I assume you meant to say "a differentiable function f has the values ..." and not g.
Since f is differentiable, the mean value theorem holds, so you can approximate
f ' (2.5) ≈ (f (2.6) - f (2.4)) / (2.6 - 2.4) = (24 - 18) / (0.2) = 30
Two functions are shown in the table below f(x) equals -X squared plus 4X +12 And G(x)
equals X +2
Answer:
[tex]x = -2; x = 5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = -x^2 + 4x + 12[/tex]
[tex]g(x) = x +2[/tex]
Required
For what value of x is: [tex]f(x) = g(x)[/tex]
[tex]f(x) = g(x)[/tex] implies that
[tex]-x^2 + 4x + 12 = x + 2[/tex]
Collect like terms
[tex]-x^2 + 4x -x + 12 -2 = 0[/tex]
[tex]-x^2 + 3x + 10 = 0[/tex]
Expand
[tex]-x^2 + 5x-2x + 10 = 0[/tex]
Factorize
[tex]-x(x - 5)-2(x - 5) = 0[/tex]
Factor out x - 5
[tex](-x - 2)(x - 5) = 0[/tex]
Solve for x
[tex]-x - 2 = 0; x - 5 = 0[/tex]
So:
[tex]x = -2; x = 5[/tex]
If y=e3t is a solution to the differential equation
d2ydt2−9dydt+ky=0,
find the value of the constant k and the general solution to this equation.
Answer:
k=18, general solution does not exist.
Step-by-step explanation:
If f(t)=y=e3t is a solution to the differential equation
d2ydt2−9dydt+ky=0,
then
y = e^(3t)
y' = dy/dt = 3y
y'' = d2ydt2 = 9y
y'' - 9y' + ky = 0
9y - 9(3y) + ky = 0
(9-27+k)y = 0
solve for y
(9-27+k) = 0
k = 18
general solution is when y=e^(3t)=0, or t-> -infinity
Find the answer to b and check if a is correct and explain plsss
Answer:
a. 105.84 cm²
b. 136 cm²
Step-by-step explanation:
a. The prism is a cube
Surface area of the cube = 6a²
a = 4.2 cm
Plug in the value
Surface area = 6*4.2²
Surface area = 105.84 cm²
b. The prism is a triangular prism
Surface area of triangular prism = bh + L(s1 + s2 + s3)
b = 6 ft
h = 4 ft
L = 7 ft
s1 = 5 ft
s2 = 5 ft
s3 = 6 ft
Surface area = 6*4 + 7(5 + 5 + 6)
Surface area = 24 +7(16)
Surface area = 24 + 112
Surface area = 136 cm²
Josiah baked 24 cookies. He gave 1/6 of them to his family before he took them to his friend's house. How many cookies did he give his family?
Answer:
4 cookies
Step-by-step explanation:
24 x (1/6) = 24/6 = 4
Answer:
4
Step-by-step explanation:
1/6 can be represented as a percentage 1 divided by 6 = 0.1667...multiply that by 24 and you get 4 with a few decimals that round up to four as you would not want to give them a partial cookie....
The sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb,
gbg, ggb, 999). After identifying the sample space for a couple having four children, find the probability of getting one girl and three
boys in any order).
Identify the sample space for a couple having four children.
(Use a comma to separate answers as needed.)
Enter your answer in the answer box and then click
Answer:
bbbb,
bbbg, bbgb, bgbb, gbbb,
bbgg, bgbg, bggb, gbgb, gbbg, ggbb,
bggg, gbgg, ggbg, gggb,
gggg
Step-by-step explanation:
3 children: bbb, bbg, bgb, gbb, bgg, gbg, ggb, ggg
4 children: bbbb, bbbg, bbgb, bgbb, gbbb, bbgg, bgbg, bggb, gbgb, ggbb, bggg, gbgg, ggbg, gggb, gggg
You need to take a methodological approach;
The 2 easiest are the possibility of all boys and all girls;
Then consider 3 boys and 1 girl:
bbbg, bbgb, bgbb, gbbb
Then 2 boys and 2 girls:
bbgg, bgbg, bggb, gbgb, gbbg, ggbb
Lastly, 1 boy and 3 girls:
bggg, gbgg, ggbg, gggb
In total, there are 16 possibilities
P.S. interesting to note is that the number of possibilities here follows the pattern of Pascal's triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
The last row is relevant here;
There is 1 possibility where there are 4 boys;
There are 4 possibilities (in terms of the order of birth) where there are 3 boys and 1 girl;
There are 6 possibilities where there are 2 boys and 2 girls
There are 4 possibilities where there is 1 boy and 3 girls;
There is 1 possibility where there are 4 girls;
The pattern ∴ is 1 4 6 4 1, as the 5th row of Pascal's triangle reads;
If your talking about 3 children, it would match the 4th row of Pascal's triangle;
So, 1 possibility of 3 boys;
3 possibilities of 2 boys and 1 girl;
3 possibilities of 1 boy and 2 girls;
And 1 possibility of 3 girls;
If your talking about 10 children, it would match the 11th row of Pascal's triangle.
