Answer: (9, 10800)
Step-by-step explanation:
We will first let x be the number of years and y be the total cost.
In that case, let's plug in the values for each into the equation y=mx+b, where m is the slope and b is the y-intercept.
The y-intercept will be the value we start with before any years pass, so it will be the installation cost. The slope is how fast the total cost will increase. Since the operation costs have to be added on every year, it will be our slope.
With that in mind, let's create both of our equations:
y = 900x + 2700 (Oil system)y = 200x + 9000 (Solar system)Since y is solved for in the first equation, we can substitute it into the second equation:
[tex]900x + 2700 = 200x + 9000[/tex]
[tex]700x + 2700 = 9000[/tex] [Subtracting 200x from both sides]
[tex]700x = 6300[/tex] [Subtracting 2700 from both sides]
[tex]x = 9[/tex] [Dividing both sides by 700]
We can now substitute 9 for x in any equation and solve for y. Here I substituted it into the first one:
[tex]y = 900(9) + 2700[/tex]
[tex]y = 8100 + 2700[/tex] [Multiplying]
[tex]y = 10800[/tex] [Adding]
Hence, the solution to this linear system is (9, 10800).
Compute without a calculator:
$$(72\cdot 78\cdot 85\cdot 90\cdot 98)\div (68\cdot 84\cdot 91\cdot 108).$$
(There's an easier way than multiplying out the giant products $72\cdot 78\cdot 85\cdot 90\cdot 98$ and $68\cdot 84\cdot 91\cdot 108$!)
Take the prime factorization of each factor in the product.
[tex]\dfrac{72 \times 78 \times 85 \times 90 \times98}{68 \times 84 \times 91 \times 108} \\\\ ~~~~~~~~ = \dfrac{(2^3\times3^2)\times(2\times3\times13)\times(5\times17)\times(2\times3^2\times5)\times(2\times7^2)}{(2^2\times17)\times(2^2\times3\times7)\times(7\times13)\times(2^2\times3^3)} \\\\ ~~~~~~~~ = \dfrac{2^6 \times 3^5 \times 5^2 \times 7^2 \times 13 \times 17}{2^6 \times 3^4 \times 7^2 \times 13 \times 17} \\\\ ~~~~~~~~ = 3 \times 5^2 = \boxed{75}[/tex]
Amanda makes $40,000 and gets an annual raise of $3,000. Marie makes $45,000 and gets an annual raise of $2,500. How many years will it take Amanda and Marie to make the same salary?
Answer:
Six years
Step-by-step explanation:
because it will divided the twoo digit and mutiple it self
I have no clue what this question is asking nor how to answer it
Which of the following numbers are solutions of the sentence x-3< 2?
| -3
|| 0
||| 2
IV 5
II only
III only
I and III only
I, II, and III only
Or
I, II, III, and IV
Answer:
IV 5
Step-by-step explanation:
you have to solve for x:
x-3<2
x-3+3<2+3
x=5
could you put the brainlyest Icon for me? I have 1500 points, but no brainlyest, so I can't move up the ranks.
FInd the solution for the ordered pair
2x + y = 5 and x + y = 6
Answer:
(-1,7)
Step-by-step explanation:
Use elimination, x = -1, y = 7
Answer:
(-1, 7)
Step-by-step explanation:
Elimination Method:Elimination: Step 1
Write in standard form (you can have negatives)
(standard form= Ax+By=C)
Elimination: Step 2
Create(find) opposites
Elimination: Step 3
Add to cancel one variable
Elimination: Step 4
Solve for variable
Elimination: Step 5
Substitute into other equation to find other variable
Substitution (Method)
In a linear system of equations, substitution results in one equation with one variable. The solution to a linear system is an ordered pair, not just a single value.
Problem:
Solve 2x+y=5;x+y=6
Steps:
I will solve your system by substitution.
(You can also solve this system by elimination.)
2x+y=5;x+y=6
Step: Solve 2x+y=5 for y:
2x+y+−2x=5+−2x(Add -2x to both sides)
y=−2x+5
Step: Substitute −2x+5 for yin x+y=6:
x+y=6
x+−2x+5=6
−x+5=6(Simplify both sides of the equation)
−x+5+−5=6+−5(Add -5 to both sides)
−x=1
-x/-1 = 1/-1 (Divide both sides by -1)
x=−1
Step: Substitute −1 for x in y=−2x+5:
y=−2x+5
y=(−2)(−1)+5
y=7(Simplify both sides of the equation)
Answer:
x=−1 and y=7
A bank charges 12% simple interest p.a. on a cash loans for R10 000,must repay the loan over 4 years.
