Answer: 25
Step-by-step explanation:
We know this because 5 × 5 = 25
or 5² = 25
and also √25 = 5
a construction is shown in the following diagram. an arc was formed by having point a and point b as the center and using the same radius. based on this diagram, which statement is not true?
The statement that is not true: The arc is not a semicircle.
The arc in the diagram does not appear to be a semicircle because it is not a complete circle and the two points, a and b, do not appear to be the same distance from each other.Analysis of an Arc Formed by Two Points with the Same RadiusThe diagram shows an arc that is formed by two points, point a and point b, with the same radius. The arc does not appear to be a semicircle because it is not a complete circle and the two points, a and b, do not appear to be the same distance from each other.
This means that the statement “The arc is a semicircle” is not true. Additionally, the arc could be an ellipse or some other curved shape, depending on the location of the two points, a and b, relative to each other.
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Find the length of the curve.
x=3t² +5₁y = 2t³ +5,0 ≤t≤1
The length of the curve will be given by the definite integral
\(\displaystyle \int_0^1 \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt\)
From the given parametric equations, we get derivatives
\(x(t) = 3t^2 + 5 \implies \dfrac{dx}{dt} = 6t\)
\(y(t) = 2t^3 + 5 \implies \dfrac{dy}{dt} = 6t^2\)
Then the arc length integral becomes
\(\displaystyle \int_0^1 \sqrt{\left(6t\right)^2 + \left(6t^2\right)^2} \, dt = \int_0^1 \sqrt{36t^2 + 36t^4} \, dt \\\\ = \int_0^1 6|t| \sqrt{1 + t^2} \, dt\)
Since 0 ≤ t ≤ 1, we have |t| = t, so
\(\displaystyle \int_0^1 6|t| \sqrt{1 + t^2} \, dt = 6 \int_0^1 t \sqrt{1 + t^2} \, dt\)
For the remaining integral, substitute \(u = 1 + t^2\) and \(du = 2t \, dt\). Then
\(\displaystyle 6 \int_0^1 t \sqrt{1 + t^2} \, dt = 3 \int_1^2 \sqrt{u} \, du \\\\ = 3\times \frac23 u^{3/2} \bigg|_{u=1}^2 \\\\ = 2 \left(2^{3/2} - 1^{3/2}\right) = 2^{5/2} - 2 = \boxed{4\sqrt2-2}\)
f(x)=x^2-5x-36 and g(x)=x−9, find f(x)÷g(x) and express the result as a polynomial in simplest form.
Answer: x+4
Step-by-step explanation:
PLEASE HELP ME QUICK!!!
Answer:
Option D. \(g(x)=5(0.8)^{x}+2\)
Step-by-step explanation:
Main concepts
Concept 1: identifying horizontal asymptote
Concept 2: assuring decreasing exponential function
Concept 1. identifying horizontal asymptote
Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis. A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number. Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units. Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.
Concept 2. assuring decreasing exponential function
Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".
If "b" is between 0 and 1 (a "small" number), the function will decrease.If "b" is larger than 1 (a "big" number), the function will increase.Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.
To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.
Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.
Which line is parallel to line CD in this figure?
line FA
line FC
line AD
A figure with 4 lines. Line A F is the same distance from line C D at every point. Line A D intersects line A F at point A and line C D at point D. Line F C intersects line A F at point F and line C D at point C.
The line that is parallel to line CD in the figure is A. Line FA
From the provided information, line FA is the same distance from line CD at every point, meaning that these lines are parallel.
What do parallel lines mean?Parallel lines are lines on a flat surface that never meet or cross each other.
When two lines are straight from beginning to end, they are parallel. Their distance is always the same at all points.
Some properties of parallel lines include:
Their corresponding angles are equal.The interior angles are also equal when another line cuts across them.From the given figure, we can see that FA||CD.
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After a 90% reduction, you purchase a new soft drink machine on sale for $66. What was the original price of the soft drink machine?
The original price was
GEZER
Answer:
$660.
