Which of the following expressions represents the statement below?

four added to seven times a number

A.
7(n + 4)
B.
7n + 4
C.
4n + 7
D.
4(n + 7)

Answer:

To locate the number 8 and its opposite on the number line, we can use the given number line:

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Number 8 is located to the right of zero. Its opposite can be found by moving an equal distance to the left of zero. Since the number line is symmetric about zero, the opposite of 8 would be -8.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑ ↑

So, the opposite of 8 is -8. They are related to zero as equal distances on opposite sides of zero on the number line.

Now, let's address exercises 2-3:

a. To locate the opposite of 9, we need to move an equal distance to the left of zero. The opposite of 9 is -9.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑

b. To locate the opposite of -2, we need to move an equal distance to the right of zero. The opposite of -2 is 2.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑

c. To locate the opposite of 4, we need to move an equal distance to the left of zero. The opposite of 4 is -4.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑

So, the opposites of the given numbers are:

9 → -9

-2 → 2

4 → -4

They are related to zero as equal distances on opposite sides of zero on the number line.

Step-by-step explanation:

Answer: D

Step-by-step explanation: You just have to substitute the numbers for the variable in each equation till you get the right one. Sorry, but I don't remember the formula for it.

Answer:

7 1/3

Step-by-step explanation:

1 2/3 - ( -5 2/3)

Subtracting a negative is like adding

1 2/3 + 5 2/3

6 4/3

Simplify the fraction

6 3/3 + 1/3

7 1/3

1 ²/3 – (– 5 ²/3= 7 ⅓

- + - = +

(negative plus negative, equals = plus)

+ (+) + = -

(plus, plus plus, equals= negative

- (+) + = -

(negative plus, plus equals= negative

hope it helps pa brainliest pls pa follow nadin tysm

Answer: -2x

Step-by-step explanation:

i'm pretty sure that's right ;)

Answer:

170, 171, 172

Step-by-step explanation:

x + x + 1 + x + 2 = 513

3x + 3 = 513

3x = 510

x = 170

x + 1 = 171

x + 2 = 172

Answer:

A

Step-by-step explanation:

i got it right on the exam

Answer:

blah

Step-by-step explanation:

blah + blah = blah

blah x blah = blah

blah / blah = blah

blah - blah = blah

Answer:

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

Step-by-step explanation:

r = rate of boat (speed of boat)

t = time

d = distance.

c = rate of current (speed of current)

with the current, the formula becomes (r + c) * t = d

against the current, the formula becomes (r - c) * t = d

going with the current, the boat takes 1 hour to travel 12 miles.

therefore:

(r + c) * t = d becomes (r + c) * 1 = 12

going against the current, the boat takes 1.5 hour to travel the same 12 miles.

therefore:

(r - c) * t = d becomes (r - c) * 1.5 = 12.

your two equations that need to be solved simultancously are:

(r + c) * 1 = 12

(r - c) * 1.5 = 12

divide both sides of the second equation by 1.5 and leave the first equaion as is to get:

r + c = 12

r - c = 8

add the equations together to get:

2 * r = 20

solve for r to get:

r = 20 / 2 = 10

(r + c) * 1 = 12 becomes (10 + c) * 1 = 12

simplify to get 10 + c = 12

solve for c to get c = 12 - 10 = 2

(r - c) * 1 = 8 becomes (10 - c) * 1 = 8

simplify to get 10 - c = 8

solve for c to get c = 10 - 8 = 2

you have:

r = 10

c = 2

that's your solution.

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

The expression is simplified to r²( r + 1) - (q - s²)

Algebraic expressions are mathematical expressions made up of variables and constants.

They are mostly made up of algebraic operations such as addition, subtraction, division, multiplication, bracket, parenthesis, etc

Given the expression;

r3 – [q + (r – s)2 ]

With the knowledge of BODMAS, we expand the bracket

r³ - q + ( r + s²)

r³ - q + r² - s²

Now, let's collect like terms

r³ + r² - q - s²

(r³ + r²) - (q - s²)

Factor out r, we then have;

r²( r + 1) - (q - s²)

The expression is simplified to r²( r + 1) - (q - s²)

Thus, the expression is simplified to r²( r + 1) - (q - s²)

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Answer:

Step-by-step explanation:

At least two sides have the same length.

