Answer:
Step-by-step explanation:
Explanation:
The
average rate of change
of g(x) over an interval between 2 points (a ,g(a)) and (b ,g(b) is the slope of the
secant line
connecting the 2 points.
To calculate the average rate of change between the 2 points use.
∣
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
g
(
b
)
−
g
(
a
)
b
−
a
a
a
∣
∣
∣
−−−−−−−−−−−−−−−
g
(
6
)
=
6
2
−
6
+
3
=
33
and
g
(
4
)
=
4
2
−
4
+
3
=
15
Thus the average rate of change between (4 ,15) and (6 ,33) is
33
−
15
6
−
4
=
18
2
=
9
This means that the average of all the slopes of lines tangent to the graph of g(x) between (4 ,15) and (6 ,33) is 9
Which of the following is equivalent to 0 equals 3 x squared minus 12 x minus 15 when completing the square?
After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
What is a quadratic equation?"It is a polynomial equation with degree two."
What is completing the square method?"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "
For given example,
We have been given a quadratic equation.
[tex]3x^{2} -12x-15=0[/tex]
First we divide above quadratic equation by 3,
[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex] ................(i)
Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]
[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]
Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),
[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]
Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
Learn more about completing the square here:
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is the value of these expressions the same? explain.
Answer:
No.
Step-by-step explanation:
Using the order of operations:
4 · 6 - 4 = 20 (Multiplication is done first.)
4 · (6 - 4) = 8 (Parentheses is done first.)
Triangles ABC and DEF are similar. Find the missing angles.
Jim took a loan of R30 000.00 for 18 months at a simple interest rate of 12.5% per year. Determine the amount that Jim
will pay in 18 months.
Answer:
R35625
Step-by-step explanation:
(R30,000×.125×18/12)+R30000
=R35625
Turn 43 1/23 into an improper fraction
Answer:
990/23
Step-by-step explanation:
Step 1
Multiply the denominator by the whole number
23 × 43 = 989
Step 2
Add the answer from Step 1 to the numerator
989 + 1 = 990
Step 3
Write answer from Step 2 over the denominator
990/23
I hope this answer helps you out! Brainliest would be appreciated.
1km make how many cm
Answer:
100000
Step-by-step explanation:
When Asia was young, her father marked her height on the door frame every month. He noticed that between the ages of one and three, he could predict her height (in inches) by taking her age in months, adding 75 inches, and multiplying the result by one-third.
Create an equation linking her predicted height, h, with her age in months, m, and solve to find when her height will be 30 inches.
Answer:
15 months old.
Step-by-step explanation:
Let m = months and h = height:
h = 1/3(m + 75) ⇔ h = 1/3m + 25
Let h = 30:
[tex]30=\frac{1}{3}m+25\\5=\frac{1}{3}m\\15=m[/tex]
Therefore, when Asia is 30 inches tall, she will be 15 months old.
Sophia runs twice as fast as her friend Mia. If mia runs 3 mph how long will it tske sophia to run 6 miles? 9 miles?
Answer:
It will take Sophia 1 hour to run 6 miles.
And 1 1/2 hours for 9 miles.
Step-by-step explanation:
urgent !!!!!! plz image below
Answer:
[tex]216\ km^2[/tex]
Step-by-step explanation:
1. Approach
The surface area of a three-dimensional figure is the two-dimensional distance around the figure. The easiest way to find the surface area of a figure is to find the area of each of its facets, then add up the area to get the total surface area. The given pyramid is composed of four congruent triangles and a square. Find the area of one of the triangles, and then the area of the rectangle. Multiply the area of the triangle by four to account for the fact that there are four congruent triangles. Then add the area of the base to the result, the result attained is the surface area of the prism.
2. Find the area of the triangles
The formula to find the area of a triangle is the following:
[tex]A_t=\frac{b*h}{2}[/tex]
Where (b) represents the base and (h) represents the height of the triangle. Substitute the given values into the formula and solve for the answer.
[tex]A_t=\frac{b*h}{2}[/tex]
[tex]A_t=\frac{9*7.5}{2}[/tex]
[tex]A_t=\frac{67.5}{2}[/tex]
[tex]A_t=33.75[/tex]
3. Find the area of the rectangle
The formula to find the area of a rectangle is the following,
[tex]A_r=b*h[/tex]
Substitute the given values in and solve,
[tex]A_r=b*h[/tex]
[tex]A_r=9*9[/tex]
[tex]A_r=81[/tex]
4. Find the total surface area
Multiply the area of the triangle by four to account for the fact that there are four triangles. Then add its area to the area of the rectangle.
