Answer:17
Step-by-step explanation:
The mean of the ages of 5 brothers is 13 years.
12, 16, O, 14, 8
Answer:
O = 15
Step-by-step explanation:
.mean ' is the average
(12 + 16 + O + 14 + 8) / 5 = 13
50 + O = 65
O = 15
If f is a second-degree polynomial function such that f(3)=5, f'(3)=6, and f''(3)=4, what is the value of f(2) ?
so let's say the equation is y = ax² + bx + c, where a,b,c are constants.
we know that f(3) = 5, or namely when x = 3 , y = 5.
we also know that f'(3) = 6, or namely the slope at the point (3,5) is 6.
we also know that at (3,5) the 2nd derivative is 4, so a positive number simply tell us its concavity, is up, so is a parabola opening upwards.
[tex]y=ax^2+bx+c\implies \left. \cfrac{dy}{dx}=2ax+b \right|_{x=3}~~ = ~~ 6\implies 6=2ax+b \\\\\\ 6=2a(\stackrel{x}{3})+b\implies 6=6a+b\implies 6-6a=b\implies \boxed{6(1-a)=b} \\\\[-0.35em] ~\dotfill\\\\ \left. \cfrac{d^2y}{dx^2}=2a \right|_{x=3}~~ = ~~4\implies 2a=4\implies a=\cfrac{4}{2}\implies \boxed{a=2}~\hfill \boxed{-6=b} \\\\[-0.35em] ~\dotfill[/tex]
[tex]y=2x^2-6x+c\qquad \begin{cases} x=3\\ y = 5 \end{cases}\implies 5=2(3)^2-6(3)+c\implies \boxed{5=c} \\\\\\ y=2x^2-6x+5~\hfill y(2)=2(2)^2-6(2)+5\implies \blacktriangleright y(2)=1 \blacktriangleleft[/tex]
solve and ( SHOW YOUR WORK !! )
Answer:
yea
Step-by-step explanation:
A circle has its center at (2,-4). The radius of the circle extends to the
point (2,5). What is the approximate circumference of the circle?
⚫️114 units
⚫️14 units
⚫️28 units
⚫️57 units
Check the picture below, so the circle looks more or less like so, with a radius of 9.
[tex]\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies C=2\pi (9)\implies C\approx 57[/tex]
What is the name of the Platonic solid shown below?
A. Hexahedron
B. Dodecahedron
C. Tetrahedron
D. Octahedron
Answer: c
Step-by-step explanation: The cube represents the earth, the octahedron represents the air, the tetrahedron represents the fire, the icosahedron represents the water, and the dodecahedron represents the universe
The name of the platonic solid shown is hexahedron.
What are different types of solids?Tetrahedron - A tetrahedron, also referred to as a triangle pyramid, is a polyhedron with four triangular faces, six straight edges, and four vertex corners in geometry.
Hexahedron - Any polyhedron with six faces is called a hexahedron.
Octahedron - An octahedron is a polyhedron with eight faces in geometry.
Dodecahedron - In geometry, a dodecahedron or duo decahedron is any polyhedron with twelve flat faces.
The figure given in the question has clearly six flat faces and hence according to the definitions it is a hexahedron.
Learn more about shapes on:
brainly.com/question/303508
#SPJ7
The complete question is attached.
Pls I need this today right now pls
Answer:
ur right its A
Step-by-step explanation:
solve for x ~
[tex]4x - 16 = 64[/tex]
ty ^^
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \:4x - 16 = 64[/tex]
[tex]\qquad \sf \dashrightarrow \:4(x - 4) = 64[/tex]
[tex]\qquad \sf \dashrightarrow \:(x - 4) = 64 \div 4[/tex]
[tex]\qquad \sf \dashrightarrow \:x - 4 = 16[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 16 + 4[/tex]
[tex]\qquad \sf \dashrightarrow \:x =20[/tex]
[tex] \boxed{ \bf \huge \: Answer \: }[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: 4x - 16 = 64[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: 4x = 64 + 16[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: 4x = 40[/tex]
[tex] \: [/tex]
[tex] \sf \large \: x = \cancel \frac{80}{4} [/tex]
[tex] \: \: [/tex]
[tex] \sf \large x = 20[/tex]
[tex] \: \: [/tex]
Hope It's Helps uh Miss<3"
[tex]\begin{equation}\text { Question: If } \ln (x+y)=4 \times y \text {. Find } \frac{d^{2} y}{d x^{2}} \text { at } x=0 \text {. }\end{equation}[/tex]
I think you meant to say
[tex]\ln(x+y) = 4xy[/tex]
and not "4 times y" on the right side (which would lead to a complex value for y when x = 0). Note that when x = 0, the equation reduces to ln(y) = 0, so that y = 1.
