See below for the proof of the equation 4h² - 4dh + x² = 0 using the Pythagoras theorem
How to prove the equation?The Pythagoras theorem states that:
Hypotenuse² = Opposite² + Adjacent²
The question is incomplete, as the figure is not given.
So, I will complete the proof using the following parameters:
Hypotenuse = 2√dhOpposite = xAdjacent = 2hSubstitute the above values in the following equation
Hypotenuse² = Opposite² + Adjacent²
So, we have:
(2√dh)² = x² + (2h)²
Evaluate the exponents
4dh = x² + 4h²
Subtract 4dh from both sides
0 = x² + 4h² - 4dh
Rewrite as:
4h² - 4dh + x² = 0
Hence, the equation has been proved
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the length of one base of a trapezoid is 19 meters and the length of the other base is 27 meters. find the length of the median.
Answer:
23 m
Step-by-step explanation:
the median is calculated as
half the sum of the parallel bases , then
median = [tex]\frac{19+27}{2}[/tex] = [tex]\frac{46}{2}[/tex] = 23
90 POINTS!! PLEASE HELP, IF YOU GIVE CORRECT ANSWER ILL GIVE YOU BRAINLIEST!!
Answer:
B) 2.19 %
Step-by-step explanation:
The rule of 70 is used to estimate the time (in years) it takes for an investment to double.
Rule of 70 Formula
[tex]\textsf{Number of Years to Double}=\sf \dfrac{70}{\textsf{Annual Growth Rate}}[/tex]
Given:
Number of Years to Double = 32Substituting this into the formula and solving
[tex]\implies \sf 32=\sf \dfrac{70}{\textsf{Annual Growth Rate}}[/tex]
[tex]\implies \textsf{Annual Growth Rate}=\sf \dfrac{70}{32}[/tex]
[tex]\implies \textsf{Annual Growth Rate}=\sf 2.1875[/tex]
[tex]\implies \textsf{Annual Growth Rate}=\sf 2.19 \% \: (nearest\:hundredth)[/tex]
Answer:
I think it is B
Step-by-step explanation:
hope it will help you
What is the radius of a sphere with a volume of 32398cm3 cm
to the nearest tenth of a centimeter?
Answer:
The answer is 19.8cm to the nearest tenth
If f(x) = x+10, find f(7)
[tex]f(x)=x+10\\\\f(7)=(7)+10\\\\f(7)=17[/tex]
the answer is 17.
Answer:
The answer is 17, x±10 =10+7= 17
A box of donuts has 12
total. One-fourth of
the donuts have sprinkles.
Of the remaining donuts,
one-third have cherry filling.
The rest are plain. How
many plain donuts are in
the box?
Answer:
6 donuts are left in the box
Step-by-step explanation:
12 divided by 4 is 3. take those three out of the 12. you are left with nine. 9 divided by 3 is 3. subtract three from the nine. you are left with 6.
David wants to hang a mirror in his room. The mirror and frame must have an area of 8 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x.
2x2 + 14x − 2 = 0
3x2 + 10x − 8 = 0
4x2 + 10x − 2 = 0
x2 + 7x − 8 = 0
Answer:
Represent the thickness of the frame by x.
Framing the mirror will increase both its length and width by 2x. The area of the mirror with the frame is the product of the length and width which can mathematically be expressed as,
A = (3+2x)(2+2x) = 8
The equation above can be simplified into 4x^2 + 10x -2=0.
This equation can still be further simplified by dividing it by 2. However, it will give an answer which is not found on the choices. Thus, the answer is the third choice.
Answer:
The correct option would be C
Step-by-step explanation:
I hope this helps, if it doesn't then just message me and ill be more than happy to help :)
Find the circumference of a circle whose radius is 16. Leave your answer in terms of π.
Answer:
32π
Step-by-step explanation:
The equation for the circumference of a circle is as follows:
C = 2 π r
Since r = 16:
C = 2 π (16) = 32π
I really need help!! Imagine you bought a car that is valued at $20,000 but depreciates at a rate of 15% per year. How much is the car worth after 5 years? What is your classmate’s error, what is the correct equation, and what is the value of the car after 5 years?
thanks
Answer:
[tex]20000 \times 0.15 \times 5 = 15000 \\ 20000+15000=35000
Step-by-step explanation:
20000 times (0.15 is rate) times years (5)
Answer you get is 15000 , then you have to take 20000+15000=35000
simplify 3^-6*(3^4/3^0)^2
Answer:
Thhe simplified form of the expression is 9
Indices are expressed as power or exponent which is raised to a number or a variable.