At least two angles have the same measure.

The base angles (angles opposite the equal sides) have the same measure.

The altitude (perpendicular segment from the base to the vertex) bisects the base and the corresponding base angle.

The median (segment connecting the vertex to the midpoint of the base) is also an altitude, angle bisector, and perpendicular bisector of the base.

Based on these characteristics, the properties that belong to all isosceles triangles are:

At least two sides have the same length.

At least two angles have the same measure.

The base angles have the same measure.

Therefore, the correct options are:

At least two sides have the same length.

At least two angles have the same measure.

The base angles have the same measure.

Answer:

14.387

Step-by-step explanation:

Answer:

80 %

Step-by-step explanation:

FRACTIONS

X/100 = 25,390/32,000

CROSS MULTIPLICATION

X * 32,000 = 32,000X

25,390*100 = 2,539,000

DIVIDE

2,539,000/32,000 = 32000X/32000- CANCEL

X = 79.34375 % Round - X = 80%

Answer: 19

Step-by-step explanation: Since there is no one middle number we have to find the mean of the two middle numbers. Once you find the mean for 24 and 11 you will see that the answer is 19.

Answer:

The median is the middle number in numerical order.

Numerical order - \(11,12,14,24,27,72\)

There are 6 numbers.

The median is 19.

The value of e from the given equation is -1.78

Linear functions are function that has a leading degree of 1

Given the expression below;

0.75(8+e)=2-1.25e

Expand to have;

0.75(8) + 0.75e = 2-1.25e

6 + 0.75e = 2 - 1.5e

6-2 = -1.5e - 0.75e

4 = -2.25e

e = 4/-2.25

e = -1.78

Hence the value of e from the given equation is -1.78

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One pound of the item will cost 4.74 bill

Step-by-step explanation:

In this problem, we are told that Delia bought 4.5 pounds of fruit

and paid with a toa total bill of 20+5= 25 bill

and also she received a  change of 3.67

this means that the item she bought cost 25-3.67= 21.33bill

now if 4.5 pounds of items cost 21.33 bill

then 1 pound will cost Xbill

cross multiply and solve for Xbill

X= 21.33/4.5

X= 4.74 bill

One pound of the item will cost 4.74 bill

10 . 43 = S - 7.52

S = 17.95

Answer:37

Step-by-step explanation: The unanimous Declaration of the thirteen united States of America, When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security.--Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.

The point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

Given that:

y = total cost

x = miles

We are also given the system of linear equations that models the scenario given as:

y = 0.27x + 27 --> equation 1

y = 0.21x + 45 --> equation 2

To find the value of x, make both equations equal to each other and solve:

0.27x + 27 = 0.21x + 45

Combine like terms

0.27x - 0.21x = -27 + 45

0.06x = 18

Divide both sides by 0.06

0.06x/0.06 = 18/0.06

x = 300

To find the value of y, plug in the value of x into equation 1, and find y:

y = 0.27(300) + 27

y = 81 + 27

y = 108

Thus, the point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

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The amount remaining after 50 years is approximately 45.5% of the Initial amount, A₀.

The given exponential function represents the amount A(t) (in grams) of cesium-137 remaining after t years:

A(t) = A₀ * (1/2)^(t/30)

We are asked to find the initial amount A₀ and the amount remaining after 50 years.

1. Initial amount:

The initial amount, A₀, is the amount of cesium-137 present at t = 0 years. To find A₀, we substitute t = 0 into the equation:

A(0) = A₀ * (1/2)^(0/30)

A(0) = A₀ * 1

Since anything raised to the power of zero is 1, we have A(0) = A₀ * 1, which simplifies to A(0) = A₀.

Therefore, the initial amount of the sample is A₀.

2. Amount after 50 years:

To find the amount remaining after 50 years, we substitute t = 50 into the equation:

A(50) = A₀ * (1/2)^(50/30)

Now we can calculate the amount using the given formula:

A(50) = A₀ * (1/2)^(5/3)

To round the answer to the nearest gram, we evaluate the expression and round the result to the nearest gram:

A(50) = A₀ * 0.455

A(50) ≈ A₀ * 0.455

Therefore, the amount remaining after 50 years is approximately 45.5% of the initial amount, A₀.

