Step-by-step explanation:
Hello there!
Here is the solution to our problem:
To begin with, we give our equations labels as below;
3m − n = 2 ...................eq.1
2m + n = − 7 ..................eq.2
Then, Let's manipulate eq.2
2m + n = − 7
n = -7 - 2m ...............eq3
And finally substitute the manipulated eq.3 into eq.1
3m − n = 2
3m − (-7 - 2m) = 2
3m + 7 + 2m = 2
5m = -5
m = -1
Substitute the value of m into eq.3
n = -7 - 2(-1)
= -5
In terms of x and y;
(x,y) : (m, n) => (-1, -5)
Therefore (m, n) = (-1, -5)
I hope this helps.
Have a nice studies.
please please help me I'll give whaever
answer:
1769.344983 or 1769.34 (depends on what you’re rounding to)
explanation:
- the equation for a cylinder‘s surface area is: (2 π r h)+(2 π r^2)
so 2 just means x2
π is just pi
r is your radius and for this equation your radius is 8 cm
and h is your height so for this equation your height is 27.2 cm
- so the equation filled in is:
(2 x π x 8 x 27.2) + (2 x π8^2) = 1769.344983 or 1769.34
(2 x π x 8 x 27.2) = 1367.221123
(2 x π8^2) = 402.1238597
1367.221123 + 402.1238597 = 1769.344983
hope this helps :)
solve for b
−9b)+b=2b−(b+1)
Answer:
[tex]b = \frac{1}{9}[/tex]
Step-by-step explanation:
-9b + b = 2b - (b + 1)
Let's simplify by taking out the parenthesis.
-9b + b = 2b - b - 1
Now, we add like terms.
-8b = b - 1
Now, let's subtract b from both sides of the equal sign in order to isolate b.
-8b - b = b - 1 - b
Simplify!
-9b = -1
Divide both sides by -9.
-9b ÷ b = -1 ÷ -9
Simplify.
[tex]b = \frac{1}{9}[/tex]
Answer:
[tex]b = \frac{1}{9} [/tex]
Step-by-step explanation:
[tex] - 9b + b = 2b - (b + 1) [/tex]
Solve the brackets.
[tex] - 9b + b = 2b - b - 1[/tex]
Combine like terms.
[tex] - 8b = b - 1[/tex]
Take b to the left side.
[tex] - 8b - b = - 1[/tex]
Combine like terms.
[tex] - 9b = - 1[/tex]
Divide both sides by -9.
[tex] \frac{ - 9b}{ - 9} = \frac{ - 1}{ - 9} \\ b = \frac{1}{9} [/tex]
help please? 50 points if correct
Answer:
15400 in² :)))!
Step-by-step explanation:
Input Data:
Radius = 70 in
Objective:
Find the area of the circle.
Solution:
Area = πr2
= 3.14 x (70) ^2
= 3.14 x (4900)
Area = 15400 in²
Explain why the "+ C" is not needed in the antiderivative when evaluating a definite integral.
The reason the "+ C" is not needed in the antiderivative when evaluating a definite integral is; The C's cancel each other out as desired.
How to represent Integrals?
Let us say we want to estimate the definite integral;
I = [tex]\int\limits^a_b {f'(x)} \, dx[/tex]
Now, for any C, f(x) + C is an antiderivative of f′(x).
From fundamental theorem of Calculus, we can say that;
[tex]I = \int\limits^a_b {f'(x)} \, dx = \phi(a) - \phi(b)[/tex]
where Ф(x) is any antiderivative of f'(x). Thus, Ф(x) = f(x) + C would not work because the C's will cancel each other.
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Write the prime for factorization of 4
Answer:
2×2 mark me brainlist
4divided by 22×2Write these ratios in their simplest form. You must show all your workings:
a. 2 litres:600ml
b.8h:1day
c.3km:250m
The simplest form of the given ratios are : 10:3 , 1:3 , and 12:1
What is Ratio?A ratio indicates how many times one number contains another.
