Solve, using the substitution method.

3m − n = 2

2m + n = − 7


(−1, −5)


(–10, –1)


(–2, –5)


(−5, 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]

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

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

Answer:

-15876

Step-by-step explanation:

|correct me if I'm not correct|

(Hope it's Help)

[keep safe]

The number is 15876

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.

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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Answer:

1 + 3 + 5 + A+9 divide by 5​

Step-by-step explanation:

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%

Answer:

he width of the ravin is 47

Using the together rate, it is found that it will take them 18 minutes to prepare the cards working together.

The together rate is the sum of each separate rate.

In this problem:

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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By applying the Theorem of Intersecting Secant, the measure of angle WT is equal to 51°.

By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey 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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Answer:

I believe it's true. Good Luck! :)

Step-by-step explanation:

Applying the tangent ratio, the angle of elevation of the sun, to the nearest degree, is: 36°.

In a right triangle, tan ∅ = opposite length / adjacent length is the tangent ratio.

Given the following:

Apply the tangent ratio:

tan ∅ = 125/172

tan ∅ = 125/172

∅ = tan^(-1)(125/172)

∅ ≈ 36°

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3(5x+7)-6(4-2x) - given

15x+21-24+12x - distributive property

27x-3 - combine like terms

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

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

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 reason the "+ C" is not needed in the antiderivative when evaluating a definite integral is; The C's cancel each other out as desired.

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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Answer:

Step-by-step explanation:

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 :)

Based on the expenses involved in running the property, and the rental amount, the return on the investment would be 18.82%.

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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The simplest form of the given ratios are : 10:3 , 1:3 , and 12:1

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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The probability to that the student chosen plays football or cricket or both is;

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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The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)

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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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 )

Triangles 3 and 4 are isosceles right angles because they have same length.

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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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

Answer:

2×2 mark me brainlist

Answer:

67m²

Step-by-step explanation:

12m + 6m + 4m + 36 m 8m = 67m²

Answer:

2/5

Step-by-step explanation: