Give the first four terms of the arithmetic sequence
for which a₁ = 12 and d = -2.
A 12, 10, 8, 6
B 12, -24, 48, -96
C 12, 14, 16, 18
D 10, 8, 6, 4

Answer:

3(x+1)<18

3x+3<18

3x<15

x<5

Step-by-step explanation:

Answer:

w < 1.5

Step-by-step explanation:

We solve these almost identical to solving equations. By going backwards in the process.

14 - 12.5 = 1.5

w < 1.5

Hope this helps!

The measure of angle B is approximately equal to 56.31 degrees, rounded to two decimal places.

An angle measure is a numerical value that represents the amount of rotation between two intersecting lines, line segments or rays. It is typically measured in degrees, although other units of measurement such as radians and grads may also be used. The size of an angle can range from 0 degrees (corresponding to no rotation or a straight line) to 360 degrees (corresponding to a full rotation). In geometry, angles are used to describe the relationships between lines and shapes, and are an important concept in fields such as trigonometry and calculus.

To find the measure of angle B given cot B = 0.57736, we can use the inverse tangent function.

The tangent of an angle is the ratio of the opposite side to the adjacent side,

So cot B = adjacent side / opposite side.

By taking the inverse tangent of both sides and substituting cot B for adjacent side / opposite side, we arrive at the equation

B = arctan(cot B).

Evaluating arctan(cot B) using a calculator gives us the measure of angle B as,

B = arctan(cot B) = 56.31° (rounded to two decimal places)

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The complete question is: "Given cot B = 0.57736, determine the measure of angle B".

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

18

Step-by-step explanation:

If 12 is one-third of a number, to find the number, we have to multiply 12x3, which equals 36. To find one-half of 36, divide 36/2, which equals 18.

Hope this helped you!! Have a wonderful day C:

The fraction of one-half of the number such that one-third of it is 12 will be 18.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, the fraction is the division of the two numbers but the division is not wholly complete.

Suppose that number is x.

One-third = (1/3)x

It is equal to 12 so,

(1/3)x = 12

x = 36

Now one-half of 36 will be (1/2)36 = 18

Hence "The fraction of one-half of the number such that one-third of it is 12 will be 18".

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Answer:

8 × 10¹

Step-by-step explanation:

don't panic. just breathe deeply and then think logically.

0.002 ... what is that ? 2 10ths ? 2 hundredths ? 2 thousandths ? 2 tenthousandths ?

the 3rd position after the decimal point is for 1/1000.

and that means 10^-3. in the same way as 1000 is 10³.

so, it is 2 × 10^-3.

the other rounded number is then 4 × 10⁴.

now, we are multiplying both numbers

2×10^-3 × 4×10⁴

what do we do ?

we combine the same types of factors, like the basic constants : 2×4 = 8

and 10^-3 × 10⁴.

what hairball when we multiply the same base number with exponents ? we add the exponents :

10^-3 × 10⁴ = 10¹ = 10

because -3 + 4 = 1

and so, the result is

8 × 10¹

Answer:

C

Step-by-step explanation:

First, note that the parent quadratic function has the equation \(f(x)=x^2\).

All quadratic functions are parabolas. Eliminate A.

The vertex of \(f(x)=x^2\) is on the origin point (0,0), not in Quadrant III. Eliminate B.

\(f(x)=x^2\) is definitely a function. Eliminate D.

The correct answer is C. The function covers Quadrant I and II.

Answer:

•They are congruent from what it looks like.

Congruent means that they are exactly of size and shape, and they show scale factors of 1.  

Hence the option A and C are correct.

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Answer:

1/6

Step-by-step explanation:

(3 1/3)/20=(10/3)×(1/20)=10/60=1/6

Answer:

3

is the answer

Answer:

3

Step-by-step explanation:

Answer:

The mode is 20 because it is has been seen 3 times and the median is 20 because it is in the middle

Step-by-step explanation:

12, 15, 16, 19, 20, 20, 20, 23, 24, 25, 25, 105, 209

Answer:

x = 3

Step-by-step explanation:

Using the pythagoras theorem;

hyp^2 = opp^2 + adj^2

(x+2)^2 = 5^2 + (x-3)^2

Expand

x²+4x+4 = 25 + x²-6x+9

x²+4x+4-25-x²+6x - 9 = 0

10x - 30 = 0

10x = 30

x = 30/10

x = 3

Hence the value of x is 3

Both the fox and the dog need to make 28 leaps before the fox is caught.

