You are heading to a drive-in movie and will need exact cash at the entrance for everyone in your car to get in. The cost is $6.50 per person. Write an expression that represents the total cash needed for your car based on the number of people, p, in your car.

The value of [tex]a_{5}[/tex] is 2500, when [tex]a_{1}=4[/tex] and [tex]5a_{n-1}[/tex].

Given that, [tex]a_{1}=4[/tex] and [tex]5a_{n-1}[/tex].

We need to find the value of [tex]a_{5}[/tex].

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Now, to find the value of [tex]a_{5}[/tex] :

[tex]a_{2} =5a_{2-1}=5a_{1}=5 \times4=20[/tex]

[tex]a_{3} =5a_{3-1}=5a_{2}=5 \times20=100[/tex]

[tex]a_{4} =5a_{4-1}=5a_{3}=5 \times100=500[/tex]

[tex]a_{5} =5a_{5-1}=5a_{4}=5 \times500=2500[/tex]

Therefore, the value of [tex]a_{5}[/tex] is 2500.

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Let that be x

The number he chooses, in the beginning, was 888.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

Given that Sahil chooses a number, then divides it by 8, adds 8 to the answer. Then multiply the answer by 8.

Let the unknown number be represented by x.

Therefore,

(x/8+8)8 = 952

x/8+8 = 119

x/8 = 119-8

x/8 = 111

x = 111(8)

x = 888

Therefore, the unknown number would be; 888.

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Answer:

Wrong

Step-by-step explanation:

Let cost of Albert's fuel be x.

When cost of fuel rises by 10% :

When consumption is reduced by 10% :

So clearly there is a 1% change in expenditure. Hence, Albert's claim is wrong.

Answer:

Albert is wrong -- explanation below

Step-by-step explanation:

Albert's expenditure "C" on fuel at any point in time is the product of the unit price, "p", and the amount of fuel purchased, "n".

In an equation form, [tex]C=pn[/tex].

Looking at some time before the changes, let's denote the unit price, the amount of fuel, and the expenditure with subscripts "1" to denote specific values at time 1, before the changes.

[tex]C_1 = p_1 n_1[/tex]

After the changes, note that p1 increased by 10%, and amount of fuel decreased by 10%.

Understanding changing percentages

For values that stay the same, we would multiply by 100% (or 1.00), since multiplying by 1 doesn't change the value.

For a 10% increase, we need 100%+10% which equals 110% or 1.10

For a 10% decrease, we need 100%-10% which equals 90% or 0.90

So, the new prices and amounts and costs at some later time, time 2, are given by [tex]C_2 = p_2 n_2[/tex], where [tex]p_2 = 1.10p_1[/tex] and [tex]n_2 = 0.90n_1[/tex].

Substituting:

[tex]C_2 = p_2 n_2[/tex]

[tex]C_2 = (1.10p_1) (0.90n_1)[/tex]

[tex]C_2 = 0.99 p_1 n_1[/tex]

But remember that [tex]C_1 = p_1 n_1[/tex], so

[tex]C_2 = 0.99 C_1[/tex]

In other words, the next expenditure is 99% as much as (or 1% less than) the old expenditure.

Thus, Albert is incorrect to state that there was NO change in his expenditure.

Answer: [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

perpendicular = opposite recipricol

-3 = [tex]\frac{1}{3}[/tex]

switch the sign and flip it (3/1 => 1/3)

Answer:

3. n>or=0

5. n>or=0

Step-by-step explanation:

3. -1<or=2n+4-5

    =-1<or=2n-1

    =1-1<or=2n

    =0<or=2n

     =n>or=0.

5. 0<or=2n+3n

  =0<or5n

  =n>or=0

Answer:

17.20465053

Step-by-step explanation:

17.20465053 or

17.2 (to 1 dp)

Answer:

Third side has to be greater than 4 and less than 24.

Step-by-step explanation:

A triangle is valid if the sum of two sides is greater than the third side. That has to be the case for each of the sides. So let the sides of triangle be a, b and c.

a + b > c

a + c > b

b + c > a

Given:

a = 10

b = 14

We are looking for the third side, c.

First inequality:

a + b > c

10 + 14 > c

24 > c

This tells us that c has to be less than 24.

Second inequality:

a + c > b

c > b - a

c > 14 - 10

c > 4

This tells us that c has to be grater than 4.

Third inequality:

b + c > a

c > a - b

c > 10 - 14

c > -4

This tells us that c has to be greater than -4. But we also know that c has to be greater than 4, so we take 4 as the minimal value for c.

Final answer:

4 < c < 24

Third side has to be greater than 4 and less than 24.