(Maths can be so cool XD)
Write the word sentence as an inequality.
A number x is greater than 0.
Answer:
x>0
I am very certain.
brainliest?
Find the value of x.
A. 30
B. 60
C. 90
D. 120
Some one else didn’t add a picture
QUESTION:- Find the value of x.
A. 30
B. 60
C. 90
D. 120
ANSWER:-
ALL ANGLE SUMS HAVE SAME LOGIC OF STRAIGHT LINE ANGLES = 180°
[tex]y + x + y - x = 180[/tex]
[tex]2y = 180 \\ y = 90[/tex]
[tex]2x + y + x = 180[/tex]
[tex]3x + 90 = 180 \\ 3x = 90 \\ x = 30 \degree[/tex]
Answer:
30 degrees
Step-by-step explanation:
2x + y + x = 180
y + x + y - x = 180
3x + y = 180
2y = 180
y = 90
3x + 90 = 180
3x = 90
x = 30
i have 30 sweets and 15 chocolate in a basket.If i take five sweets out the basket,what is the ratio(in its simplest form)of the number of chocolate th the number of sweets left in the basket?
Answer:
If you take 5 sweet out of the basket, then the ratio of the number of chocolate to the number of sweet left in the basket is. \frac{5} {30 - 5} = 5/25 = 1/5
Step-by-step explanation:
What inequality is shown by the graph?
Step-by-step explanation:
2x - 10y > -20
=> x - 5y > -10
or x - 5y +10 > 0
What is the solution of |4 − y| = 1?
A. y = 3 or y = 5
B. y = −3 or y = −5
C. y = −3 or y = 5
D. y = 3 or y = −5
A is the answer.
Answer:
A
Step-by-step explanation:
|4 − y| = 1
drop absolute value lines
create two problems
4 - y = 1
and
4 - y = -1
solve for y
The sales tax on a sofa that cost 575$ was 43.13 What was the percent sales tax? PLS HELP ASAP NEED TO SHOW WORK!! AND STEP BY STEP
Answer:
07.50086956521739% (round it)
Step-by-step explanation:
Find what percent 43.13 (Number A) is of 575 (Number B). To do this you divide Number A by Number B.
43.13 / 575 = 0.0750086956521739
Move the decimal point two places to the right.
007.50086956521739
Get rid of the zeros.
7.50086956521739
Answer:
07.5%
Step-by-step explanation:
you toss six coins at the same time. how many possible outcomes are there?
64
36
12
6
Answer:
64 outcomes
Step-by-step explanation:
Let the number of coins be n.Let the number of outcomes per coin be X.Given the following data;
Number of coins = 6
Number of outcomes for a single coin = 2
A single coin comprises of a head (H) and a tail (T), thus, the number of outcomes for a single coin is two (2).
To find how many possible outcomes we would have from tossing six coins at the same time, we would use the following formula;
[tex] Number \; of \; outcomes = X^{n} [/tex]
Substituting the values, we have;
Number of outcomes = 2⁶
2⁶ = 2 * 2 * 2 * 2 * 2 * 2
2⁶ = 64
Number of outcomes = 64
Therefore, the number of outcomes for a single coin tossed at the same time is equal to sixty four (64). It would have a total of 32 heads (H) and a total of 32 tails (T).
Someone help me please
9514 1404 393
Answer:
$448
Step-by-step explanation:
The given formula will tell you the amount of interest earned:
I = Prt
I = $400·0.02·6 = $48
The account balance will be the sum of the original deposit and the interest it earns:
$400 +48 = $448 . . . . balance after 6 years
Solve the system using substitution.
y = 4x – 8
y = 2x + 10
Answer:
9,28
Step-by-step explanation:
see image below:)
What type of correlation is shown in the graph ? positive no correlation linear negative
Answer:
positive
Step-by-step explanation:
Two trains leave a train station at the same time. One travels north at 12 miles per hour. The other train travels south at 9 miles per hour. In
how many hours will the two trains be 88.2 miles apart?