Given that,

The fox has a start of 60 leaps.

The fox can make 3 leaps to the dogs 2.

This means that for every 3 leaps taken by the fox, the dog will take 2.

The dog travels in only 3 leaps as far as the fox goes in 7.

This means that for every 3 leaps the dog takes, the fox takes 7 leaps.

Now, we have to find out how many leaps the fox and the dog need to make before the fox is caught.

Assume that the fox and the dog both sprint for "x" number of jumps before the fox is apprehended.

For the fox,

The total distance travelled would be ⇒  60 + 3x

(since the fox can make 3 leaps for every 2 leaps of the dog, and the fox starts with a 60-leap advantage).

For the dog,

The total distance travelled would be ⇒ 2x

(since the dog can make 2 leaps for every 3 leaps of the fox).

Now we know that the dog travels in only 3 leaps as far as the fox goes in 7,

Therefore,

3 leaps of the dog = 7 leaps of the fox

This can be expressed as:

2x = (60 + 3x)( 7/3 )

Simplifying this equation, we get:

2x = 140 + 7x

5x = 140

x = 28

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Answer:

your rise is 2 and your run is 7

Step-by-step explanation:

rise/run = 2/7

The two column proof below has shown us that the LP ≅ LQ by definition of segment congruence.

We are told that Point M is the midpoint of PQ, and LM is the perpendicular bisector of PQ. Thus, the two-column proof to show that LP = LQ is as follows;

Statement 1; PM ≅ QM, LM ⊥ PQ

Reason 1; Given

Statement 2; LM ≅ LM

Reason 2; Reflexive Property of Congruence

Statement 3; ∠PML ≅ ∠QML

Reason 3; Right angle congruence theorem

Statement 4; ΔPML ≅ ΔQML

Reason 4; SAS congruence theorem

Statement 5; ∠PML ≅ ∠QML

Reason 5; Corresponding parts of congruent triangles are congruent

Statement 6; LP ≅ LQ

Reason 6; Definition of segment congruence

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The value for differential equation is found as -

\(\frac{dP}{dt} =\frac{d}{dt} (\frac{c_1e^t}{1+c_1e^t})\\\)

\(\frac{dP}{dt} - (\frac{c_1e^t}{(1+c_1e^t)} )(1-\frac{c_1e^t}{(1+c_1e^t)^2})\\ =(\frac{c_1e^t}{(1+c_1e^t)^2} )-(\frac{c_1e^t}{1+c_1e^t})(1-\frac{c_1e^t}{1+c_1e^t})=0\)

What is differential equation?

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

The equation given is - \(P=\frac{c_1e^t}{1+c_1e^t}\)

Take derivative with respect to t -

\(\frac{dP}{dt} =\frac{d}{dt} (\frac{c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =\frac{d}{dt}c_1 (\frac{e^t}{1+c_1e^t})\)

By Quotient rule \(\frac{d}{dt} \frac{u}{v} =\frac{v\frac{du}{dt}- u\frac{dv}{dt}}{v^2}\) -

\(\frac{dP}{dt} =c_1 (\frac{(1+c_1e^t)\frac{d}{dt}(e^t)-(e^t)\frac{d}{dt}(1+c_1e^t)}{(1+c_1e^t)} )\\\frac{dP}{dt} =c_1 (\frac{(1+c_1e^t)(e^t)-(e^t)(0+c_1e^t)}{(1+c_1e^t)} )\)

(\(\frac{d}{dx} e^t=e^t\) and \(\frac{d}{dx} c_1=0\) here \(c_1=\)constant)

\(\frac{dP}{dt} =c_1e^t (\frac{(1+c_1e^t-c_1e^t)}{(1+c_1e^t)^2} )\\\frac{dP}{dt} = (\frac{(c_1e^t)}{(1+c_1e^t)^2} )\)