Step-by-step explanation:
So when we apply a discount to a product we multiply the price of the product (let's all is x) for the percentage of the discount (let's apply 90% as the probnlem says) so then we have the following operation:
x ⋅ (1-0.9) = y
Variable y is the price at which you bought the product, it's $66, on this case. Therefore, this is the expression we have:
x ⋅ (1-0.9) = $66
Now, to get the original value of the product (x), we solve the equation for x:
x ⋅ (1-0.9) = $66
x= $66 / (1-0.9)
x= $66 / (0.1)
x= $660
• Why did we multiply by 1-0.9?
This is because we were looking for the 10% of the original price, since it's a 90% discount. A simple way to solve the problem would've been to just divide the price by 0.1 (10%), because that's what remains after you discount 90% of the price.
-------------------------------------------------------------------------------------------
A different example would be the following:
What was the original price of a product bought for $48 if it has a 60% discount?
x is original price.
Since a 60% discount was applied, 40% of the price remains at full price. Therefore, we multiply the original price (x) by 40%:
x ⋅ 40%= $48
x= $48 / 40%
x= $48 / 0.4
x= 120
$120 was the original price.
What is the product? (3x-b)(2x^2-7x+1) A. -12x^2+42x-6 B. -12x^2+21x+6 C. 6x^3-33x^2+45x-6 D. 6x^3-27x^2-39x+6
Answer:
C.6x³-33x² + 45x-6
Step-by-step explanation:
(3x-6)(2x^2-7x+1)
= 3x(2x² - 21x +1) -6(2x² - 7x+1)
= (6x³ - 21x² + 3x) - (12x² - 42x+6)
= 6x³ - 21x² + 3x -12x² + 42x -6
= 6x³-33x² + 45x-6
Which is the
4
graph of f(x) = 4[*?
-3-2--1₁-
-2-
2 3 4 5 6
4
1
1-2--11-
-2
2 3
56
4
2-11.
-2-
23
56
Option 2 is the correct graph for the function f(x) = \(4[(1/2)^{x}]\) .
Given ,
f(x) = \(4[(1/2)^{x}]\)
Mathematically the graph will of exponential in nature.
So,
Let us assume few values to understand the nature of graph.
Firstly,
Let x= 1
f(x) = \(4[(1/2)^{1}]\)
f(x) = 2
Let x = 2
f(x) = \(4[(1/2)^{2}]\)
f(x) = 1
Let x = 3
f(x) = \(4[(1/2)^{3}]\)
f(x) = 0.5
Thus from these values of f(x) corresponding to the values of x second graph will be correct .
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Find the smallest whole number by which 16087 should be multiplied or divided to get a perfect square
There is no whole number by which you can multiply or divide 16087 to make it a perfect square.
To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.
In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.
To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.
A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.
Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.
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Solve open parentheses square root of 6 close parentheses to the 8 x power = 216x−3.
Answer:
x = 6.0139
Step-by-step explanation:
1) think of the first side of the equation as: 6^(8/2) - simplify by dividing the 8 by 2 to get 6^4.
2) The Equation now is 6^4 = 216x - 3, turn 6^4 into 1296 and add 3 to both sides to get 1299 = 216x.
3)Divide both sides by 216 to get x = 6.0139 (which is approximately close to 6 but technically plugging the answer into the equation in step 2 would yield 1296 = 1296).
Answer:
-9
Step-by-step explanation:
\((\sqrt{6}) ^8^{x} = 216^x^{-3}\)
step one: create equal bases
\(6^{1/2} (^8^{x} )\)
\(6^3 =216\)
so it would be
\(6^{1/2} (^8^{x} ) = (6^3)^x^{-3}\)
\(6^{4x} = (6^3)^{3x-9}\)
the bases cancel out leaving:
\(4x=3x-9\)
Step 2: Solve for the variable
\(4x=3x-9\)
subtract 3x from each side
leaving x = -9
Find the volume of the cylinder whose radius is 2 cm and height is 7 cm
Using the formula for the volume of a cylinder, we have:
V=π*(r^2)*(h)
V=π*(2^2)*(7) cm^3 (Replacing the values)
V=π*(4)*(7) cm^3 (Raising 2 to the power of 2)
V= 87.96 cm^3 (Multiplying)
The answer is 87.96 cm^3
Select the correct answer.
Answer:it might be A
subtract: (2x^2-6x+7) - (5x^+2x-8)
Answer:
2x^2 - 6x + 7 - (5x^2 + 2x - 8)
Distributive a -1 to each term in the parentheses.
2x^2 - 6x + 7 - 5x^2 - 2x + 8
Combine like terms.
-3x^2 - 8x + 15 is the expression after being subtracted.
Answer:
−3x² − 8x − 1Step-by-step explanation:
(2x² − 6x + 7) − (5x² + 2x +8)
To find the opposite of 5x² + 2x + 8, find the opposite of each term.
2x² − 6x + 7 − 5x² − 2x − 8
Combine 2x² and −5x² to get −3x²
−3x² − 6x + 7 − 2x − 8
Combine −6x and −2x to get −8x.
−3x² − 8x + 7 − 8
Subtract 8 from 7 to get −1.
−3x² − 8x − 1
Shayna paid $7.10 for a pizza. She now has $6.79. With how much money did she
start? Explain and show your work."
Answer:
all u have to do is...
Step-by-step explanation:
add 7.10 and 6.79 together to get your answer hope this helped!!
IF IT DID PLZ GIVE ME BRAINIEST!!
Answer:
$13.89
Step-by-step explanation:
This is very simple. Shanya had paid $7.10 for the pizza, leaving her with $6.79 leftover. All you have to do to find the original amount is by adding back the amount that was taken away. So $6.79 + $7.10 = $13.89. This is the amount she had started off with.
Find the sum and difference (first mixed number minus the second mixed number) for the following pair of mixed numbers. The answer should be written as a mixed number.
Answer:
Sum = 15 8/15, Difference = 1 2/15
Step-by-step explanation:
8⅓, 71/5
A. Sum
8⅓ + 7 1/5
Convert to improper fraction
25/3 + 36/5
Find the LCM of 3 and 5. The result is 15. Divide 15 by the denominator of each fraction and multiply the result obtained with the numerator. The result is shown below:
[(25×5) + (36×3)] / 15
[125 + 108] / 15
233 / 15
Convert to mixed fraction
15 8/15
B. Difference
8⅓ – 7 1/5
Convert to improper fraction
25/3 – 36/5
Find the LCM of 3 and 5. The result is 15. Divide 15 by the denominator of each fraction and multiply the result obtained with the numerator. The result is shown below:
[(25×5) – (36×3)] / 15
[125 – 108] / 15
17 / 15
Convert to mixed fraction
1 2/15
SUMMARY:
Sum = 15 8/15, Difference = 1 2/15
Help! I’ll mark your brainly
Answer:
To graph the solution set of an inequality with two variables, first graph the boundary with a dashed or solid line depending on the inequality. If given a strict inequality, use a dashed line for the boundary. If given an inclusive inequality, use a solid line. Next, choose a test point not on the boundary.
Step-by-step explanation:
Answer:
I can`t really graph it for you but I can explain how. You know what a coordinate plane looks like, with 4 quadrants? Look it up and turn each of the squares into a plane. Once it`s labeled, you can graph them.
For problem 1, you`ll want to make your first point at the coordinate (0, 0). Then, move one up and one right and make another point (This is the slope of 1x). Continue doing that across, and then the other way going down left as well.
Since it is an inequality, a certain part must be shaded. If y < x, then it is lesser than the slope. Shade the entire area below the line.
For problem 2, you`ll want to make your first point at the coordinate (0, 2). Then move one to the right and 3 down. Finish the line. Since y is once again less than x, shade the area below the line.