Implicitly differentiating both sides with respect to x, taking y = y(x), and solving for dy/dx gives
[tex]\dfrac{1+\frac{dy}{dx}}{x+y} = 4y + 4x\dfrac{dy}{dx}[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{4xy+4y^2-1}{1-4x^2-4xy}[/tex]
Note that when x = 0 and y = 1, we have dy/dx = 3.
Differentiate both sides again with respect to x :
[tex]\dfrac{d^2y}{dx^2} = \dfrac{(1-4x^2-4xy)\left(4y+4x\frac{dy}{dx}+8y\frac{dy}{dx}\right)-(4xy+4y^2-1)\left(-8x-4y-4x\frac{dy}{dx}\right)}{(1-4x^2-4xy)^2}[/tex]
No need to simplify; just plug in x = 0, y = 1, and dy/dx = 3 to get
[tex]\dfrac{d^2y}{dx^2} \bigg|_{x=0} = \boxed{40}[/tex]
What will the balance be after 10 years if $1500 is invested at 1.5% interest compounded continuously?
Answer:
A = $1,742.75
A = P + I
Where
P is the principal (1,500.00)
I is the interest (242.75)
Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 1.5/100
r = 0.015 rate per year,
Then solve the equation for A
[tex]A = Pe^{rt}\\A = 1,500.00(2.71828)^{(0.015)(10)}\\A = $1,742.75[/tex]
Summary:
The total amount with compound interest on a principal of $1,500.00 at a rate of 1.5% per year compounded continuously over 10 years is $1,742.75.
Figure 1
Figure 2
B
D
E
С
Z
128 cm
2
am
Area of Figure 1 =
Area of Figure 2 =
Perimeter of Figure 1 = 24 cm
Perimeter of Figure 2 = 21 cm
BC=
DE = 7 cm
Tip: Go to the internet and put the topic you are focused more on that you posted in Brainly
Step-by-step explanation:
Try it to give you some help
Find the Missing numbers:
250/20=25/?
Drawing a 3 cards that are all 9 from a deck of cards
Answer:
the answer is 3 :))
Step-by-step explanation:
9/3= 3
Brennan has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.15 times as many villagers as he had in the one before. The game gave Brennan 5 villagers to start with. Explain to Brennan how to create an equation to predict the number of villagers in any specific town. Then show how to use your equation to solve for the number of villagers he can create to live in the 15th town.
Answer:
Use the geometric sequence formula since you are multiplying each town's villagers by the amount your teacher gave you.
Step-by-step explanation:
Plug in the parts of the formula from the numbers given in the question, then you can calculate the number of villagers needed for the 15th town.
Answer:
35.375 Villagers Live in the 15th village
Step-by-step explanation:
Brennan can use the Geometric Sequence formula to predict the number of villagers in the 15th town.
(work attached)
In a writing competition, the first place winner receives 1/2 of the prize money. The second runner up receives 1/4 of what the winner won. What was the total amount of prize money distributed if the winner receives $8000
Answer:
10,000 is the total amount of.money that was distributed
In a computer game , Reese scored 13,925 points. Manny scored 2,742 points more than Reese. How many points did manny score?
Answer:
16,667
Step-by-step explanation:
13,925 + 2,742 = 16,667
Answer:
Bonjour
Step-by-step explanation:
Reese : 13 925
Manny : 2 742 de plus que Reese donc 13 925 + 2 742
13 925 + 2 742 = 16 667
Manny a marqué 16 667 points.
The length of a rectangle multilayered by 3 is equal to 4 times its width. The perimeter is 8 2/5 feet. Find the length and the width.
The required length of the rectangle is 12/5 feet and the width is 9/5 feet.
What is the equation model?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let's denote the length of the rectangle as L and the width as W.
From the problem statement, we know that:
3L = 4W (equation 1)
We also know that the perimeter P is given by:
P = 2L + 2W = 8 2/5 feet
Multiplying both sides by 5 to get rid of the fraction, we get:
10L + 10W = 42
Dividing by 2, we get:
5L + 5W = 21 (equation 2)
Now we can use equations 1 and 2 to solve for L and W.
