Using the image below, find the x value for the point that divides the line segment AB into a ratio of 2:3.

A. -1
B. -0.4
C. 0
D. 0.5

Answer:

x=-3y+12

Step-by-step explanation:

[tex]4-\frac{x}{3}=y[/tex]

You can subtract y from both sides and add (x/3) to both sides to isolate the variable that you're trying to solve.

[tex]-y+4=\frac{x}{3}[/tex]

Multiply both sides by 3

[tex]-3y+12=x[/tex]

The linear expressions are subtracted to:

-2x + 17. Option A

-4x - 2. Option B

 2x + 6. Option B

Algebraic expressions are expressions made up of variables, terms, factors, coefficients, and constants.

They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc.

Given the expression:

A. (4x + 8) - (6x - 9)

expand the bracket

4x + 8 - 6x + 9

collect like terms

-2x + 17

B. (3x - 4) - (7x - 2)

expand the bracket

3x - 4 - 7x + 2

collect like terms

-4x - 2

C. (10x + 2) - (8x - 4)

expand the bracket

10x + 2 - 8x + 4

collect like terms

2x + 6

Thus, the linear expressions are subtracted to -2x + 17, -4x - 2,  2x + 6

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Using probability we can say that the event that Gavin rolls an even number on a number cube is as likely as not.

Probability is the study of chance. The likely chance that an event can occur in a random experiment written as a fraction is called probability.

Probability of a event is calculated as the ratio of the favorable outcomes of an event to all the possible outcomes of the event.

Given as experiment: A number cube is rolled by Gavin.

Event : An even number comes up on the face of the cube.

Favorable outcomes : {2,4,6} = 3 outcomes

Total outcomes or sample space: {1,2,3,4,5,6} = 6 outcomes

Probability that an even number comes up:3/6=1/2

Probability that an even number does not come up=1-1/2=1/2

From the above probabilities we see that :

P(even)=P(not even)=1/2

Hence the Gavin rolls an even number is as likely as not likely.

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Answer:

5

Step-by-step explanation:

[tex]\frac{3^8}{3^3}=3^{8-3}=3^{\boxed{5}}[/tex]

Answer:

3⁸

3³

(since they have the same numbers , you subtract → divide means subtract → law of indices)

Answer = 3⁸ - 3³

= 3⁵

Neptune is 7. 76 × 10^2 times farther than Mercury from the sun. Option B

A ratio can be defined as the comparison of two or more number indicating their sizes in relation to each other.

It also explains how any times a number contains another.

From the information given, we have;

To determine the distance Neptune is from the sum than Mercury, we divide the distance for Neptune by that of Mercury

= 4.5 x 10^10/  5.8 x 10^7

= 776. 86

Turn into scientific notation

= 7. 76 × 10^2

Thus, Neptune is 7. 76 × 10^2 times farther than Mercury from the sun. Option B

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Answer: 70 cats

Step-by-step explanation:

add 2+7 = 9
90/9 = 10
multiply 2x10 = 20 dogs
10x7= 70 cats.

The amount of force on the grain of rice is 23.52 × 10⁻⁵ newtons.

The right format for scientific notation is a × 10ᵇ, where an is an integer or decimal number with an absolute value more than or equal to one and less than ten, or 1 < |a| < 10. For the scientific notation to be mathematically equivalent to the original value, b must be a power of 10.

The Force of a particle is given as:

F = ma, where m is the mass and a is the acceleration.

Now, the mass of a grain of rice is 2.4 × 10⁻⁵ kg.

The acceleration due to gravity is 9.8 m/s².

Therefore, the force on the grain of rice is :

F = ma

F = 2.4 × 10⁻⁵ kg × 9.8 m/s²

F = 23.52 × 10⁻⁵ newtons

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The statement as an inequality expression is 739214 < x < 740000

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The statement is given as

"The number on Riben's ticket has a value between the values 739214 and 740000”

Let the value on the ticket be x

So, the statement can be represented as

"x has a value between the values 739214 and 740000”

"Between" means the values are exclusive

So, the statement can be represented as

739214 < x < 740000

Hence, the statement as an inequality expression is 739214 < x < 740000

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Possible question

Represent the following statement as an inequality

"The number on Riben's ticket has a value between the values 739214 and 740000”

Answer:

The outliers affect the mean, median, and other percentiles

Step-by-step explanation:

Because extreme points are highlighted in a box plot, it is simple to identify data points for further investigation. You may discover that the outliers are errors in your data or that they are unusual for another reason.