According to the law of indices
\begin{gathered}a^n \times a^m = a^{n+m}\\a^n \div a^m = a^{n-m}\end{gathered}
a
n
×a
m
=a
n+m
a
n
÷a
m
=a
n−m
Given the expression
3^{-6} \times (\dfrac{3^4}{3^0} )^23
−6
×(
3
0
3
4
)
2
This can also be expressed as:
\begin{gathered}=\dfrac{1}{3^6} \times (\frac{3^4}{1})^2 \ (3^0 =1)\\= \dfrac{1}{3^6} \times 3^8\\=\dfrac{3^8}{3^6}\\=3^{8-6}\\=3^2\\=9\\\end{gathered}
=
3
6
1
×(
1
3
4
)
2
(3
0
=1)
=
3
6
1
×3
8
=
3
6
3
8
=3
8−6
=3
2
=9
This shows that the simplified form of the expression is 9
the functions fx and gx are shown on the graph. using fx what us the equation that represents gx
The equation for the function g(x) = log₃(x+4) after applying the transformation x → (x+4).
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have equation of the graph:
[tex]\rm f(x) = log_3x[/tex]
Apply transformation in the parent function:
Replace x → (x+4)
The parent function will shift 4 units to the left.
And function becomes:
[tex]\rm g(x) = log_3(x+4)[/tex]
Thus, the equation for the function g(x) = log₃(x+4) after applying the transformation x → (x+4).
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Find the volume of the sphere. Round your answer to the nearest tenth.
Answer:
268.08 cm
Step-by-step explanation:
we all know that the FORMULA for a sphere is v=4/3 x π x r^3, so we just SUBSTITUTE.
V=4/3 x π x 4^3
which leaves us with 268.08 cm ^2 maybe??
(hope this helps)
What is the circumference of the given circle in terms of pi.
it’s timed please help :)
A cylinder has a circumference of 16pi inches and a height of 20 inches. what is the surface area of a cylinder in square inches?
Answer:
1407.43
Step-by-step explanation:
The eqaution for surface area of a cylinder is 2πr+2π[tex]r^{2}[/tex]'
but you already got the circumference so you work backwards
16pi/pi=16
16/2=8
r=8
h=20
So you plug it into the eqaution
2π8*20+2π8^2=1407.43
Using the equation, y=5x²−17x −12, determine the roots.
A) (-4, 0) and (0.6, 0)
b) (-4, 0) and (-0.6, 0)
c) (4, 0) and (-0.6, 0)
d) (4, 0) and (0.6, 0)
Answer:
c
Step-by-step explanation:
y = 5x² - 17x - 12
to find the roots let y = 0 , that is
5x² - 17x - 12 = 0
Factorising the quadratic
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 5 × - 12 = - 60 and sum = - 17
the factors are - 20 and + 3
use these factors to split the x- term
5x² - 20x + 3x - 12 = 0 ( factor first/second and third/fourth terms )
5x(x - 4) + 3(x - 4) = 0 ← factor out (x - 4) from each term
(x - 4)(5x + 3) = 0
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
5x + 3 = 0 ⇒ 5x = - 3 ⇒ x = - [tex]\frac{3}{5}[/tex] = - 0.6
roots are (4, 0 ) and (- 0.6, 0 )
choose the polynomial that is written in standard form
Answer: I don't know
Step-by-step explanation:
There are no choices. The question stated choose the polynomial which means it should have choices.
Correct me if I'm wrong though. Hope you won't be offended.
Answer:
Please read explanation... it always helps... trust me...
Step-by-step explanation:
alrighty sooo....
when a polynomial is written in standard form that means that the exponents are in order from greatest to least.... (i hope that isn't confusing....)
here is an example:
x^6 + x^5 + x^2 + 23 --> this polynomial is in standard form because the exponents are in order from least to greatest..... 6 then 5 then 2 then 1
(remember that a number like 23 have an invisible 1 as the exponent....
(btw, this symbol ^ means "to the power of")
I really hope this helps!!!!
Please solve the inequality and give the steps needed to solve: x²-13x+36 ≤ 0
I need help to find the blank spaces for the chart
Suppose a car rental firm wants to estimate the average number of kilometers traveled per day by each of its cars rented in a certain city. A random sample of 20 cars rented in that city reveals that the sample mean travel distance per day is 85.5 kilometers, with a population standard deviation of 19.3 kilometers. Compute a 99% confidence interval to estimate Q. (2 points) Interpret your answer. (1 point)
Using the z-distribution, it is found that the 99% confidence interval to estimate Q is (74.4, 96.6). The interpretation is that we are 99% sure that the true mean for all cars rented in the city is between these two values.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters of the interval are given as follows:
[tex]\overline{x} = 85.5, \sigma = 19.3, n = 20[/tex].
Hence the bounds of the interval are given as follows:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 85.5 - 2.575\frac{19.3}{\sqrt{20}} = 74.4[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 85.5 + 2.575\frac{19.3}{\sqrt{20}} = 96.6[/tex]
The interpretation is that we are 99% sure that the true mean for all cars rented in the city is between these two values.
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Is this employee correct? please help and explain your thinking.
Answer: yes it is
Step-by-step explanation:
Write an explicit formula for an, the nth term of the sequence 13, 20, 27, ....
Answer: an
Submit Answer
Answer:
See below ~
Step-by-step explanation:
Finding the common difference :
20 - 137Formula :
aₙ = aₙ₋₁ + 7Answer:
[tex]\large \boxed{\sf 7n + 6}[/tex]
Explanation:
Sequence: 13, 20, 27,...
