not specify you have to simplify, put 70/100. HOWEVER, if it says you have to simplify, simplify. Divide common factors from both the numerator & denominator:
(70/100)/(10/10) = 7/10
7/10 is your simplified fraction. 70/100 is your non-simplified fraction.
~
I have two fair dice both numbered 1 to 6. I throw both dice and add both numbers together. What is the probability that the number I get a multiple of 5
Answer:7/36
Step-by-step explanation:
Firstly, I would draw a table to visually see what the outcomes are. There are many methods but this is what i find to be the easiest so here it goes!!!
I hope the pic helps! If you have any questions feel free to ask!
Evaluate (–1)8 + (–1)7 + –16 + –14 – (–1)2.
Answer:
Step-by-step explanation:
-8 - 7 - 16 - 14 + 2 = -43
[tex]\sqrt{4x+15} -3\sqrt{x} =0[/tex]
[tex]
\sqrt{4x+15}-3\sqrt{x}=0 \\
\sqrt{4x+15}=3\sqrt{x} \\
4x+15=9x \\
-5x=-15 \\
x=\boxed{3}
[/tex]
Hope this helps.
r3t40
Solve I = Prt for P when I = 5,480, r = .04, and t = 7.
Answer: P = 19,571.42857142857
Step-by-step explanation:
Plug in the variables.
5480 = x(.04)(7)
.04*7=.28
5480=.28x
.28x/.28=x
5480/.28=19,571.42857142857
19,571.42857142857(.04)(7)=5480
P = 19,571.42857142857
Answer:
19571.43
Step-by-step explanation:
We are asked to solve for P using formula [tex]I=Prt[/tex], when [tex]I=5480; r=0.04\text{ and }t=7[/tex].
Upon substituting our given values in simple interest formula, we will get:
[tex]5480=P*0.04*7[/tex]
[tex]5480=P*0.28[/tex]
Switch sides:
[tex]P*0.28=5480[/tex]
Now, we will divide both sides of our given equation by 0.28 as:
[tex]\frac{P*0.28}{0.28}=\frac{5480}{0.28}[/tex]
[tex]P=19571.42857[/tex]
[tex]P\approx 19571.43[/tex]
Therefore, the principal amount (P) is approximately 19571.43.
Emily, Jean, and Amanda live in apartments on the 5th, 6th, and 7th floors. One girl likes baseball, one likes football, and one likes soccer. The girl on the 6th floor is the football fan. The girl on the 5th floor thinks soccer is boring. What sport does the girl on the 7th floor like?
Answer:
soccer
Step-by-step explanation:
Neither the 5th-floor nor 6-floor girl likes soccer, so that must be the sport of choice on the 7th floor.
What is 7.884 rounded to the nearest hundredth
-----------------------------
The Answer is 7.88
-----------------------------
Answer:
The answer here would be 7.88
Hope this helps!
describe the translation y=x^2+5
Answer:
The transformation moves the graph of the function up 5 units
Step-by-step explanation:
If we have a function f(x) then the transformation
[tex]g (x) = f (x) + c[/tex] vertically shifts the graph of f(x) c units
If [tex]c> 0[/tex] the graph moves c units up
If [tex]c <0[/tex] the graph moves c units down
In this case the main function is [tex]f (x) = x ^ 2[/tex]
and [tex]g (x) = f (x) + 5 = x ^ 2 +5[/tex]
Therefore the transformation moves the graph of the function up 5 units
ANSWER
[tex]y = {x}^{2} + 5[/tex]
EXPLANATION
The given function is
[tex]y = {x}^{2} + 5[/tex]
The base of this function is
[tex]f(x) = {x}^{2} [/tex]
The translation is of the form.
[tex]y = f(x) + k[/tex]
where k is a vertical translation k units up.
[tex]y = {x}^{2} + 5[/tex]
Therefore the translation is a shift up by 5 units.
Need help with a math question
Answer:
7.0711
= 7.1 (rounded to nearest tenth)
Step-by-step explanation:
see attached.