Calculate the interest which is gonna be paid to the loan?
Answer:
$4800
Step-by-step explanation:
Let's use the simple interest formula, P(1+rt), to find the final amount of the loan
10000(1+.12*4) = 14800, the final amount
14800 - 10000 = 4800 total in interest
Suppose we want to choose 5 letters, without replacement, from 15 distinct letters.
[tex]order \: does \: not \:matter \\ sample \: space = 15 \: letters \\ no \: repetition\\ P(A) = 15C5 = 3003 \: ways[/tex]
100 POINTS
Find the volume of the composite solid.
A ) 1099.01 m^3
B) 104.67 m^3
C) 889.67 m^3
D) 785 m^3
Volume of a cylinder: PI x radius^2 x height
= 3.14 x 5^2 x 10 = 785 m^3
Volume of a cone: pi x radius^2 x height/3
= 3.14 x 5^2 x 4/3 = 104.67 m^3
Total volume = 785 + 104.67 = 889.67 M63
Answer: C. 889.67 M^3
Answer:
[tex]\textsf{C)}\quad \sf 889.67\: m^3[/tex]
Step-by-step explanation:
The given composite solid is made up of a cylinder and a cone.
To find the volume of the composite solid, find the volume of the cylinder and the volume of the cone, then add them together.
Volume of a cylinder:
[tex]\sf V=\pi r^2 h[/tex]
(where r is the radius and h is the height)
Given:
r = 5 mh = 10 mSubstitute the given values into the formula and solve for V:
[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cylinder & = \sf \pi (5)^2(10)\\ & = \sf 250 \pi \:\:m^3 \end{aligned}[/tex]
Volume of a cone:
[tex]\sf V=\dfrac{1}{3} \pi r^2 h[/tex]
(where r is the radius and h is the height)
Given:
r = 5 mh = 4 mSubstitute the given values into the formula and solve for V:
[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cone & = \sf \dfrac{1}{3} \pi (5)^2(4)\\ & = \sf \dfrac{100}{3}\pi \:\:m^3 \end{aligned}[/tex]
Therefore, the volume of the composite solid is:
[tex]\begin{aligned}\implies \sf Volume\:of\:composite\:solid & = \sf Cylinder\:volume+Cone\:volume\\ & = \sf 250\pi + \dfrac{100}{3}\pi \\ & = \sf \dfrac{850}{3} \pi \\ & = \sf \dfrac{850}{3} \times 3.14 \\ & = \sf 889.67\:m^3\:(2\:d.p.)\end{aligned}[/tex]
find each lettered angle
Answer:
a = 103°
b = 103°
c = 97°
d = 83°
e = 154°
Maritza desea ir de viaje con su familia, que está conformada por ella, su esposo y sus 3 hijos. Ella comprará pasajes cuyo costo es de S/75 por persona (sólo ida), también desea comprar un paquete turístico para cuatro personas cuyo valor es de S/800, además contrató 3 habitaciones por el precio de S/60 cada una. También se proyectó gastar en alimentación 150 diarios y una bolsa de viaje de S/130 por persona. Si su viaje es de 5 días y 4 noches y actualmente ella cuenta con S/1000 y su esposo con S/1800, ¿Cuánto dinero les falta para cubrir todos los gastos de su viaje?
El dinero que le falta a Maritza y su esposo para viajar es 330.
¿Cuánto dinero les falta?Para calcular el dinero que les falta debemos identificar la cifra total que les va a costar el viaje:
75 x 10 = 75080060 x 3 = 180 150 x 5 = 750130 x 5 = 650750 + 800 + 180 + 750 + 650 = 3,130El valor total del viaje es s/3,130, entonces les faltarían s/330.
3,130 - 2,800 = 330
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a using the strategy to determine the area of the large rectangle
b explain how this strategy relates to the binomial multiplication
c focused on multiplying two binomials, explain a strategy that can be used to multiply any two polynomials
The area of the large rectangle by using the strategy is; 168cm².
What is the area of tge large rectangle?The area of the rectangle can be determined by multiplying the length and width of the rectangle as follows;
Area = Length × width
Area = (10cm + 4cm) × (10cm × 2cm)
Area = (100+20+40+8)cm²
Area = 168 cm².