Now, \(\frac{dP}{dt} =P(1-P)\) -

\(\frac{dP}{dt} - (\frac{c_1e^t}{(1+c_1e^t)} )(1-\frac{c_1e^t}{(1+c_1e^t)^2})\\ =(\frac{c_1e^t}{(1+c_1e^t)^2} )-(\frac{c_1e^t}{1+c_1e^t})(1-\frac{c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{1}{1+c_1e^t}-1+\frac{c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{1-(1+c_1e^t)+c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{1-1-c_1e^t+c_1e^t}{1+c_1e^t})\\\)

\(\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{0}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(0)\\\frac{dP}{dt} =0\)

Therefore, the value is \(\frac{dP}{dt} =0\).

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Answer:

Step-by-step explanation:

there are 2 ways to graph equations. I'll teach u the faster way.

step 1) graph the y-intercept.

so the slop-intercept form of a line is y=mx+b. b represents the y-intercept and m represents the slope. u need two points to graph a line, the first point will be the y intercept. in this case, the y-intercept is -5. so this is what you should do: (the underlined star represents a point. also, the underlined star is on point -5.)

                     | y

                     |

                     |

                     |

------------------------------------------------------------x

                     |

                     |

                     |

                     |

                    *

                     |

step 2) graph the second point using the slope.

slope equals rise over run. (m=rise/run.) in this case, the slope is 5/1. To graph the second point, u should RISE up by 5 and RUN to the right by one:  (the underlined star is on point 1.)

                     | y

                     |

                     |

                     |

-----------------------*-------------------------------------x

                     |

                     |

                     |

                     |

                    *

                     |

now draw a line through those two points.

still confused? watch the first video that pops up after searching: how to graph a line

i couldnt insert the link to the vid for whatever reason but that vid helped me learn

Answer:

Calculate property taxes based on assessed value and a tax rate. California property tax calculations with annual assessment increases up to 2% ... Tax Rate: The annual tax rate used to compute your property taxes.

The probability that Ahmad selects two blue marbles from the two jars is of:

10%.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

Ahmad moves 2 blue marbles from one jar to another jar, hence the distribution of colors on each jar will be given as follows:

Hence the probability of selecting a blue marble from each jar will be given as follows:

Then the probability of both marbles being blue is of:

p = 3/13 x 7/17 = 0.1 = 10%. (rounded).

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Answer:

$15.69

Step-by-step explanation:

multiply the retail price by 1.06 to get the price after taxes.

find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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The graph cannot be used to complete the table of values and the missing value of a is 7

The graph represents the given parameter

There are no points plotted on the graph

This means that the table of values cannot be completed

Hence, the graph cannot be used to complete the table of values

The table represents the given parameter

On the table, we have the following points

(x, y) = (0, -2), (2, 4), (3, a)

Also, we have that the points fall on a line

This means that the points make a linear equation

By analyzing the x and y values, we can see that

As x increases by 2, y increases by 6

This means that as x increases by 1, y increases by 3

So, when x = 3, the value of y is

y = 4 + 3

Evaluate

y  = 7

Rewrite as

a= 7

Hence, the missing value of a is 7

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100+75+70+x= 360° (sum of interior angles of quadrilateral)

x= 360-245= 115°

Answer:

When dealing with radicals and exponents, one must realize that fractional exponents deals directly with radicals. In that sense, sqrt(x) = x^½. In a fractional exponent, the numerator represents the actual exponent of the number. So, for x^2/3, the x is being squared.For the denominator, that deals with the radical. The index, to be exact. The index describes what kind of radical (or root) is being taken: square, cube, fourth, fifth, and so on. So, for our example x^2/3, x is squared, and that quantity is under a cube root (or a radical with a 3).^^^Exponential fractions still follow the same rules of simplifying, so...

x^2/4 = x^1/2 = sqrt(x)

Step-by-step explanation:

When dealing with radicals and exponents, one must realize that fractional exponents deals directly with radicals. In that sense, sqrt(x) = x^1/2

Now, how to go about doing this:

In a fractional exponent, the numerator represents the actual exponent of the number. So, for x^2/3, the x is being squared.