For this case we have by definition, that the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
According to the given data, we have the following points:[tex](x_ {1}, y_ {1}) = (6, -5)\\(x_ {2}, y_ {2}) = (- 1, -4)[/tex]
Substituting the points in the formula we have:
[tex]d = \sqrt {(- 1-6) ^ 2 + (- 4 - (- 5)) ^ 2}\\d = \sqrt {(- 7) ^ 2 + (- 4 + 5) ^ 2}\\d = \sqrt {(- 7) ^ 2 + (1) ^ 2}\\d = \sqrt {49 + 1}\\d = \sqrt {50}\\d = 7.0711[/tex]
Rounding off we have to:
[tex]d = 7.1[/tex]
ANswer:
[tex]d = 7.1[/tex]
Which rays form the sides of IHG? PLZ HELP FAST
C and F are the answers, im pretty sure
i got you
The set of rays form the sides of angle IHG include the following;
C. ray IH
F. ray HG.
What is a line segment?In Mathematics and Euclidean Geometry, a line segment is the part of a line in a geometric figure that is bounded by two distinct end points. This ultimately implies that, a line segment typically has a fixed length.
In Mathematics and Euclidean geometry, a ray is composed of two points that are joined by a straight line such as ray IH and ray HG.
By critically observing the figure showing angle IHG, we can reasonably infer and logically deduce that both ray IH and ray HG form it sides.
Read more on line segment here: brainly.com/question/628636
#SPJ3
question is in the picture, will mark brainliest
Answer:
B
Step-by-step explanation:
h(t)=-4.9t^2+ v_0t+h_0
v_0 represents initial velocity
h_0 represents initial height
we use -4.9 for the coefficient of t^2 because we dealing with meters and seconds
(If it was feet and seconds it would have been -16 instead of -4.9)
Anyways v_0 is 15m/s (We will just put 15 to make it look less complicated)
and from the ground means the initial height was h_0=0
So the answer is B.
Find the unit rate. Enter your answer as a mixed number. A fertilizer covers 2 /3 square foot in 1 /2 hour.
[tex]\bf \stackrel{\textit{rate}}{\cfrac{~~\frac{2}{3}~~}{\frac{1}{2}}\cfrac{ft^2}{hr}}\implies \cfrac{2}{3}\cdot \cfrac{2}{1}\implies \cfrac{4}{3}\implies 1\frac{1}{3}\frac{ft^2}{hr}[/tex]
Which system of equations is represented by the graph?
Answer:
C
Step-by-step explanation:
y=x is a line that has slope 1 meaning it go ups (increases) from left to right.
So that puts us at choice A or C.
Both A or C differ by the numerator for the other function.
We can find the x-intercept for A and C by setting the numerator equal to 0 and solving for x.
Let's do that:
A: -x-10=0 C. -x+10=0
-x=10 -x=-10
x=-10 x=10
A says x-intercept -10
C says x-intercept 10
Your graph intercepts the x-axis at 10 so the answer is C.
A company has determined that it's weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, why, when the company sells X items?
Answer:
b
Step-by-step explanation:
(08.03 LC) A system of two equations is shown below: Equation C: a = 4b + 5 Equation D: a = 6b − 2 What value of a can be substituted into equation D to solve the system of equations? (5 points)
Answer:
4b + 5
Step-by-step explanation:
Equation C tells us ...
a = 4b + 5
so, the value "4b +5" can be substituted for "a" in Equation D.
_____
In algebra, things that are equal are interchangeable. One can always be substituted for the other.
the value of 'a' that can be substituted into Equation D to solve the system of equations is 19.
To solve the system of equations given by Equation C: a = 4b + 5 and Equation D: a = 6b \\- 2, we are looking for a value of a which satisfies both equations simultaneously. Since equations C and D both define 'a' in terms of 'b', we can set them equal to each other to find the value of 'b', and then use that value to find 'a'.
Step 1: Set Equation C equal to Equation D, since they both equal 'a'.
4b + 5 = 6b - 2.
Step 2: Solve for 'b'.
Subtract '4b' from both sides: 5 = 2b \\- 2.
Add 2 to both sides: 7 = 2b.
Divide both sides by 2: b = 7/2 or 3.5.
Step 3: Substitute the value of 'b' into either Equation C or D to find 'a'.
Using Equation C: a = 4(3.5) + 5 = 14 + 5 = 19.
Therefore, the value of 'a' that can be substituted into Equation D to solve the system of equations is 19.
Thanks guys for all the help :)
Answer:
(2, 6) .
Step-by-step explanation:
The point A has coordinates (5, 9) and B has coordinates (-1, 3).