The strategy used above entails that the two binomials used to represent the length and width of the rectangle are multiplied according to binomial multiplication.
The strategy is that each term of the first binomials is used to multiply the terms in the second polynomial and the aggregate result of the multiplications is determined.
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Find the area of the region that lies inside both curves.
r² = 2 sin(2θ), r=1
The area of the region that lies inside both curves r² = 2sin(2θ), r = 1 is -0.1287 square units.
How to find the area of the region that lies inside both curves?Since the curves are
r² = 2sin(2θ) and r = 1.We find their point of intersection.
So, r² = r²
2sin(2θ) = 1²
2sin(2θ) = 1
sin(2θ) = 1/2
2θ = sin⁻¹(1/2)
2θ = π/6
θ = π/12
So, we integrate the area from θ = 0 to θ = π/12
Now the area A of the region between two curves between θ = α to θ = β is
[tex]A = \int\limits^{\beta }_\alpha ({r^{2} - r^{'2} }) \, d\theta[/tex]
So, the area betwwen the curves r² = 2sin(2θ), r = 1 between θ = 0 to θ = π/12 is
[tex]A = \int\limits^{\frac{\pi}{12} }_0 ({r^{2} - r^{'2} }) \, d\theta \\= \int\limits^{\frac{\pi}{12} }_0 ({2sin2\theta - 1^{2} }) \, d\theta\\= \int\limits^{\frac{\pi}{12} }_0 ({2sin2\theta - 1}) \, d\theta\\= \int\limits^{\frac{\pi}{12} }_0 {2sin2\theta}\, d\theta - \int\limits^{\frac{\pi}{12} }_0 {1} \, d\theta\\= [2(-cos2\theta)/2 - \theta]_{0}^{\frac{\pi}{12} } \\= [-cos2\theta - \theta]_{0}^{\frac{\pi}{12} } \\= -cos2\frac{\pi}{12} - \frac{\pi}{12} - ( -cos2(0) - 0)\\[/tex]
[tex]= -cos2(\frac{\pi}{12}) - \frac{\pi}{12} - ( -cos2(0) - 0)\\= -cos\frac{\pi}{6}- \frac{\pi}{12} - ( -cos0 - 0)\\= -cos\frac{\pi}{6}- \frac{\pi}{12} - ( -1)\\= -(\frac{\sqrt{3} }{2} ) - \frac{\pi}{12} + 1\\= -0.8660 - 0.2618 + 1\\= -1.1278 + 1\\= -0.1278[/tex]
So, the area of the region that lies inside both curves r² = 2sin(2θ), r = 1 is -0.1287 square units.
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need help with this
Answer:
[tex]x^4-20x^3 +175x^2 -750x+1250[/tex]
Step-by-step explanation:
By the conjugate root theorem, 5+5i is also a root.
[tex]f(x)=a(x-5)^2 (x-5-5i)(x-5+5i) \\ \\
= a(x^2 - 10x+25)((x-5)^2 - (5i)^2) \\ \\
= a(x^2 - 10x+25)(x^2 - 10x+25+25) \\ \\
= a(x^2-10x+25)(x^2-10x+50) \\ \\
= a(x^4- 10x^3 + 50x^2 - 10x^3 + 100x^2 - 500x + 25x^2 - 250x+1250) \\ \\
= a(x^4-20x^3 +175x^2 -750x+1250) \\ \\ [/tex]
Calculate a and b if
[tex] \sqrt{ \frac{ {7}^{2014} - {7}^{2012} }{12} } = a( {7}^{b} )[/tex]
and a is not a multiple of 7.
Notice that
[tex]7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}[/tex]
[tex]12=2^2\times3[/tex], so
[tex]\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}[/tex]
Then taking the positive square root gives
[tex]\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}[/tex]
so [tex]\boxed{a=2}[/tex] and [tex]\boxed{b=1006}[/tex].
PLSSSSSSSSSSSSSSS HELP pls
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: 10x + 30 = 90[/tex]
[ according to given figure ]
[tex]\qquad \sf \dashrightarrow \: 10x = 90 - 30[/tex]
[tex]\qquad \sf \dashrightarrow \: 10x = 60[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 60 \div 10[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 6 \degree[/tex]
Correct choice is D
A(4,3) B(1/2, 1/5) C( 3/4, 7/4). Which point lies on the circumstance of the unit circle?