[tex]A_t+A_t+A_t+A_t+A_r=A[/tex]
[tex]4(A_t)+(A_r)=A[/tex]
[tex]4*33.75+81=A[/tex]
[tex]135+81=A[/tex]
[tex]216=A[/tex]
I need help with this I will appreciate if I get an answer for this problem
Answer:
what's the problem!?......
angle CDT is the opposite angle of ADN
and the segment DF=FN, so AD= AN
and thats why angle FAN= angle FAD
here, Angle FAN =60,
therefore, FAD=60, and AFD = 90 so angle ADN must be 30 degree
and the opposite of ADN is CDT, and the opposite angles are equal.
Hope u got it.
A student received the following grades: An A in Statistics (4 credits), a B in
Physics II (5 credits), and a D in Tennis (1 credit).Assuming A = 4 grade points, B = 3 grade points, C = 2 grade points, D = 1 grade point, and F = 0 grade points, the student's grade point average is:
Answer:
B) 3
Step-by-step explanation:
4+5+1/3=10/3=3.333~3
Answer:
B) 3
Step-by-step explanation:
simplify 27- 9+(12-5)÷4 with solution
Answer:
It's 28 3/4
Step-by-step explanation:
Answer:
Answer is 19.5
Step-by-step explanation:
27-9+(12-5)÷4
27-9+6÷4 [BOD MAS Rule]
27-9+1.5
28.5-9
19.5
Venn diagrams: unions, intersections, and complements
Attached is the photo reference
Answer:
a) 0
b) 2,3,4,5,6,7
c)3,4,6,7
Step-by-step explanation:
What is the complete factorization of the polynomial below?
x3 + 4x2 + 16x + 64
Answer: (x+4) ( x-4i)(x+4i)
Discussion:
Factor the polynomial:
x^3+4x^2+16x+64 = (x +4 ) ( x^2 + 16) (*)
Factor x^2 +1 6 over the complex numbers:
x^2 + 16 = (x -4i)(x+4i) (**)
Combing (*) and (**) gives the full factorization
(x+4) ( x-4i)(x+4i)
Find the remainder when f(x) = x^3- 6x^2 +3x -1 divided by 2x-3
Answer:
Remainder is -53/8
Step-by-step explanation:
the divisor is (2x - 3):
make x the subject:
[tex]2x - 3 = 0 \\ 2x = 3 \\ x = \frac{3}{2} [/tex]
substitute for x in the function:
[tex]f(x) = {x}^{3} - 6 {x}^{2} + 3x - 1 \\ f( \frac{3}{2} ) = {( \frac{3}{2}) }^{3} - 6 {( \frac{3}{2}) }^{2} + 3( \frac{3}{2} ) - 1 \\ \\ f( \frac{3}{2} ) = \frac{ - 53}{8} [/tex]
Which decimal is equivalent to
15/100?
A- O 0.015
B- 0.15
C-o 1.5
D- 0.0015
Answer:
D
Step-by-step explanation:
0.0015
hope this helps
pls help me
How many solutions exist for the system below?
y = -2x + 3
y = -2.3x
Answer:
0
Step-by-step explanation:
for y= -2*(3^x), as x is greater, the slope is steeper, and since the two graphs don't intercept in the picture we can see, they won't ever intercept because the slop of y=-2x+3 stays the same. as x becomes greater the distance between the two graphs is larger
Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 5 inches. The heights of 9 randomly selected students are 66, 71, 63, 74, 69, 64, 66, 68 and 67.
Answer:
The mean is about 68 (67.5555)
Step-by-step explanation:
(63+64+66+66+67+68+69+71+74) / 9 ≈ 68
what is differnciation
Answer:
Differentiation is concerned with things like speeds and accelerations, slopes and curves ect. These are Rates of Change, they are things that are defined locally. The Fundamental Theorem of Calculus is that Integration and Differentiation are the inverse of each other.
Help please! Thanks!
Find the length of the segment indicated.