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√10 · √6 = √(10 · 6) =

= √60 = √(4 · 15) = √(2² · 15) = 2√15

The distance between point G and H is 4√2 units51.96 unit²

An equation is a expression that shows the relationship between numbers and variables.

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the origin is:

\(AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\)

Let us take point G as out reference point (origin)

Hence:

G = (0, 0) and H = (4, -4)

\(GH=\sqrt{(-4-0)^2+(4-0)^2}=4\sqrt{2}\ units\)

The distance is 4√2 units

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Answer:

7:1

Step-by-step explanation:

217 divided by 31 is 7 so each student would get seven cookies.

Answer:

I am not certain but it's either the last one or second to last my bet is -4<x<4 but you can try I am not certain tho

Answer:2, 7, 7, 6

Step-by-step explanation:

Answer:

1) 8/4 = 2

2) 21/3 = 7

3) 56/8 = 7

4) 48/8 = 6

Step-by-step explanation:

To convert a fraction into a whole number: Divide the numerator by the denominator.

What's a numerator?:

A numerator is the part of a fraction above the line. So, 8 in 8/4 is the numerator.

What's a denominator?:

A denominator is the  bottom number in a fraction. So, 4 in 8/4 is the denominator.

1) 8/4 = 8 divided by 4 = 2.

2) 21/3 = 21 divided by 3 = 7

3)56/ 8 = 56 divided by 8 = 7

4) 48 / 8 = 48 divided by 8 = 6

she could have scored the 10 points in 302400 ways.

The given parameters are

n= total points =10

r1 =one-point free throw = 1

r2 = two-point field goals = 2

r3 =  three-point field goals = 3

The number of ways (k) she could have scored the points is:

k=(n!)/(r1!×r2!×r3!)

The factorial function is a mathematical formula represented by an exclamation mark "!".

k= 10!/(1!×2!×3!)

k= 3628800/(1×2×6)

k= 302400

so.. she could have scored the 10 points in 302400 ways.

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9514 1404 393

Answer:

  (√17 -4√595)/102

Step-by-step explanation:

To use the sine of the angle sum formula, we need to know the sine and cosine of each of the angles.

  sin(sin^-1(1/6)) = 1/6 . . . . a first-quadrant angle

  cos(sin^-1(1/6)) = √(1 -(1/6)²) = √(35/36) = (√35)/6

  sin(tan^-1(-4)) = -4/√(1+(-4)²) = -4/√17 . . . . a 4th-quadrant angle

  cos(tan^-1(-4)) = √(1 -(-4/√17)²) = 1/√17

The sum of angles formula is ...

  sin(α+β) = sin(α)cos(β) +cos(α)sin(β)

So, our sine is ...

  \(\sin\left(\sin^{-1}\left(\dfrac{1}{6}\right)+\tan^{-1}(-4)\right)=\dfrac{1}{6}\cdot\dfrac{1}{\sqrt{17}}+\dfrac{\sqrt{35}}{6}\cdot\dfrac{-4}{\sqrt{17}}\\\\=\dfrac{1-4\sqrt{35}}{6\sqrt{17}}=\boxed{\dfrac{\sqrt{17}-4\sqrt{595}}{102}}\)

Two linear functions that have different slopes will give graphs that intersect at a point known as the solution to the two functions

Part A: The point at which the graphs of the functions intersect is (0.4, 1)

Part B: The solution to the equation f(x) = g(x) is f(x) = g(x) = 1 when x = 0.1

The reason the above values are correct are as follows:

The functions graphed by Juan Carlos are f(x) = 5x - 2, and g(x) = -5·x + 2

Part A:

The point on the graph the functions intersect is given by the point where the values of the function are equal as follows;

At the intersection point, f(x) = g(x), therefore;

At the intersection point, 5x - 2 = -5·x + 2

5x - 2 = -5·x + 2

5x + 5·x = 2 + 2

10·x = 4

\(x = \dfrac{4}{10} = \dfrac{2}{5} = 0.4\)

x = 0.4

The value of the function at the intersection point f(0.4) = 5×0.2 - 2 = 1

f(0.4) = 1

The coordinates of the intersection point on the graph, (f(x), x) is (0.4, 1)

Part B:

The solution of the equation f(x) = g(x) as found above, is given by the x-value at the point of intersection, which is f(x) = g(x) = 1 when x = 0.4

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