For problem 3, make a point at the coordinate (0, -1). Then move up 2 and one right and make a point. Finish the line. This time, y is greater than x, so shade the area ABOVE the line.
For problem 4, make a point at (0, -1). Then, move up 2 and 3 right. Continue and finish the line. Since the symbol states that it is greater than OR equal to (thus the line under it) make sure your line is dotted, rather than a regular line. This is how my teacher had me do it with inequalities, but I`m not sure what your teacher is telling you. Since it is still greater than, shade the area above the dotted line.
If you have any questions please comment, I`m happy to help.
NO LINKS!!
A principal P, invested 9.5% compounded continuously, increases to an amount K times the original principal after t years, where t = ln(K)/0.095.
a. Complete the table. (Round your answers to one decimal place)
K t
1
2
3
4
6
8
10
12
b. Sketch the graph of the function.
Answer:
\(\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}\)
See attachment for the graph.
Step-by-step explanation:
Part (a)Given equation for t:
\(t=\dfrac{\ln (K)}{0.095}\)
Substitute the given values of K into the equation for t and round the answers to one decimal place:
\(\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}\)
Part (b)To sketch the graph of the given function (see attachment):
Plot the values of K along the x-axis.Plot the values of t along the y-axis.Plot the points from the table from part (a).Draw a curve through the plotted points.What is the m∠J, to the nearest tenth? JLK is right angle triangle. The length of JL is 9.4 and length of LK is 15.1. explaination?
The angle m∠J in the right angle triangle is 58.1 degrees.
How to find the angle of a triangle?One of the angle of a right tangle triangle is 90 degrees. The sum of
angles in a triangle is 180 degrees.
Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.
Hence,
tan ∠J = opposite / adjacent
tan ∠J = 15.1 / 9.4
∠J = tan⁻¹ 1.60638297872
∠J = 58.0909229196
Therefore,
m∠J = 58.1 degrees
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x²-3x+1=0
O A. 3±√15
OB. 3+√5
3± √5
o c. 2121224
OD. 5±10
3
Answer:
X=3+-√5/3
Step-by-step explanation:
x=-b+-√b^2-4ac/2
=3+-√(-3)^2-4(1)(1)/2
Suppose an elevator starts at street level (0), goes down 4 floors to the parking deck
and then goes up 9 floors to the conference center. The conference center is on what Suppose an elevator starts at street level (0), goes down 4 floors to the parking deck
and then goes up 9 floors to the conference center. The conference center is on what floor?
Answer:
5
Step-by-step explanation:
0-4= -4
-4+9=5
Answer: The 5th Floor
Step-by-step explanation:
0 - 4 = - 4
- 4 + 9 = 5
what is 3/4 divided by 11/20
Answer:
11/15
Step-by-step explanation:
11/20 / 3/4
11/20*4/3
44/60
22/30
11/15
Answer:
15/11
Step-by-step explanation:
3/4 divided by 11/20?
Reduce the expression, if possible, by canceling the common factors.
Exact Form: 15/11
decimal form: 1.36
mixed number form: 1 4/11
Determine the total surface area and volume of each figure.
The total surface area of solid is,
S = 220 m²
And, The volume of the prism is, 200 m³
We have to given that;
A solid prism is shown in figure.
Since, The surface area of a prism is,
S = (2 × Base Area) + (Base perimeter × height)
Where, "S" is the surface area of the prism.
Hence, We get;
base area = 5 x 10 = 50 m²
height = 4 m
Base Perimeter = 2 (5 + 10) = 30
Hence, We get;
S = (2 x 50) + (30 x 4)
S = 100 + 120
S = 220 m²
Since, A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is expressed as;
V = base area × height.