The midpoint is (5 + -1)/2 , (9 + 3)/2.
= (2, 6) Answer.
Determine whether triangle TJD is congruent to triangle SEK
given
T (-4,-2), J (0,5), D (1,-1), S (-1,3), E (3,10), K (4,4)
and explain the reason.
Select one:
a. Yes, by SSS
b. No, by AAS
c. No, by ASA
d. Yes, by SAS
Answer:
I believe it is SSS
Step-by-step explanation:
because all the sides are exactly the same length
PLS HELP BRAINLIEST WILL BE GIVEN :D
Answer:
56
Step-by-step explanation:
By tracing the lines on the tree diagram, we see the probability of both being red is 0.5 × 0.6 = 0.3.
The probability of both being blue is 0.5 × 0.4 = 0.2.
So we would expect to get both blue 2/3 of the times we get both red.
X = 2/3 (84)
X = 56
Julia has saved 108 sand dollars and wants to give them away equally to x friends. Write an expression to show how many sand dollars each of Julia’s friends will receive. Then, find the total number of sand dollars each of Julia’s friends will get if Julia gives them to 12 friends.
Answer:
s = 108/x . . . . s = sand dollars each friend getseach of the 12 friends gets 9 sand dollarsStep-by-step explanation:
The point of a fraction is to express the size of something that has been divided into a number of parts equal to the denominator. For example, 1/3 represents the amount when 1 unit is divided into 3 parts.
Here, Julia has 108 that she wants to divide into x parts. The fraction 108/x will tell the size of each part.
__
When x=12, the fraction becomes 108/12 = 9/1 = 9. Each friend gets 9 sand dollars.
An auditorium has 100 seats for every 10 rows. Each row has the same number of seats. If s represents the number of seats and r represents the number of rows, which equation represents this proportional relationship? A. s = 10r B. C. 100s = r D. 100s = 10r
Answer: A
Step-by-step explanation:
S=10r
Answer:
A. s = 10rStep-by-step explanation:
that's right on plato
The expression 4x4x4, x gives the perimeter of a square with a side length of xxx units. What is the perimeter of a square with a side length of \dfrac57 7 5 ? start fraction, 5, divided by, 7, end fraction units?
Answer:
[tex]\dfrac{20}{7}\ \text{units}[/tex]
Step-by-step explanation:
Put the side length where x is, then do the arithmetic.
P = 4x
P = 4(5/7) = 20/7
The perimeter is 20/7 units.
Circle A has a radius with the length of 5 units. Calculate the exact length of the apothem, line segment AH . In your final answer, include your calculations.
Check the picture below.
In a study, the sample is chosen by putting people's names on a dartboard, and blindly throwing darts to select 5 names. what is the sampling method?
Answer:
Random Sampling
Step-by-step explanation:
Random sampling is when people are chose at random from a population.
Population is the chits that have been put up on the dart board.
Blindly throwing darts to select 5 names is selecting randomly. In this case, there will be no bias involved in it as names are chosen blindly.
!!
Answer: Random sampling method.
Step-by-step explanation:
A random sampling is a sampling technique in which a researcher randomly picks participants for the sample such that the chances for each participants to get selected is equal.
Given : In a study, the sample is chosen by putting people's names on a dartboard, and blindly throwing darts to select 5 names.
Here , the probability to throw dart on any any name is equal because they throwing it blindly.
Thus, this sampling method is a random sampling method.
Frankie is practicing for a 5?kilometer race. His normal time is 31 minutes 24 seconds. Yesterday it took him only 29 minutes 47 seconds. How much faster was Frankie yesterday than his normal time?
Answer: 1 minute 37 seconds (97 secs)
Step-by-step explanation:
31 x 60 = 1860
1860 + 24 = 1884
29 x 60 = 1740
1740 + 47 = 1787
1884 - 1787 = 97
What is the value of x in the following equation? –3x – 2 = 2x + 8
-10 -2 2 10
Answer:
-2
Step-by-step explanation:
-3x -2 = 2x +8
-2 = 5x +8 . . . . . . add 3x
-10 = 5x . . . . . . . . subtract 8
-2 = x . . . . . . . . . . divide by 5
Answer:
-2
Step-by-step explanation:
-3x-2=2x+8 subtract 2x to both sides
-5x-2=8 add 2 to both sides
-5x=10 divide by -5
answer is -2