O 4.7 hours
O 4.2 hours
O 2.1 hours
O 8.4 hours
Answer:
4.2 hours
Step-by-step explanation:
I need the answer the question is in the picture
Answer:
D) 1 3/4
Step-by-step explanation:
Will Mark Brainlest help pleaseeeeee
Answer:
h(2) = 7/4
h(-3) = -2
h(-2) = 11/(-8)
h(-3) - h(-2) = -(5/8)
Step-by-step explanation:
h(x) = (2x^2-x+1) / (3x-2)
h(2) = (2*2^2 - 2 + 1) / (3*2 - 2)
= (8 - 2 + 1) / (6 - 2)
= 7/4
h(-3) = {2*(-3)^2 - (-3) + 1} / {3*(-3) - 2}
= (18 + 3 + 1) / (-9 - 2)
= 22/(-11)
= -2
h(-2) = {2*(-2)^2 - (-2) + 1} / {3*(-2) - 2}
= (8 + 2 + 1) / (-6 - 2)
= 11/(-8)
h(-3) - h(-2) = (-2) - {11/(-8)}
= -(5/8)
Hope this will help. Please give me brainliest.
[tex]h(3) - h( - 2) = - \frac{5}{ 8} \\ \\ [/tex]
[tex]\boxed{h(x) = \frac{2 {x}^{2} - x + 1}{3x - 2}}[/tex]
[tex]h(2) = \frac{2 {(2)}^{2} - (2) + 1}{3(2) - 2} [/tex]
[tex]h(2) = \frac{2 {(4)} - 2 + 1}{6 - 2} [/tex]
[tex]h(2) = \frac{ 8 - 1}{4} [/tex]
[tex]h(2) = \frac{7}{4}[/tex]
[tex]h( - 3) = \frac{2 {( - 3)}^{2} - ( - 3) + 1}{3( - 3) - 2} \\ h( - 3) = \frac{2 (9) + 3 + 1}{ - 9- 2} \\ h( - 3) = \frac{18 + 4}{ - 11} \\ h( - 3) = \frac{22}{ - 11} \\ h(-3) = -2[/tex]
[tex]h( - 2) = \frac{2 {( - 2)}^{2} - ( - 2) + 1}{3( - 2) - 2} \\ h( - 2) = \frac{2 (4) + 2+ 1}{- 6 - 2} \\ h( - 2) = \frac{8 + 3}{- 8} \\ h( - 2) = \frac{11}{- 8} [/tex]
[tex]h(3) - h( - 2) = -2 - \frac{11}{- 8} \\=-2 + \frac{11}{ 8} \\ =- \frac{5}{ 8} [/tex]
What is the value of m?
[tex] \huge \underline \mathcal{Answer}[/tex]
The given angles forms linear pair, and we know the angles forming linear pair are supplementary,
Therefore,
Angle MHJ + Angle MHL = 180°
Let's solve :
[tex](5m + 100) \degree + (2 m + 10) \degree = 180 \degree[/tex][tex]7m + 110 \degree = 180 \degree[/tex][tex]7m = 70 \degree[/tex][tex]m = 10 \degree[/tex]Value of variable m = 10°
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
What is the surface area of the rectangular prism below? 8 19 8
Answer:
736 units squared (c)
Step-by-step explanation:
Took the quiz
On a piece of paper, graph y = -x2 + 4x - 3 and identify the zeros. Then determine which answer choice matches the graph that you drew and correctly identifies the zeros.
Answer:
C. 1 and 3
Step-by-step explanation:
Look below (Will give brianliest)
NO link and pls explain
Answer:
80
Step-by-step explanation:
brainliest please ;>
Geometry question finding radius and area
Thank You!!
Answer:
The radius of Circle D is 8 cm.
The perimeter of ΔABC is (24 + 6√7) cm.
Step-by-step explanation:
First, let the intersection point below D be K and let the intersection point between A and B be J.
Since segment BK, which passes through the center of the circle, is perpendicular to chord AC, BK also bisects AC. Hence, AK = CK.
Connect points A and D to create radius AD. Note that BD is also a radius. Hence, AD = BD.
For ΔABK, by the Pythagorean Theorem:
[tex]AB^2=(BD+1)^2+AK^2[/tex]
Since AB = 12:
[tex]144=(BD+1)^2+AK^2[/tex]
For ΔADK, by the Pythagorean Theorem:
[tex]AD^2=1^2+AK^2[/tex]
Since AD = BD:
[tex]BD^2=1+AK^2[/tex]
Subtract the second equation into the first:
[tex]144-(BD^2)=(BD+1)^2+AK^2-(1+AK^2)[/tex]
Simplify:
[tex]144-BD^2=BD^2+2BD+1-1[/tex]
Hence:
[tex]2BD^2+2BD-144=0[/tex]
Simplify:
[tex]BD^2+BD-72=0[/tex]
Factor:
[tex](BD+9)(BD-8)=0[/tex]
By the Zero Product Property:
[tex]BD=-9\text{ or } BD=8[/tex]
Since the radius must be positive, the radius is 8 cm.
Since we already know AB and BC, we need to find AC to find the perimeter.
Note that AC = AK + CK = 2AK.
From the second equation:
[tex]BD^2=1+AK^2[/tex]
Thus:
[tex]AK=\sqrt{BD^2-1}=\sqrt{(8)^2-1}=\sqrt{63}=3\sqrt{7}[/tex]
Hence:
[tex]AC=2(AK)=2(3\sqrt7)=6\sqrt7[/tex]
Therefore, the perimeter of ΔABC is:
[tex]P=(12)+(12)+(6\sqrt7)=24+6\sqrt7\text{ cm}[/tex]
How much interest will be earned on a $1600 investment at 7.72% compounded
quarterly for 9 years?
Answer:
A = $3,198.17
A = P + I where
P (principal) = $1,600.00
I (interest) = $1,598.17
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 7.72/100
r = 0.0772 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 1,600.00(1 + 0.0772/12)(12)(9)
A = 1,600.00(1 + 0.006433333)(108)
A = $3,198.17
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $1,600.00 at a rate of 7.72% per year compounded 12 times per year over 9 years is $3,198.17.
The company has only two division division eight and division be last year division a made 60% of the companies total revenue and division be made 40% of the total revenue this year division as revenue has decreased by 35% and division bees revenue has decreased by 5% which division had higher revenue this year?
9514 1404 393
Answer:
Division A
Step-by-step explanation:
Suppose last year's revenue for the company was 100 units.
Last year's Division A revenue was 0.60×100 = 60. This year's revenue is 1-35% = 65% of last year's, so is ...
60 × 0.65 = 39 . . . . units
__
Last year's Division B revenue was 0.40×100 = 40. This year's revenue is 1-5% = 95% of last year's, so is ...
40 × 0.95 = 38 . . . . units
__
At 39 units this year, Division A still has the higher revenue than Division B at 38 units.
I will give BRAINLIEST to whoever answers correctly first!!!
Sophie wants to buy a pair of scissors that cost $1.82. If she gives the cashier a five dollar bill, how
much change should she get back?
Answer:
Sophie will get $3.18 back in change.
Step-by-step explanation:
You do 5.00-1.82 and you get 3.18, which is equal to the change that Sophie will get.
Given that ABCD is a rectangle, find the perimeter of the figure below. Round your answer to the nearest tenth. *
Options
18 ft
19.7 ft
21 ft
24.4 ft
9514 1404 393
Answer:
(b) 19.7 ft
Step-by-step explanation:
The perimeter of the figure is the sum of the lengths of the 3 straight sides and half the circumference of a 3-ft circle.
P = 6 + 3 + 6 + (1/2)(π)(3) = 15 +3/2π ≈ 19.712 . . . feet
The perimeter is about 19.7 feet.
What is the result when 16x + 9 is subtracted from 4x + 6
Answer:
(4x+9)-(16x+9) = 4x+9-16x-9
= -12x
225 ft2
81 ft2
Three squares are joined below at their vertices to form a right triangle. Find X, the side
length of the square marked in the diagram.
12 feet
144 feet
48 feet
17.5 feet
Answer:
12 ft
Step-by-step explanation:
we know the areas of the 2 top squares.
the area of a square is simply the square of its side length.
=>
81 ft² means side length is 9 ft.
225 ft² means side length is 15 ft.
these are also 2 of the sides of the right triangle.
the third side we get by using Pythagoras :
c² = a² + b²
with c being the side opposite of the 90 degree angle.
so,
225 = 81 + x²
as x is also the third side of the triangle.
=> 144 = x²
x = 12 ft
What is the value of x?
Answer:
value of x i think correct answer is 2