First, we can substitute equation 1 into equation 2 to get an equation in terms of W:
5L + 15L/4 = 21
Multiplying both sides by 4, we get:
20L + 15L = 84
35L = 84
L = 84/35 = 12/5 feet
Now we can substitute the value of L into equation 1 to get the value of W:
3L = 4W
3(12/5) = 4W
W = 9/5 feet
Therefore, the length of the rectangle is 12/5 feet and the width is 9/5 feet.
Learn more about models here:
https://brainly.com/question/22591166
#SPJ7
I need to solve for “x” and then for “y”.
Step-by-step explanation:
[tex]13 - 4y = 1 - y(opposite \: angles \: of \: a \: parallelogram \: are \: equal) \\ 13 - 4y = 1 - y \\ - 4y + y = 1 - 13 \\ - 3y = - 12 \\ y = \frac{ - 12}{ - 3} \\ y = 4 \\ \\ 7x - 3 = 6x + 3(opposite \: angles \: of \: a \: parallelogram \: are \: equal) \\ 7x - 3 = 6x + 3 \\ 7x - 6x = 3 + 3 \\ x = 6 \\ x = 6 \: \: \: \: \: y = 4[/tex]
Please help!!! I'm struggling
Step-by-step explanation:
please mark me as brainlest
Answer:
I hope it helped you
Step-by-step explanation:
Pls refer the given attachment
An open box is to be made from a square piece of cardboard, 18 inches by 18 inches, by removing a small square from each corner and folding up the flaps to form the sides. What are the dimensions of the box of greatest volume that can be constructed in this way
The dimension of the box of the greatest volume that can be constructed in this way is 12x12x3 and the volume is 432.
How to solve the dimension?
Let x be the side of the square to remove. Then the volume of the box is:
V(x) = (18 - 2x)² * x = 324x - 72x² + 4x³
To find the maximum volume, differentiate and set it to 0:
V'(x) = 324 - 144x + 12x²
0 = x² - 12x + 27
0 = (x - 9)(x - 3)
x = 3 or 9
When x = 3,
V"(x) =-144+24x
V"(3) =-144+72=-72<0
so volume is maximum at x=3
Therefore the box is 12x12x3 and the volume is 432.
Learn more about dimension on:
https://brainly.com/question/26740257
The circumference of a circle is 17π in. What is the area, in square inches? Express your answer in terms of π?
Answer:
22.97
Step-by-step explanation:
17 divided by pi is 5.41
5.41 divided by 2 is 2.075
r^2(pi)
is 2.075 x 2.075 x 3.41 is 22.97
Using the three Indicated points on the given line and the concept of similar triangles, show and explain why the slope of the line is the same between any two of these three points. calculate the slope of the line
Answer:
it is the same because slope is a measure of steepness.
Step-by-step explanation:
(0,1) (2,4)
4-1/2-0=3/2
slope=3/2
solve .-. ~
[tex] \\ \\x - \frac{1}{2} \geqslant 43 \\ [/tex]
thankyou .-.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \tt \dashrightarrow \:x - \dfrac{1}{2} \geqslant 43 [/tex]
[tex]\qquad \tt \dashrightarrow \:x \geqslant43 + \dfrac{1}{2} [/tex]
[tex]\qquad \tt \dashrightarrow \:x \geqslant \dfrac{86 + 1}{2} [/tex]
[tex]\qquad \tt \dashrightarrow \:x \geqslant \dfrac{87}{2} [/tex]
hope this helps Belinda aunty ~
300,000+5,000+80+8· 1/100 +9· 1/10,000
Answer:
305,080.0809
Step-by-step explanation:
3 x 100,000 : digit 3 is in the hundred thousands place
5 x 1000 : digit 5 is in the thousands place
8 x 10 : digit 8 is in the tens place
8 x 1/100 : digit 8 is in the hundredths place which means it is the second number after the decimal
9 x 1/10,000 : digit 9 is in the ten thousandths place which means it is the fourth number after the decimal
we get the following number:
305080.0809
a] The area of a square is 200 cm² Find the length of its diagonal.