Find common difference: second term - first term = 20 - 13 = 7
As it is an explicit arithmetic term:
⇒ a + (n - 1)d (a is the first term, d is common difference)
⇒ 13 + (n -1)(7)
⇒ 7n - 7 + 13
⇒ 7n + 6
Fill in the blanks so that the standard and factored forms match
-x^4-5x^3+__ x^2 +10x=(x+__)(2x-x^3)
Answer:
-x^4-5x^3+2x²+ 10x = (x+5)(2x-x³)
Step by Step explanation
Naming the coefficient of x² as "a" and the independent temine of the first parenthesis as "b", we got:
-x^4-5x^3+ ax^2 +10x=(x+b)(2x-x^3)
- x⁴-5x^3+ ax^2 +10x = 2x²- x⁴+2bx-bx³
-5x^3+ ax^2 +10x = -bx³+2x²+2bx
( Matching the exponents)
For x: 2b= 10; b=10/2.
b=5
For x²: a=2
For x³: -b=-5
b=5
classify the system as consistent independent inconsistent or coincident { 3x - 6y = -12 x - 2y = -8
Find Determinant value
[tex]\\ \rm\Rrightarrow \left|\begin{array}{cc}\rm 3&\rm -6\\ \rm 1&\rm -2\end{array}\right|[/tex]
[tex]\\ \rm\Rrightarrow -6+6[/tex]
[tex]\\ \rm\Rrightarrow 0[/tex]
System is inconsistentapply the distributive property to multiply the following
1. 9×15
2.48×4
3.65×5
4.8×87
5.38×3
Candle a and candle b were lit at the same time. candle a could last 3 hours and candle b could last 5 hours. after 1 hour, both candles were equal in length. what was the ratio of the length of candle a to the length of candle b at first.
The ratio of the length of candle A to the length of candle B at first will be 3 / 5.
What are ratios and proportions?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
Candle A and candle B were lit at the same time. candle a could last 3 hours and candle b could last 5 hours. after 1 hour, both candles were equal in length.
Then the ratio of the length of the candle A to the length of candle B at first will be
Let the length of candle A is x and the length of candle B be y.
The common speed will be S.
Then we have
Time = length / speed
For candle A, we have
Candle A = x / S = 3 ...1
For candle B, we have
Candle B = y / S = 5 ...2
From equations 1 and 2, we have
x / 3 = y / 5
x / y = 3 / 5
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NEED ANSWER PLEASE ASAP
A company makes chocolate candies in the shape of a solid sphere. Each piece of candy has a diameter of 3cm. If a box contains 30 pieces of candy, how much chocolate does the box contain? Use 3.14 for pie, and do not round your answer.
Step-by-step explanation:
282.8cm³
Since the volume of each chocolate candy is in the shape of a sphere, it's volume is the volume of a sphere.
12. The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors.
C(x)=2300+60x
R(x)=820x−x2
Answer:
$ 142100
Step-by-step explanation:
Profit is the difference between the revenue and the cost
P(x) = R(x) - C(x)
= 820x - x² - (2300 + 60x)
= 820x - x² - 2300 - 60x
= -x² + 820x - 60x - 2300
P(x) = -x² + 760x - 2300
We can find the maximum profit of the company by finding the maximum of the parabolic function.a = -1 ; b = 760 and c = -2300
[tex]\sf \boxed{P_{max} = c - \dfrac{b^2}{4a}}[/tex]
[tex]\sf = -2300 - \dfrac{760^{2}}{4*(-1)}[/tex]
[tex]\sf = -2300 +\dfrac{577600}{4}\\\\ = -2300 + 144400\\= 142100[/tex]
[tex]\sf \boxed{P_{max}= \$ 142100}[/tex]
You start at (5, -2). You move up 4 units. Where do you end?
Answer:
(5,2)
Step-by-step explanation:
if it’s (x,y) and 4 to the y to get 2
A factory produces 1,250,000 toys each year. The number of toys is expected to increase by about 150% per year. Which model can be used to find the number of toys, n (in millions), being produced in t years? n = StartFraction 2. 5 (1. 5) Over t EndFraction, t not-equals 0 n = 1. 5 t squared 1. 25 n = 1. 5 t 1. 25 n = 1. 25 times 2. 5 Superscript t.
Answer:
see the attachment!
i hope this can help you!
A block of sugar maple wood has a mass of 82.8 g and density of 0.69 g/cm3. the block is a rectangular prism with a length of 5 cm and a width of 4 cm. what is the height of the block of sugar maple? enter your answer in the box.
The density of an object is the ratio of the mass of the object to its volume. The height of the block of sugar maple is 6cm
Density of an objectThe density of an object is the ratio of the mass of the object to its volume. Mathematically;
Density = mass/volume
Given the following
Mass of block = 82.8grams
Density = 0.69g/cm^3
volume = lwh
Volume = 20h
Substitute
0.69 = 82.8/20h
20h = 82.8/0.69
20h = 120
h = 6cm
Hence the height of the block of sugar maple is 6cm
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6cm
Step-by-step explanation i can confirm that the answer is 6 ;}