[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &\$14500\\ P=\textit{initial amount}\dotfill &\$22500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6\\ \end{cases}[/tex]
[tex]14500=22500(1 - \frac{r}{100})^{6}\implies \cfrac{14500}{22500}=\left( \cfrac{100-r}{100} \right)^6\implies \cfrac{29}{45}=\left( \cfrac{100-r}{100} \right)^6 \\\\\\ \sqrt[6]{\cfrac{29}{45}}=\cfrac{100-r}{100}\implies 100\sqrt[6]{\cfrac{29}{45}}=100-r \\\\\\ r=100-100\sqrt[6]{\cfrac{29}{45}}\implies r\approx \stackrel{\%}{7.06}[/tex]
The following figure shows a right triangular prism. (help pls :( )
Which expression represents the surface area of the prism?
Choose 1 answer:
Answer: b
Step-by-step explanation:
The expression represents the surface area of the prism is 2.24+120+160+200. Therefore, option B is the correct answer.
Here a triangular prism has been provided with some measurements.
We have to find Which expression can be used to find the surface area of the following triangular prism.
What is the formula to find the total surface area triangular prism?The formula for the surface area of a triangular prism is formed by adding up the area of all the rectangular and triangular faces of a prism. Observe the following figure of a triangular prism to know the dimensions that are considered to frame the formula.
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 +S2 + S3)L + bh
Here, S1, S2 and S3 are sides of triangles, l=length of the prism, b=base and h=height.
Now, (6+8+10)20+8×6=120+160+200+48
=2.24+120+160+200
The expression represents the surface area of the prism is 2.24+120+160+200. Therefore, option B is the correct answer.
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There are 6 blue chips for every 4 green chips. How many green chips will there be with 15 blue chips?
Answer:
6
Step-by-step explanation:
Its simple,
first you find the multiplier, to do this you do:
6/4 which is 2.5
then we do 15 / 2.5
which is 6
Evaluate sin 360°. Round your answer to the nearest hundredth if necessary.
Answer:
0
Step-by-step explanation:
just plug it into a calculator
Lorena paid $450 for a sneaker and there is a 9% advertised discount. What is the discount price?
Answer:
$40.50
Step-by-step explanation:
9% of 450 is 40.5
What is the quotient when (x+3) is divided into the polynomial 2x2 + 3x-9?
O A. 2x-5 with no remainder
B. X+ 3 with a remainder of -2
O c. 2x+ 1 with no remainder
D. 2x-3 with no remainder
Problem: 2x^2+3x-9
For a polynomial of the form, ax^2+bx+c rewrite the middle term as the sum of two terms whose product a·c=2·-9=-18 and whose sum is b=3.
Factor 3 out of 3x
2x^2+3(x)-9
Rewrite 3 as -3 plus 6.
2x^2+(-3+6)x-9
Apply the distributive property
2x^2(-3x+6x)-9
Remove the parentheses
2x^2-3x+6x-9
Factor out the greatest common factor from each group
Group the first two terms and the last two terms
(2x^2-3x) (6x-9)
Factor out the greatest common factor in each group.
x(2x-3)+3(2x-3)
Factor the polynomial by factoring out the greatest common factor, 2x-3
(x+3) (2x-3). So, the quotient is 2x-3
Thus, the correct answer is Option D 2x-3 with no remainder
A woodworking artist makes two types of carvings: type X and type Y. He spends 2 hours making each type X carving and 3 hours making each type Y carving, and he can spend up to 30 hours each week making carvings. His materials cost him $6 for each type X carving and $4 for each type Y carving, and he must keep his weekly cost for materials to $120 or less. If x is the number of type X carvings he makes in a week and y is the number of type Y carvings he makes in a week, which of the following systems of inequalities models this situation?
A. 2x + 3y ≥ 30, 6x + 4y ≤ 120
B. 2x + 3y ≥ 30, 6x + 4y ≥ 120
C. 2x + 3y ≤ 30, 6x + 4y ≤ 120
D. 2x + 3y ≤ 30, 6x + 4y ≥ 120
The linear systems of inequalities model this situation will be 2x + 3y ≥ 30 and 6x + 4y ≤ 120. Then the correct option is A.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A woodworking artist makes two types of carvings: type X and type Y.
He spends 2 hours making each type X carving and 3 hours making each type Y carving, and he can spend up to 30 hours each week making carvings.
His materials cost him $6 for each type X carving and $4 for each type Y carving, and he must keep his weekly cost for materials to $120 or less.
If x is the number of type X carvings he makes in a week and y is the number of type Y carvings he makes in a week.
Then the linear systems of inequalities models this situation will be
2x + 3y ≥ 30 and 6x + 4y ≤ 120
Thus, the correct option is A.
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(x+3)^2+4=46
what is the solution of this equation
Answer:
x = -3 + √42
Step-by-step explanation:
1) Expand the square
2) Distribute
3) Distribute
4) Distribute
5) Combine like terms
6) Add the numbers
7) Move terms to the left side
8) Subtract the numbers
9) Use the quadratic formula
10) Simplify
11) Separate the equations
12) Solve
Therefore, the solution of this equation is x = -3 + √42
Step-by-step explanation:
(x + 3)² + 4 = 46
(x + 3)² = 42
x + 3 = ±sqrt(42)
x = ±sqrt(42) - 3
x1 = sqrt(42) - 3 = 3.480740698...
x2 = -sqrt(42) - 3 = -9.480740698...
x/7 ≥ -6 please help me solve for x
Answer:
x ≥ -42
Step-by-step explanation:
[tex]\frac{x}{7} > =-6[/tex]
[tex]\frac{x}{7}\cdot 7 > =-6\cdot 7[/tex]
[tex]\frac{1}{7}\cdot 7x > =-6\cdot 7[/tex]
[tex]x > =-6\cdot 7[/tex]
[tex]x > =-42[/tex]
Shortcut
• Multiply positive 7 by negative 6 to find x as a shortcut.
Hello, can I please get some help :))
Answer:
add the seven to one and divide by three then subtract two
PLS HELP ME
1. What is the length of (AB)?
2. What is the length of (BC)?
3. What is the perimeter of this rectangle?
The length of AB is 4.12 units, length of BC is 8.25 units and Perimeter of rectangle ABCD is 24.74 units.
What is Perimeter of Rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Here,
A (-3, 3) and B (1, 4)
then, Length of AB = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
= [tex]\sqrt{(1-(-3))^2+(4-3)^2 }[/tex]
= [tex]\sqrt{4^2 + 1^2}[/tex]
= [tex]\sqrt{17}[/tex] units.
= 4.12 units
B (1, 4) and C (3, -4)
then, Length of BC = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
= [tex]\sqrt{(3 - 1)^2+(-4 - 4)^2 }[/tex]
= [tex]\sqrt{4 + 64}[/tex]
= [tex]\sqrt{68}[/tex]
= 8.25 units
Perimeter of Rectangle = 2 ( AB + BC )
= 2 ( 4.12 + 8.25 )
= 2 X 12.37
= 24.74 units
Thus, the length of AB is 4.12 units, length of BC is 8.25 units and Perimeter of rectangle ABCD is 24.74 units.
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The function (x)-47x
represents the number of jumping jacks j(x) you can do in x minutes. How many jumping jacks can you do in 15 minutes?
Given the function, j(x) = 47x, the number of jumps you can do in 15 minutes is: 705.
What is a Function?A function models the relationship between an input value and its corresponding output value.
Given the function, j(x) = 47x, number of jumping jacks you do in 15 minutes, is:
j(15) = 47(15)
j(15) = 705
Number of jumping jack in 15 minutes is: 705.
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The base diameter and the height of a cone are both
equal to x units.