For the denominator, that deals with the radical. The index, to be exact. The index describes what KIND of radical (or root) is being taken: square, cube, fourth, fifth, and so on. So, for our example x^2/3, x is squared, and that quantity is under a cube root (or a radical with a 3). Here are some more examples to help you understand a bit more:

x^6/5 = Fifth root of x^6

x^3/1 = x^3

^^^Exponential fractions still follow the same rules of simplifying, so...

x^2/4 = x^1/2 = sqrt(x)

Answer:

The unit rate is $4 for 1 pound of rice.

Step-by-step explanation:

P.S Can I have brainliest?

Answer:

$4 per pound

Step-by-step explanation:

Unit rates are in terms of 1.

8/2 = 4

So $8 for 2 pounds is equivalent to $4 for 1 pound.

Answer:

6+(10−4) ^2-20  

Subtract 4 from 10 to get 6.

6+6 ^2-20  

Calculate 6 to the power of 2 and get 36.

6+36−20

Add 6 and 36 to get 42.

42−20

Subtract 20 from 42 to get 22.

Step-by-step explanation:

So basically, the answer is 22. let me know if i am wrong or right i haven't done these in the longest hope you have a good day :)

The 19  tykes  given away by the Shelter, that have room for only 4  tykes  per family.        

The number of different canine families that could be created from the 19  tykes  given away by the  sanctum, we need to calculate the number of combinations. room for only 4  tykes , we need to choose 4  tykes  from the aggregate of 19  tykes . The order of the  tykes  in the family doesn't count, as long as we choose different  tykes  for each family.  The number of combinations can be calculated using the formula for combinations  C( n, r) =  n!/( r!( n- r)!)  Where C( n, r) represents the number of combinations of choosing r  particulars from a set of n  particulars.  In this case, we've n =  19( total number of  tykes ) and r =  4( number of  tykes  per family).  Plugging these values into the formula, we get  C( 19, 4) =  19!/( 4!( 19- 4)!)  Calculating the factorial values  19! =  19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =  ! =  4 × 3 × 2 × 1 =  24  15! =  15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =   Substituting these values into the formula  C( 19, 4) = /( 24 ×)  ≈ 91,390  The 19  tykes  given away by the  sanctum, considering that you have room for only 4  tykes  per family.

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Answer: 11/9

Step-by-step explanation:

you would cross out the two 4s(using butterfly method) and make them 1s. So 11 x 1 and 1 x 9 = 11/9

Answer:

11/4 times 4/9 is 11/9

Step-by-step explanation:

We have to find,

(11/4) times 4/9

\((11/4)(4/9) = (11*4/4*9)\)

We can cancel the 4s from the numeratorand denominator to get,

\((11*4/4*9) = (11*1/1*9) = 11/9\\=11/9\)

The answer is 11/9

Answer:

It's in England

Step-by-step explanation:

England is the furthest west red dot on top (furthest left). England is also known as the United Kingdom or Britain, and it's an island.

Megalithic Site Name: Stonehenge

Nation/Country/State: United Kingdom, England

District/Region/Parish/County: Salisbury, Amesbury

Local Location: Salisbury Plain

GPS: 51°10'44" N, 1°49'35" W

Grid: SU 1224 4218

The Least common multiple (LCM)  The time at which both bells will ring together is 10:45 am, and the Subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

The time at which both bells will ring together, we need to find the least common multiple (LCM) of the intervals at which each bell rings.

The first bell rings every 45 minutes, and the second bell rings every minute. We want to find the point at which both intervals align, meaning they both divide evenly into the same amount of time.

To find the LCM, we can list the multiples of each interval until we find a common multiple.

Multiples of 45 minutes: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...

Multiples of 1 minute: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

From the lists above, we can observe that the least common multiple occurs when both intervals coincide at the same time, which is 45 minutes.

Thus, the two bells will ring together every 45 minutes.

If we consider the initial adjustment time of 10:00 am, the first time both bells will ring together is at 10:45 am. After that, they will continue to ring together every 45 minutes throughout the day.

Therefore, the time at which both bells will ring together is 10:45 am, and the subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

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