Now, For given figure,
Volume of the prism = base area × height
base area = 5 x 10 = 50 m²
height = 4 m
Hence, Volume = 50 × 4 m³
= 200 m³
Thus, The volume of the prism is, 200 m³
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You are currently paying $1,800 per year for insurance. The insurance company informs you that after five years of no
claims and moving into a different risk pool your rates will go down 13%. How much will you be paying next year?
a) $234
b) $1,566
c) $1,777
d) $1,800
An amount of Birr 500 is deposited in an account at the end of each six-month period with an interest computed at 6% compounded semi-annually. How many years does it take for the amount to reach Birr 56,398.43?
It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.
We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.
Let's substitute the given values into the formula and solve for t:
56,398.43 = 500(1 + 0.06/2)^(2t)
Divide both sides by 500:
112.79686 = (1 + 0.03)^(2t)
Take the natural logarithm of both sides to eliminate the exponent:
ln(112.79686) = ln(1.03)^(2t)
Using the property of logarithms, we can bring down the exponent:
ln(112.79686) = 2t * ln(1.03)
Now, divide both sides by 2 * ln(1.03):
t = ln(112.79686) / (2 * ln(1.03))
Using a calculator, we find t ≈ 17.12.
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1). Solve for n n - 72 = 83 *
Helpppppppppp
Answer:
N=155 I am pretty sure thats the answer
A cylinder has a height of 20 cm and a diameter of
6 cm. What is the volume, in cubic centimeters, of the
cylinder? Use 3.14 for T.
If
R
=
{
x
|
x
>
0
}
and
S
=
{
x
|
x
<
3
}
, what is the number of integers in
R
∩
S
?
A. Zero
B. Two
C. Three
D. Four
As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.
In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.
In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.
The intersection of two sets contains only the elements that are present in both sets. In this case,
R ∩ S = {x | x > 0 and x < 3}
The integers that are present in this set are 1 and 2.
Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.
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(4x + 24)/x
since the expression is an integer, x
How many different integer values are there?
Step-by-step explanation:
this is an integer of the interior comes from into juice
Answer:
x= -8
Step-by-step explanation:
4x+ 24= x
4x - x = -24
3x = -24
x = -24/3
x = -8
1) Matching.
The United States won 104 gold (g), silver s, and bronze (b) medals in the 2012 Summer Olympics.
____________a. Select the linear equation in standard form for three unknowns:
____________b. The United States won 46 gold medals and the same number each of silver and bronze medals. Select the relationship between the number of silver to bronze medals in an equation of two unknowns.
_____________c. With the information given in b, solve the linear equation in a for the number of gold, silver, and bronze medals won.
a. =g + s + b=104
b. =g=29, s=46, b=29
c. =g=b
d. =s=b
e =-g=46, s=29, b=29
f. =g + s + b=100
The linear equation in standard form is g + s + b=104, the relationship between silver to bronze medals is g = s and the solution is g=46, s=29, b=29
How to select the linear equation in standard form for three unknowns?
(a) Since the United States won 104 gold (g), silver s, and bronze (b) medals in the 2012 Summer Olympics.
This means the sum of gold (g), silver s, and bronze (b) medals is equal to 104. Thus, the linear equation in standard form is:
g + s + b = 104
(b) Since the United States won 46 gold medals and the same number each of silver and bronze medals. This implies:
g = 46
s = b
Thus, the relationship between the number of silver to bronze medals is s = b
(c) To solve the linear equation, substitute g = 46 and s = b into the equation g + s + b = 104:
g + s + b = 104
46 + b + b = 104
46 + 2b = 104
2b = 104 -46
2b = 58
b = 58/2
b = 29
Also, s = 29 (Remember: s = b)
Thus, g = 46, s =29, b = 29
Therefore, the United States won 46 gold (g), 29 silver (s), and 29 bronze (b) medals in the 2012 Summer Olympics. Select options a., d. and e. for a., b., and c. respectively
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katy desea alquilar un barca y gastar por menos $54. El barco cuesta $7 por hora y katy tiene un cupom de descuento de $9 dolares. ¿por cuántas horas podria katy alquilar el barc
Answer:
9 horas
Explanation:
$63 por 9 horas
Cupom de descuento de $9
$63 - $9 = $54