Here, for given ratio
2 litres : 600 ml = 2000 ml : 600 ml
= 20 : 6
= 10 : 3
8 h : 1 day = 8 hrs : 24 hrs
= 8:24
= 1 : 3
3 km : 250 m = 3000 m : 250 m
= 3000 : 250
= 300 : 25
= 12 : 1
Thus, the simplest form of the given ratios are : 10:3 , 1:3 , and 12:1.
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It takes Kenesha 45 minutes to prepare 20 greeting cards. It takes Paula 30 minutes to prepare the same number of cards. Working together at this rate, how long will it take them to prepare the cards?
Using the together rate, it is found that it will take them 18 minutes to prepare the cards working together.
What is the together rate?The together rate is the sum of each separate rate.
In this problem:
The together rate is of 1/x.Kenesha's rate is of 1/45.Paula's rate is of 1/30.Hence, the time it will take for them to make the cards is given by:
[tex]\frac{1}{x} = \frac{1}{45} + \frac{1}{30}[/tex]
[tex]\frac{1}{x} = \frac{5}{90}[/tex]
5x = 90
x = 18 minutes.
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maria has 2 5/6 yard of fabric Jessica has 3 1/6 yards of fabric how much do they have altogether
Answer:
Step-by-step explanation:
find the 44th term in the following arithmetic sequence
2,3,4,5,....
Answer:
the answer is 45
Step-by-step explanation:
the answer is 384
Step-by-step explanation:
a1 = 2, a2 = 3, a3 = 4,
an = ?
n = 44
d = a2 - a1 = 3 - 2 = 1
d = a3 - a2 = 4 - 3 = 1
Here, the common difference is the same everywhere
So,
[tex] a_{n} = a + (n - 1) \times d[/tex]
[tex]a_{44} = 2 + (44 - 1) \times 1[/tex]
[tex]a_{44} = 2 + 43[/tex]
[tex]a_{44} = 45[/tex]
The Niagara Falls ferris wheel has a diameter of 48 meters, and one revolution takes 2.25 minutes to complete. Riders can see Niagara falls if they are higher than 41 meters above the ground. What are the time intervals when the rider can see Niagara Falls if they complete 3 complete revolutions, if the rider gets on at a height of 0.5 m at t=0 min?
The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)
How to interpret Cycle Graphs?
From the diagram attached, we can say that;
Period = 2π/k
where;
k = 2π/2.25
k = 8π/9
Thus;
h(t) = -(48/2) cos (8π/9)t + ((48/2) + 0.5)
h(t) = -24cos (8π/9)t + 24.5
Riders can see Niagara falls if they are higher than 41 meters above the ground. Thus;
41 = -24cos (8π/9)t + 24.5
41 - 24.5 = -24cos (8π/9)t
16.5 = -24cos (8π/9)t
-0.6875 = cos (8π/9)t
cos⁻¹0.6875 = (8π/9)t
t = 0.834 min
Thus, time interval is between;
0.834 < t < (2.25 - 0.834)
⇒ 0.834 < t < 1.416 and
(2.25 + 0.834) < t < (2.25 + 1.416)
⇒ (3.084, 3.666)
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convert the following equation into standard form y=-5x/8 + 3
12 to 30 Express as a fraction in the lowest terms?
Answer:
2/5
Step-by-step explanation:
Someone, please help!! if u actually know how to do it
Answer:
[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]
distance = 16.2788
Step-by-step explanation:
This question is asking you to correctly apply the distance formula. This formula determines the straight line distance between two points by applying Pythagorean's Theorem ([tex]h = \sqrt{x^{2}+y^{2} }[/tex]). The distance formula can be thought of as [tex]distance=\sqrt{(x_{1}-x_{2})^{2} +(y_{1}-y_{2})^{2}}[/tex]. It doesn't matter which order you put your coordinates into the equation as long as it's the square root of the change in x-coordinates squared + change in y-coordinates squared.