Answer:

A

Step-by-step explanation:

The rays that form the angles can extend for infinite length.

Answer:

10742527

Step-by-step explanation:

18+7(n-3)

=======================================================

Explanation:

We can rewrite the right hand side of choice C like so

18+7(n-3)

18+7(n-1-2)

18+7(n-1)+7(-2)

18+7(n-1)-14

4+7(n-1)

Which is now in the form a+d(n-1)

This confirms choice C to be arithmetic. The other choices cannot be written in the format of a+d(n-1). Choices A and B are quadratic sequences while choice D is exponential.

The first few terms of choice C are: 4, 11, 18, 25, 32, ...

To get new terms, add 7 to the previous one.

-------------

Notice how if n = 5 for instance, then,

[tex]a_n = 4+7(n-1)\\\\a_5 = 4+7(5-1)\\\\a_5 = 32\\\\[/tex]

and

[tex]b_n = 18+7(n-3)\\\\b_5 = 18+7(5-3)\\\\b_5 = 32\\\\[/tex]

This confirms that [tex]a_n = b_n[/tex] when n = 5. I'll let you check other positive integer values for n.

Answer:

[tex]\textsf{c)} \quad s_n=18+7(n-3)[/tex]

Step-by-step explanation:

An arithmetic sequence has a constant difference between each term.

General formula of an arithmetic sequence

[tex]\boxed{s_n=a+(n-1)d}[/tex]

where:

When expanded, the formulas for answer options a and b will both contain an n² term, so we can immediately discount them since an arithmetic sequence is linear.

Similarly, we can also discount option d since this formula includes an exponential term and is therefore not linear.

Therefore, the only valid answer is option c.

To confirm, rewrite the formula for c in the general form for an arithmetic sequence:

[tex]\begin{aligned}\implies s_n&=18+7(n-3)\\s_n&=18+7n-21\\s_n&=7n-3\\s_n&=7n-7+4\\s_n&=7(n-1)+4\\s_n&=4+(n-1)7\end{aligned}[/tex]

Therefore, formula that defines an arithmetic sequence is:

[tex]\boxed{s_n=18+7(n-3)}[/tex]

Answer:

[tex]\displaystyle{h = \dfrac{3V}{\pi r^2}}[/tex]

Step-by-step explanation:

Given the equation of:

[tex]\displaystyle{V=\dfrac{1}{3}\pi r^2 h}[/tex]

The equation is also reference to volume of a cone. To solve an equation for h-term, we’ll multiply both sides by 3 first to clear all denominator:

[tex]\displaystyle{V \cdot 3 = \dfrac{1}{3}\pi r^2 h \cdot 3}\\\\\displaystyle{3V = \pi r^2 h}[/tex]

Then divide both sides by [tex]\displaystyle{\pi r^2}[/tex]:

[tex]\displaystyle{\dfrac{3V}{\pi r^2}=\dfrac{\pi r^2 h}{\pi r^2}}\\\\\displaystyle{h = \dfrac{3V}{\pi r^2}}[/tex]

Based on the angles given of 1 and 5, the type of angles that they are is B. Corresponding angles.

Corresponding angles are angles that form as a result of a parallel line, or parallel lines being intersected by transverse lines. As a result, the same angles are created in certain instances.

When the angles given appear in the same position on the different transverse and parallel lines, then they are corresponding.

This means that angles 1 and 5 are corresponding angles because they appear in the same position.

In conclusion, the angles are corresponding.