Answer:
π x³ /12 is the volume of the cone if A cone has a height of x and a diameter of x
Step-by-step explanation:
The base diameter and the height of a cone are both equal to x units
Diameter of cone = x units
Radius = Diameter /2
=> Radius of cone = x/2 units
Height of cone =x units
Volume of cone = (1/3) π r²h
r = radius h = height
=> Volume of cone = (1/3)π (x/2)² * x
= (1/3) π (x²/4) * x
= (1/12) π x³
= π x³ /12 cubic units
Write the equation of the graph shown below in factored form?
Answer:
f(x) = (x − 1)2(x + 1)(x − 3)
Step-by-step explanation:
Look at where the red line crosses/ touches the x-axis. This will give you the zeros.
It crosses at -1, touches at 1, and crosses again at 3
This means the zeros are -1, 1 and 3
Now, you need to have (x+1) (x-3) and (x-1) as factors.
Therefore, the answer is f(x) = (x − 1)2(x + 1)(x − 3).
Ask an expert 2+3/10X>=13/20 Solve for inequality Thanks!
Answer:
The answer is in the picture.
Step-by-step explanation:
[tex]2+\frac{3}{10x}\geq\frac{13}{20} \\\\\frac{3}{10x}\geq\frac{13}{20} -2 \\\\\frac{3}{10x}\geq\frac{13}{20} -\frac{40}{20} \\\\\frac{3}{10x}\geq-\frac{27}{20} \\\\3\geq-\frac{27}{20}*10 x \\\\3\geq-\frac{270}{20} x\\\\3\geq-\frac{27}{2} x \\\\3*-\frac{2}{27} \leq x\\\\-\frac{6}{27} \leq x\\\\-\frac{2}{9} \leq x[/tex]
Also x cannot equal to 0 if you plug in into the original equation the answer is indefinite/not solution.
An object has a mass of 180 g and a volume of 9 cm³.
Find the density of the object in g/cm³.
g/cm³
Answer:
20 g/cm³
Step-by-step explanation:
mass = 180g
volume = 9 cm³
density =mass/volume
=180/9= 20 g/cm³
let f(x) = 3x² what is f(-2x)
answer : 12x²
steps
means put -2x where x is
let f(x) = 3x² what i f(-2x)
3(-2x)²
pemdas
-2x times -2x
4x²
3 times 4x²
12x²
Which statement about the line represented by the equation y+2=(x-5) is true
A. The slope is 3 and (-2,5) is on the line
B. The slope is 2 and (3,-5) is on the line
C. The slope is 3 and (5,-2) is on the line
D. The slope is 2 and (-3,5) is on the line
Answer:
A
Step-by-step explanation:
-2+2=5-5
0=0
the correct answer is A
Vito has a fair 20-sided die with the faces
numbered 1 through 20. Vito will roll the die
100 times. About how many times will he
likely roll a 1, 4, or 5?
A 10
B 25
C 15
D 50
Answer:
15, C
Step-by-step explanation:
Any number is equally likely to appear. Therefore, we have 3/20 * 100 = 15. This is C.
Hope this helped!
~clouddragon
84,326 dividido para 23
help will mark Brainliest!!
Answer:
8/9n - 3
Step-by-step explanation:
Answer the question below please (file attached) 50 POINTS
Answer:
They bought 6 vanilla wafers and 21 chocolate, they add up to 27.
x = amount of vanilla wafers
y = amount of chocolate wafers.
4x+y = 45
x+y= 27
Step-by-step explanation:
x = amount of vanilla wafers
y = amount of chocolate wafers
Vanilla wafers = 4$ each
Chocolate wafers = 1$ each.
So, 4x+y = 45 and x+y= 27 because they spent 47$ on 27 packs.
With both equations we can substitute.
1. Change one equation so one variable is on one side
x+y = 27 to y = 27-x
2. Substitute the variable from the other equation.
4x+y = 45 to 4x+27-x = 45
3. Solve the equation for x.
4x+27-x = 45
3x+27 = 45
3x = 18
x = 6 (amount of vanilla wafers)
4. substitute with equation.
y = 27-x to y = 27-6
5. Solve the equation for y.
y = 27-6
y = 21 (amount of chocolate wafers)
A teacher gave her class two quizzes. 25% of the class passed both quizzes and 40% of the class passed the first quiz. What percent will pass the second quiz given they passed the first quiz?