Step 1: change in x-coordinates
x1 = -2
x2 = -5
x1 - x2 = -2 - (-5) = 3
Step 2: change in y-coordinates
y1 = 6
y2 = -10
y1 - y2 = 6 - (-10) = 16
Step 3: plug into distance formula
[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]
[tex]distance=\sqrt{(3)^{2} +(16)^{2}}[/tex]
[tex]distance=\sqrt{9 +256}[/tex]
[tex]distance=\sqrt{265}[/tex]
distance = 16.2788
A number multiplied by third of itself makes the product 10584, what is the number ?
Answer:
-15876
Step-by-step explanation:
|correct me if I'm not correct|
(Hope it's Help)
[keep safe]
The number is 15876
What is Number system?Number systems are systems in mathematics that are used to express numbers in various forms and are understood by computers. A number is a mathematical value used for counting and measuring objects, and for performing arithmetic calculations. Numbers have various categories like natural numbers, whole numbers, rational and irrational numbers, and so on. Similarly, there are various types of number systems that have different properties, like the binary number system, the octal number system, the decimal number system, and the hexadecimal number system.
What are Number Systems?A number system is a system representing numbers. It is also called the system of numeration and it defines a set of values to represent a quantity. These numbers are used as digits and the most common ones are 0 and 1, that are used to represent binary numbers. Digits from 0 to 9 are used to represent other types of number systems.
Given number:
10584
So, the number multiplied by the third of itself
x* 2/3 = 10584
x= 10584* 3/2
x= 15876
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The regular price of a CN Tower Souvenir was $32, During its sale, The price was reduced down by $24, Find the percent discount
Answer:
Discount of 25%
Step-by-step explanation:
To find the percent discount, subtract the big number minus small number then divide by the original number.
[tex]\frac{32-24}{32}[/tex]
[tex]\frac{8}{32} \\[/tex]
Reduce
[tex]\frac{1}{4}[/tex]
Change to a decimal by dividing
1/4 = 0.25
Change to a percent by moving the decimal two places right.
0.25 -----> 25%
A tower that is 125 feet tall casts a shadow 173 feet long find the angle of elevation of the sun to the nearest degree
Applying the tangent ratio, the angle of elevation of the sun, to the nearest degree, is: 36°.
What is the Tangent Ratio?In a right triangle, tan ∅ = opposite length / adjacent length is the tangent ratio.
Given the following:
Angle of elevation = ∅ Opposite length = 125 ftAdjacent length = 172 ftApply the tangent ratio:
tan ∅ = 125/172
tan ∅ = 125/172
∅ = tan^(-1)(125/172)
∅ ≈ 36°
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what's the answer to this
Answer:
AC ≈ 17.3 , BC ≈ 5.3
Step-by-step explanation:
using the tangent ratio in right triangle ACD
tan51° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AD}[/tex] = [tex]\frac{AC}{14}[/tex] ( multiply both sides by 14 )
14 × tan51° = AC , then
AC ≈ 17.3 ( to the nearest tenth )
using the cosine ratio in right triangle ABC
cos72° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{17.3}[/tex] ( multiply both sides by 17.3 )
17.3 × cos72° = BC , then
BC ≈ 5.3 ( to the nearest tenth )
Buying rental property is an investment option that carries a higher risk than some other options. However, the returns can be good. Assume you have purchased a single-
family home that you intend to rent for $850 per month. You will have the following expenses:
Monthly mortgage $390
Monthly insurance $70
Semi annual property taxes $380
Repairs (yearly estimate) $500
Monthly lawn care or snow removal $125
The total yearly expenses for the rental property will be_____.00.
Based on the expenses involved in running the property, and the rental amount, the return on the investment would be 18.82%.
What is the return on investment?The ratio of net income to investment is known as return on investment (ROI). A high return on investment (ROI) indicates that the investment's benefits outweigh its cost.
ROI is a performance indicator that is used to assess an investment's effectiveness or to compare the efficiencies of several distinct investments.
First, find the amount earned per year:
= 850 x 12
= $10,200
The yearly expenses would be:
= (390 x 12) + (70 x 12) + (380 x 2) + 500 + (125 x 12)
= 4,680 + 840+ 760+ 500 + 1500
= $8280
The annual ROI is:
ROI= (10,200 - 8280) / 10,200 x 100%
ROI = 18.82%
Therefore the expenses involved in running the property, and the rental amount, the return on the investment would be 18.82%.