A. 3.1
B. 3.9
C. 3.4
D. 3.8
Answer:
C
Step-by-step explanation:
using the theorem of Pythagoras
x = sqrt * 10.2^2 - 9.6^2 *
using the calculator
x = 3.4 units
rounded to 1 decimal place
If x+1/x = 12, find the value of x^2+1/x^2
[tex]\boxed{\sf (a+b)^2=a^2+b^2+2ab}[/tex]
Now
[tex]\\ \sf\longmapsto x+\dfrac{1}{x}=12[/tex]
[tex]\\ \sf\longmapsto \left(x+\dfrac{1}{x}\right)^2=12^2[/tex]
[tex]\\ \sf\longmapsto x^2+2\times x\times \dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=144[/tex]
[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}+2=144[/tex]
[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}=144-2=142[/tex]
Answer:
122
Step-by-step explanation:
x+1/x = 12
x + 1 = 12x
x = 1/11
（1/11）² + 1 / （1/11）² = 1/121 +1 /1/121 = 122
Add.
3+ (-6) =
-6 + (-3) =
Hello can someone answer please
Answer:
hello thereeeee
ans is 23.5
Step-by-step explanation:
so lets start
first of all remove decimal of divisor 1.1/25.85 multiplying by 10
11/258.5
now first multiply by 2
now we get 22 and subtract with 25 => 25-22 = 3
so left is
38
now 11*3 = 33
so now by 3
38-33= 5
bringing another 5 down
we get 55
now quotient is 23. something ( as we bought .5 down)
and now 11*5 = 55
so
23.5 is answer
Mia walks her dog twice a day. Her evening walk is two and a half times as far as her morning walk. At the end of the week she says she walked her dog 30 miles. How long is her morning walk?
9514 1404 393
Answer:
1 11/49 ≈ 1.224 miles
Step-by-step explanation:
Let m represent the length of the morning walk. Then the length of the evening walk is 2.5m, and the total each day is m+2.5m = 3.5m.
The total for 7 days is ...
7(3.5m) = 30
m = 30/24.5 = 60/49 ≈ 1.224 . . . . miles
Mia's morning walks are 1 11/49 miles, about 1.224 miles.
In a class, students can complete extra-credit
assignments for either 7 points or 12 points. Each student can complete at most four of the 7-point assignments and
at most four of the 12-point assignments. If Barbara
completes six extra-credit assignments, what is a
possible number of points she can earn?
Answer:
31 PTS
Step-by-step explanation:
An article is marked to sell at a gain of 10%. If it be sold for Rs. 7.50 less there would be loss of 5%, find the cost price.
Answer:
750,. is answer
I hope it helps
Write the equation of the sinusoidal function shown.
A) y = 2 sin(2x)
B) y = 2 sin x + 2
C) y = 2 cos x + 2
D) y = 2 cos(2x)
Answer:
2 sin(2x)
Step-by-step explanation:
sin x stretched vertically by a factor 2 and compressed horizontally by a factor 2.
The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.
so, we get,
However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.
Hence, The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.
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Michelle would like to know how much of her loan payments will go toward interest. She has a $124,500 loan with a 5.9% interest rate that is compounded monthly. The loan has a term of 10 years. Calculate the total amount of interest that Michelle will pay over the course of the loan.
9514 1404 393
Answer:
$40,615.20
Step-by-step explanation:
The amortization formula will tell you Michelle's monthly payment.
A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . . loan value P at interest rate r for t years
A = $124,500(0.059/12)/(1 -(1 +0.059/12)^(-12·10)) ≈ $1375.96
__
The total of Michelle's 120 monthly payments is ...
12 × $1375.96 = $165,115.20
This amount pays both principal and interest, so the amount of interest she pays is ...
$165,115.20 -124,500 = $40,615.20
Michelle will pay $40,615.20 in interest over the course of the loan.
__
A calculator or spreadsheet can figure this quickly.
For the function F defined by F(x) = x2 – 2x + 4, find F(b+3).
Answer:
[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystlye F(x) = x^2 - 2x + 4[/tex]
And we want to find F(b + 3).
We can substitute:
[tex]\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4[/tex]
Expand:
[tex]\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4[/tex]
Rearrange:
[tex]\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)[/tex]
Combine like terms. Hence:
[tex]\displaystyle = b^2 +4b + 7[/tex]
In conclusion:
[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]
The distance Ab round to the nearest tenth?
Coordinates of point A is (-2 and 1)
Coordinates of point B is (1 and -1)
[tex] \begin{cases}\large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{(x_2 - x_1 ) \: + \:(y_2 - y_1 )} \\ \\ \large\bf\red{ \longrightarrow} \rm \:Distance \: = \:\sqrt{(1 - [ - 2]) ^{2} \: + \:( - 1 - 1)^{2} } \\ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{( - 3) ^{2} \: + \:( - 2) ^{2}} \\ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{6 \: + \: 4} \\ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{10} \ \\ \ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \:3.1622 \: \: units \end{cases}[/tex]