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Answer:

86-30=56

86-4=82

86-34=52

Step-by-step explanation:

The expression in terms of i  is  mathematically given as

x=√6*i

A complex number is a component of a number system that extends the real numbers by adding a specific element denoted I also known as the imaginary unit, and satisfying the equation i2 = 1;

Every complex number can be expressed in the format a + bi, where a and b are real numbers. In other words, a complex number is a number that contains both real and imaginary components.

Generally, the equation for the expression is  mathematically given as

x=√-6

Where

i=√-1

Therefore

x= √6 *√-1

x=√6*i

In conclusion, The expression in terms of i is

x=√6*i

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Answer: 59

Step-by-step explanation:

Answer:

im assuming D equals miles so id have to say 35

Step-by-step explanation:

Answer:

(a) 9a + 2

(b)  a = 5

Step-by-step explanation:

Perimeter of a triangle = sum of sides

=

2a + 1     +
3a + 2    +
4a  - 1
----------

9a + 2   Answer (a)

If perimeter = 47 , then 9a + 2  =47

Subtract 2 from both sides

==> 9a = 47 -2

9a = 45

a = 45/9

a = 5

Answer:

if there is lettuce, carrots, and broccoli... those are three ingredients.

Step-by-step explanation:

3, because of the amount of ingredients

Answer:

1.2 miles.

Step-by-step explanation:

because her weight is similar to that of a teenaged girl, she wouldn't be able to pedal very hard, or for long periods of time- she doesn't have the stamina for a cross-country ride. Therefore, using various statistics on house location in relation to park location, we can assume that the distance is about 1.2 miles.

Answer:

I think it's -62.3 feet

Step-by-step explanation:

So if a scuba diver is 75 feel below sea level that will be -75 feet and if they go up by 12.7 feet that will be -62.3 feet.

Im not quite sure but I hope this helps

Answer:

$1.62

Step-by-step explanation:

If you divide $2.43 by 3 it's 0.81 and that's the cost of one loaf of bread so multiply that by 2 and you get the cost of two loaves of bread which is $1.62

Starting with the volume of a cube with side length [tex]x[/tex],

[tex]V(x) = x^3[/tex]

differentiate both sides with respect to time [tex]t[/tex]. By the chain rule,

[tex]\dfrac{dV}{dt} = 3x^2 \dfrac{dx}{dt}[/tex]

We're given that [tex]\frac{dx}{dt} = 2\frac{\rm in}{\rm min}[/tex].

39. At the moment [tex]x=8\,\rm in[/tex], solve for [tex]\frac{dV}{dt}[/tex].

[tex]\dfrac{dV}{dt} = 3 (8\,\mathrm{in})^2 \left(2\dfrac{\rm in}{\rm min}\right) = 384 \dfrac{\rm in^3}{\rm min}[/tex]

41. Find [tex]x[/tex] when [tex]V = 55\,\rm in^3[/tex].

[tex]55\,\mathrm{in}^3 = x^3 \implies x = 55^{1/3} \,\rm in[/tex]

Solve for [tex]\frac{dV}{dt}[/tex].

[tex]\dfrac{dV}{dt} = 3 \left(55^{1/3} \,\mathrm{in}\right)^2 \left(2\dfrac{\rm in}{\rm min}\right) = 6\cdot55^{2/3}\dfrac{\rm in^3}{\rm min}[/tex]

Answer:

- 14x +3

Step-by-step explanation:

hope this helps u. : )

28

Step-by-step explanation:

Given,

No. of cameras that Gretta has : 103

No. of Cameras she misplaced : 75

1 full box contains 1 camera each

No. of full boxes that she can ship:

= No. of Cameras she has - no. of cameras she misplaced.

= 103-75

= 28

Therefore, the no. of full boxes that Gretta can ship is 28.

Answer:

x = -1

y = -5

(x,y) = (-1,-5)

x = 0

y = 0

(x,y) = (0,0)

x = 1

y = 5

(x,y) = (1,5)

Step-by-step explanation:

y = 5(-1)

y = 5*-1

y = -5

y = 5(0)

y = 5*0

y = 0

y = 5(1)

y = 5*1

y = 5

The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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