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27 As shown in the diagram below, secants PWR and PTS are drawn to circle O from external point P.
12/
O.
W
T
P5
If m/RPS = 35°and mRS = 121°, determine and state mWT.
By applying the Theorem of Intersecting Secant, the measure of angle WT is equal to 51°.
How to determine angle m<WT?By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the Theorem of Intersecting Secants.
What is the Theorem of Intersecting Secants?The Theorem of Intersecting Secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the Theorem of Intersecting Secant, angle P will be given by this formula:
m<P = ½ × (m<RS - m<WT)
Substituting the given parameters into the formula, we have;
35 = ½ × (121 - m<WT)
70 = 121 - m<WT
m<WT = 121 - 70
m<WT = 51°.
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the zeros of the function f(x) = x² + 5x - 6 are show your work
Answer:
x = - 6 , x = 1
Step-by-step explanation:
to find the zeros let f(x) = 0 , that is
x² + 5x - 6 = 0
consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term ( + 5)
the factors are + 6 and - 1 , since
6 × - 1 = - 6 and 6 - 1 = + 5 , then
(x + 6)(x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 1 = 0 ⇒ x = 1
write 25.59 in scientific notation
Answer:
2.559 × 10 to the 1st power
Step-by-step explanation:
using a SNC
Answer:
2.559 * 10^1
Step-by-step explanation:
Rules of scientific notation (that I always remember)
- the number must be between 1 and 9
- if number gets smaller, exponent gets bigger; if number gets bigger, exponents gets smaller
25.59 is bigger than 9 so we move the decimal one place value to the left
and the number gets smaller meaning the exponent increases
Find x to the equation
please help 35 points!!
Answer:
67m²
Step-by-step explanation:
12m + 6m + 4m + 36 m 8m = 67m²
Which algebraic expression is equivalent to the expression below?
3(5x + 7)-6(4- 2x)
3(5x+7)-6(4-2x) - given
15x+21-24+12x - distributive property
27x-3 - combine like terms
A total of 388 tickets were sold for the school play they were either adult tickets or student tickets the number of student tickets sold was three times the number of adult tickets sold how many adult tickets were sold
Answer:
97
Step-by-step explanation:
Number of adult tickets = a.
Number of student tickets = s.
"A total of 388 tickets were sold"
a + s = 388
"the number of student tickets sold was three times the number of adult tickets sold"
s = 3a
a + s = 388
s = 3a
Substitute s in the first equation with 3a.
a + 3a = 388
4a = 388
a = 97
Answer: 97 tickets
in a class there are 8 students who play football and cricket, 4 students who do not play football or cricket,14 students who play football and 20 students who play cricket
find the probability that a student chosen at random plays football or cricket or both
The probability to that the student chosen plays football or cricket or both is;
What is the probability that the chosen student play at least one of football and cricket?To evaluate the required probability, one must determine the total number of students in the class as follows;
Total number of students = 4 + 8 + (14-8) + (20-8) = 30.
Hence, the required probability is; (30-4)/30 = 26/30 = 13/15.
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1 + 3 + 5 + A+9 divide by 5
Answer:
1 + 3 + 5 + A+9 divide by 5
Step-by-step explanation:
A prism has three times the volume of a pyramid with the same base and altitude.
O
A. True
O
B. False
Answer:
I believe it's true. Good Luck! :)
Step-by-step explanation:
Triangles 3 and 4 are identical. They are joined in the poster to form a square. Construct a math argument to show why triangles 3 and 4 are isosceles right angles.
Triangles 3 and 4 are isosceles right angles because they have same length.
How to explain the triangle?It should be noted be noted that the square has all right angles equal. The largest angle of the triangle is the right angle m.
Here, the triangles are isosceles right angles as both the legs and the acute angles are congruent.
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Please solve (21 points)
Answer:
he width of the ravin is 47