[tex]"20cm"[/tex]
Step-by-step explanation:[tex]Area\ of\ rq=a^2[/tex]
[tex]a=\sqrt{200}=10\bullet \sqrt{2}[/tex]
[tex]d\ iargul=\sqrt{2}9[/tex]
[tex]=10\times \sqrt{2}\times \sqrt{2}[/tex]
[tex]=20cm[/tex]
I hope this helps you
:)
3/4 of tom's favorite number is 36. what number is one half of tom's favorite number
Answer: 3/4 is 75%
Step-by-step explanation: Since his fav number is 36 the half of 36 is 18 bc 18 + 18 is 36
In the figure below, L is parallel to M. Find X
Answer:
Let's first try to find the angle supplementary to measure 141°.
(Supplementary angles are two angles that add up together to equal 180°).
Set up an equation;
141 + x(unknown angle measure) = 180°
Solve for x:-
141 + x = 180
-141 -141
x = 39°.
Now that we've found one of the interior angles measure to this triangle, we will use this value to figure out the angle measure next to 'x'.
If we think of the line (highlighted in the picture I attached to this), extended, we can kind of make out of this line as a transversal cutting into the two parallel lines(L & M).
Furthermore, the measured angle 39°, is an alternate interior angle with the missing angle next to 'x'(highlighted with yellow in my picture).
And, alternate interior angles are congruent(meaning they measure the same degree).
Therefore, we can infer that the missing angle next to 'x' is also 39°.
Now that we've found one angle measure and another angle(given) next to x, we can see that angle x and those two angle measures (48° and 39°) combined are supplementary!
So now that we know that angles 48° and 39° are supplementary with x, we can find the value of x by finding it's supplement value!
Arrange an equation;
(48 + 39) + x = 180°
Simplify and solve for x:-
87 + x = 180
-87 -87
x = 93°, hence ∠X = 93°.
Kristina house is 11 3/10 Luke house is 9 2/10
Answer:
they are 3 1/10 units away from each other
Step-by-step explanation:
11 3/10 - 9 2/10
3 1/10
Find the product of
21/3 and 3/4.
Step-by-step explanation:
[tex] 2 \frac{1}{3} \times \frac{3}{4} \\
[/tex]2 1/3 = 7/3
[tex] \frac{7}{3} \times \frac{3}{4} \\ [/tex]
21/12 = 7/4
dude why is no one answering. Michelle walks 1/4
hour every day of the week (Monday through Sunday). Sandra walks 2/4
hour per day, but only on weekdays (Monday through Friday). Both Michelle and Sandra continue their routines for 9 weeks.
Calculate who walked the most over this 9 week period, and calculate how much more time this person walked than the other person. Be sure to show how you calculated each person's total walking time as a mixed fraction, and show how you calculated how much more time was walked by either Michelle or Sandra as a mixed fraction.
Answer:
Michelle walks 1 4 hour every day of the week (Monday through Sunday). Sandra walks 2 4 hour per day, but only on weekdays (Monday through Friday). Both Michelle and Sandra continue their routines for 9 weeks. Calculate who walked the most over this 9 week period, and calculate how much more time this person walked than the other person. Be sure to show how you calculated each person's total walking time as a mixed fraction, and show how you calculated how much more time was walked by either Michelle or Sandra as a mixed fraction. this is a word problom
Answer:
people are not doing it it's because that it's multiplying mixed numbers by whole numbers and we don't really need to do that
Step-by-step explanation:
prove that
[tex]4cot45 ^{2} - 3tan ^{2} 60 + 2sec ^{2}60 = 3[/tex]
help me
Answer:
[tex]4 \cot {}^{2} (45) - 3 \tan {}^{2} (60) + 2 \sec {}^{2} (60) = 3 \\ [/tex]
[tex]LHS = 4 \cot {}^{2} (45) - 3 \tan {}^{2} (60) + 2 \sec {}^{2} (60) \\[/tex]
let us first take a look at the values of the trigonometric ratios given in the question so that we get quite clear about what is to be done.
here ,
[tex] \cot(45) = 1 \\ \\ \tan(60) = \sqrt{3} \\ \\ \sec(60) = 2[/tex]
now ,
we just have to plug in the values considering certain other things given in the question and we're done!
so let's start ~
[tex]4(1) {}^{2} - 3( \sqrt{3} ) {}^{2} + 2(2) {}^{2} \\ \\ \dashrightarrow \: 4(1) - 3(3) + 2(4) \\ \\ \dashrightarrow \: 4 - 9 + 8 \\\\ \dashrightarrow \: 12 - 9 \\ \\\dashrightarrow \: 3 = RHS[/tex]
hence , proved ~
hope helpful :D