None of the three points (A, B, C) lies on the circumference of the unit circle.
What point is in the circumference of an unit circle?
Unit circles are circles centered at the origin and with a radius of 1. A point is on the circumference if and only if the distance of the point respect to the origin is equal to 1. The distance of each point is determine by Pythagorean theorem:
Point A
[tex]d = \sqrt{4^{2}+3^{2}}[/tex]
d = 5
Point B
[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{1}{5}\right)^{2} }[/tex]
d = √29 /10
d ≈ 0.539
Point C
[tex]d = \sqrt{\left(\frac{3}{4} \right)^{2}+\left(\frac{7}{4} \right)^{2}}[/tex]
d = √58 /4
d ≈ 1.904
None of the three points (A, B, C) lies on the circumference of the unit circle.
RemarkThe statement presents a typing mistake, correct form is shown below:
A(x, y) = (4, 3), B(x, y) = (1/2, 1/5), C(x, y) = (3/4, 7/4). Which point lies on the circumference of the unit circle?
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What is the answer to this system of equations? 2x - 3y= 21 and -6x + 2y = 7.
answer:
x = - 9/2
y = -10
Step-by-step explanation:
make both equations look like y =
2x-3y=21 -> -3y= -2x+21 -> y = (-2x+21)/-3 -> y = 2/3x - 7
-6x + 2y = 7 -> 2y = 6x + 7 -> y = 3x + 7/2
now make the equations equal to each other (since they both equal y)
get x
2/3x - 7 = 3x + 7/2
-7 -7/2 = 3x - 2/3x
-14/2 -7/2 = 9/3x - 2/3x
-21/2 = 7/3x
(3/7) -21/2 = x
x = (3/7) -21/2
x = - 63/14
x = - 9/2
put it back in an equation to get y
y = 3x + 7/2
y = 3(-9/2) + 7/2
y = -27/2 + 7/2
y = -20/2
y = - 10
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f(x)=√x+11. Find the inverse of f(x).
Answer:
f(x)⁻¹ = (x - 11)²
Step-by-step explanation:
To find the inverse of the function, you need to (1) swap the places of the "x" and "y" variables and then (2) solve for "y". Remember, f(x) is another way of writing "y".
y = √x + 11 <----- Original equation
x = √y + 11 <----- Swap variables
x - 11 = √y <----- Subtract 11 from both sides
(x - 11)² = (√y)² <----- Square both sides
(x - 11)² = y <----- Simplify
Another way of writing the output of an inverse function is with f(x)⁻¹.
What is the product?
The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4
How to determine the product?The expression is given as:
(6x - 2)(6 x + 2).
The above expression is a difference of two squares.
And this is represented as
(a - b)(a + b)= a^2 - b^2
So, we have
(6x - 2)(6 x + 2) = (6x)^2 - 2^2
Evaluate
(6x - 2)(6 x + 2) = 36x^2 - 4
Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4
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Complete question
What is the product?
(6x - 2)(6 x + 2).
Mark and paula are storing masks. Paula has 70% of the total number of masks. If paula has 840 more masks thatn mark, how many masks should paula give to mark si they both have an equal number of masks
Answer:
1050 masks per person.
Step-by-step explanation:
1) Create an equation to find the total number of masks
2) Solve equation and divide total by 2 to get the number of masks that can be given to both Mark and Paula so that they have equal number.
1) Since Paula has 70% of the total masks, it can be represented as 0.7 * t where t is the variable representing the total number of masks. Mark on the other hand has the remaining number of masks out of 100% which is 30%. We can express that as 0.3. We multiply that by t because he has 30% of the masks. The final equation we have is 0.3t + 840 = 0.7t. 840 because Paula has 840 more masks than Mark.
2) Solve by subtracting 0.3t from both sides leaving you with 0.4t = 840. We divide both sides by 0.4 to get 2100. That is the total number of masks. If we divide that number by 2, we get 1050.
g(r) = -20 +11r
8(11) = ?
Answer:
g(11) = 101
Step-by-step explanation:
g(r) = -20 + 11r
So in g(11), we just need to replace 'r' with '11'
g(11) = -20 + 11 (11)
--> g(11) = -20 + 121 = 101
--> g(11) = 101
Please comment down below if 8(11) wasn't a typo. I thought it was, so I replaced 8 with g. If that was intentional, I'll edit my answer as soon as possible.