Answer:
35%
Step-by-step explanation:
40% + 25% = 65% minus that bye 100 you would get 35% the reason the answer isn't 65 is because add 40+25+65=130 which a whole is equal to 100 but if you do 40+25+35= 100 so thr answer is 35% :)
Money needed to raise $1000, sell a dozen of cookies for $3 a dozen. how many dozen of cookies need to be sold to raise $1000?
Answer:
334 dozen cookies.
Step-by-step explanation:
1000=3x
Let x = dozen of cookies sold
3x=1000
x=1000/3
x=333.33
Since 333.33 isn't a whole number, we need to round it up to 334 since rounding it down to 333 won't raise 1000 dollars.
Which expression is equivalent to -36-8
What is the difference in the costs for a one-night stay with and without breakfast?
Answer:
$23.12
Step-by-step explanation:
With breakfast included the total would be $142.99. Without breakfast it would be $119.87. So to get the difference it would be:
$142.99 - $119.87 = $23.12
FInd the value of x.
Y
D
W
X
(15x-8)
X =
N
226
Let's start with the given arc and its angle.
The angle YWX is going to be half the arc length.
YWX = 1/2 (226) = 113
Angles VWX and YWX form a linear pair (or are supplementary angles), which means that their sum is 180 degrees.
(15x - 8) + 113 = 180
15x + 105 = 180
15x = 75
x = 5
Hope this helps!
Adriano loves anime and collect toys from his fav series. Each month he gains 4 toys. If Adriano has 3 toys when he start collecting, how many dose he have in 4 months.
Answer:
19 toys
Step-by-step explanation:
suppose y = sin x
what y-value corresponds to an x-value of 3pi/2
Answer: THE ANSWER ON ACELLUS IS -1
Step-by-step explanation:
I found this answer on a site used to do sin cos and tangent
The y-value corresponding to an x-value of [tex]\( \frac{3\pi}{2} \)[/tex] in the function [tex]\( y = \sin(x) \) is \( y = -1 \).[/tex]
To find the y-value corresponding to an x-value of [tex]\( \frac{3\pi}{2} \)[/tex] in the function [tex]\( y = \sin(x) \),[/tex] simply substitute [tex]\( x = \frac{3\pi}{2} \)[/tex] into the function:
[tex]\( y = \sin\left(\frac{3\pi}{2}\right) \)[/tex]
Now, let's evaluate the sine function at [tex]\( \frac{3\pi}{2} \):[/tex]
[tex]\( y = \sin\left(\frac{3\pi}{2}\right) = -1 \)[/tex]
So, the y-value corresponding to an x-value of [tex]\( \frac{3\pi}{2} \)[/tex] in the function [tex]\( y = \sin(x) \) is \( y = -1 \).[/tex]
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Jocelyn is comparing the prices of wedding cakes. Store A charges $1.50 per serving plus a $25.00 delivery charge. Store B charges $2.25 per serving and no delivery charge. If Jocelyn wants a cake with 150 servings, how much more money will it cost to purchase the cake from Store B?
The Jocelyn needs to pay $87.5 if Jocelyn order cakes from store B if store A charges $1.50 per serving plus a $25.00 delivery charge. Store B charges $2.25 per serving and no delivery charge.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the total cost is $x if Jocelyn purchase cake from store A:
x = 1.50×150 + 25
x = 225+25 = $250
Let's suppose the total cost is $y if Jocelyn purchase cake from store B:
y = 2.25×150
y = $337.5
Difference between total cost = 337.5 – 250 = $87.5
Thus, the Jocelyn needs to pay $87.5 if Jocelyn order cakes from store B if store A charges $1.50 per serving plus a $25.00 delivery charge. Store B charges $2.25 per serving and no delivery charge.
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simplify 15a^z * 4c * 5ab
[tex]300a {}^{z + 1} bc[/tex]