The circumference of a circle is 13π in. What is the area, in square inches? Express your answer in terms of \piπ.
The area of the circle with the given circumference is: 42.25π in.².
What is the Area and Circumference of a Circle?Area = πr²
Circumference = 2πr.
Given the following:
Circumference of the circle = 13π in.
Find the radius (r):
2πr = 13π
Divide both sides by 2π
2πr/2π = 13π/2π
r = 13/2
r = 6.5
Area = πr² = π(6.5²) = 42.25π in.²
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Aaron wants to make All-Tournament Team for his high school
basketball team. He needs to average at least 24 points a game
to get selected for All-Tournament Team. They are playing 4
games, in the first 3 games he scored 30, 17, and 25 points.
Answer:24
Step-by-step explanation:
Answer:
Step-by-step explanation:
Rectangle MNPQ is rotated using the origin as the center of rotation, resulting in rectangle M’N’P’Q’, as shown below.
On a coordinate plane, rectangle M N P Q has points (negative 2, 6), (0, 4), (negative 3, 1), (negative 5, 3). Rectangle M prime N prime P prime Q prime has points (6, 2), (4, 0), (1, 3), (3, 5).
Which rotation may have occurred?
a 45° rotation clockwise
a 45° rotation counterclockwise
a 90° rotation clockwise
a 90° rotation counterclockwise
Answer:
45° rotation clockwise
Step-by-step explanation:
When you plot these on the graph, the non prime ones are on quadrant 2 and when you plot the prime ones, it is on quadrant 1. This means that it is 45° to the right(clockwise)
⬇️red is prime blue is regular ⬇️
A focus group study has always been the primary way for ABC Toys Company to gather customers' opinions for marketing strategy. In the past, when a new product was popular in the market, a focus group study had incorrectly indicated that it would be unpopular with a probability of 0.275. When a new product was unpopular, a focus group had incorrectly indicated that it would be popular with a probability of 0.175. Assume that the probability of a new product being popular in the market is 0.60. What is the probability that a new product will be unpopular if a focus group study indicates that it will be unpopular?
Using conditional probability, there is a 0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.For this problem, the events are given as follows:
Event A: Study indicates that the product is unpopular.Event B: Product is unpopular.The parameters are given as follows:
P(A) = 0.6 x 0.275 + 0.4 x 0.825 = 0.495.[tex]P(A \cap B) = 0.4 \times 0.825 = 0.33[/tex]Hence the conditional probability is:
[tex]P(B|A) = \frac{0.33}{0.495} = 0.6667[/tex]
0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.
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Given b(x)=|x+41|, what is b(-10)?
Answer:
31
Step-by-step explanation:
Substitute -10 for x in b(x)=|x+41|, obtaining f(-10) = |-10 + 41|. This result simplifies to f(-10) = |31| = 31
graph
Y=-2x-3 and y=-x+6
Answer:
here ya go :)
the black line is y=-2x-3
the lavender line is y=-x+6
Which equation is represented by the graph below?
A y=In x-3
B y=In x-4
C y=e^3 -3
D y=e^3 -4
Answer:
D
Step-by-step explanation:
I assume that for C and D, you meant e^x.
Since the function is defined at 0, eliminate A and B (since ln 0 is undefined)
Between C and D, we know that when x=0, e^x = 1. Since the y intercept of the graph is -3, this means the equation is y = e^x - 4.
Find the value of variable X.
16
41
10
17.5
Using secant rule, the value of variable x in the diagram is 10.
What is a secant?A secant is a line that intersect a circle in two points.
Therefore, the following rule guides a secant.
(x + 32)32 = (20 + 28)28
Hence,
32x + 1024 = (48)28
32x + 1024 = 1344
32x = 1344 - 1024
32x = 320
divide both sides by 32
32x / 32 = 320 / 32
x = 10
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What is the difference between 89.4 and 13.621 do not round your answer
Answer:
89.4 - 13.621 = 75.779
Explanation:
Subtract 13.621 from 89.4 to get 75.779.
.
A new refrigerator that normally sells for $897.00 is on sale for 15% off. If the sales tax is 7.5%, then how much will you pay in total for the refrigerator while it’s on sale?
Answer: About 830 dollars
Step-by-step explanation: find 15% off on 897 then find 7.5 percent of 897, then add them together.