Answer:

15/7 is the answers for the question

Step-by-step explanation:

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Answer:

15/21

Step-by-step explanation:

First do 5 times 3, which is 15 (5+5+5). Then do 7 times 3, which is 21 (7+7+7). Since the denominator is 7 and there is 3 models with 7 parts each, there are 21 total parts. Out of each model, only 5 parts are highlighted/colored out of the 7. Add all the parts that are colored together to get 15. To put it simpler, 15 out of 21 parts are colored. This cannot be further simplified, giving you 15/21

Answer:

see explanation

Step-by-step explanation:

(9m + 4)² - (9m - 4)² ← expand both factors using FOIL

= 81m² + 72m + 16 - (81m² - 72m + 16) ← distribute parenthesis by - 1

= 81m² + 72m + 16 - 81m² + 72m - 16 ← collect like terms

= 144m

= 72(2m)

which is divisible by 72 for all m

Answer:

y= 2x - 3

Step-by-step explanation:

To calculate the slope (or gradient) of a line, take two points on the line whose x and y values are easy to read. Then divide the difference of they y-coordinate values by the difference of their x-coordinate values.

Here I have taken the points p (3, 3) and q (1, -1) to calculate the slope.

• slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex]

         = [tex]\frac{3 - (-1)}{3 - 1}[/tex]

         = [tex]\frac{4}{2}[/tex]

         = 2  

The intercept is the y-coordinate value of the point at which the line crosses ("intercepts") the y-axis. I've marked the intercept point with a green line.

• intercept = -3

The slope-intercept equation of a line takes the form:

y = mx + c

where 'm' is the slope and 'c' is the y-intercept.

Substituting the values we found into the equation gives us:

y = 2x + (-3)

∴ y = 2x - 3

Answer:

is b i think

hope my answer help you

Answer:

[tex]\fbox {Work is attached below.} \downarrow[/tex]

Step-by-step explanation:

Answer:

12 is the answers for the question

Step-by-step explanation:

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[tex] - | - x| = - 12 \\ - x = - 12 \\ x = 12 \: \: \: or \: \: \: x = - 12 \\ [/tex]

Solution :{-12,12} so it's D

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The equation of the line will be 3y + 8x = 165.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that:-

The given equation of the line is:-

3 x + 8 y = 4.

The slope of this line will be:-

3 x + 8 y = 4.

8y = -3x + 4

y = -3 /8x + ( 1 / 2)

y = mx + c

m = -3 / 8

Since the line is perpendicular to the other line 3x +8y = 4 so the slope will be inverse and negative for the line.

So the slope of the line will be -8 / 3

The equation of the line passing through the point will be given as:-

y - y 1 = m ( x- x1)

y - (-9) = ( -8 / 3) ( x - 8)

Y + 9 = ( -8 / 3 ) ( x -8 )

3 y = -8x + 165

3y + 8x = 165

Therefore the equation of the line will be 3y + 8x = 165.

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Answer:

The answer is 44.80 degrees

Step-by-step explanation:

First you want to find z

z = 180-(52+90)=38

and then try to determine which formula will try to give you x = Tan

Tan = Opposite/ Adjacent

Tan(38)=35/x

x=35/Tan(38)

x=44.80

The functions shown in the table below are exponential functions, will be g(x) and k(x). Then the correct option are B and D.

The complete question is attached below.

Let a is the base and x is the power of the exponent function and b is the y-intercept.

The exponent is given as

y = aˣ + b

Checking for g(x), then we have

g(x) = 5ˣ

Then the function g(x) satisfies all the condition.

Checking for k(x), then we have

k(x) = 4⁻ˣ

Then the function k(x) satisfies all the condition.

Then the correct option are B and D.

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Answer: Below is the correct data.

Fraction: [tex]\frac{23}{100}[/tex]

Decimal: 0.23

Percent: 23%

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Answer: The card is 28 cm by 23 cm

Check out the diagram below

Explanation:

I added 4 cm to each dimension of the "24 x 19". Why 4 instead of 2? Because we're effectively adding two copies of "2 cm" to each of the original length and width. Along the horizontal component, we have the left and right boundaries. Along the vertical component, we have the top and bottom boundaries. The diagram hopefully clears up any confusion you may have.

Answer: 50%

Step-by-step explanation:  50%

Answer:

B & D

Step-by-step explanation:

-4x+5=-4x-4

-4x+4x=-4-5

0=-1

So, it has no solution.

-4x+5=-4x-5

-4x+4x=-5+5

0=0

So, it has no solution too.

the initial statement is y ∝ x

to convert to an equation multiply by k the constant of variation

[tex]y = kx[/tex]

to find k use the given condition

[tex]y = 27 \\ \\ when \\ \\ x = 3[/tex]

[tex]y = kx \\ \\ k = \frac{y}{x} = \frac{27}{3} = 9[/tex]

equation is y = 9x

when x = 4 then

[tex]y = 9 \times 4 = 36.[/tex]

Answer:

y = 36

Step-by-step explanation:

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 27 when x = 3 , then

27 = 3k ( divide both sides by 3 )

9 = k

y = 9x ← equation of variation

when x = 4 , then

y = 9 × 4 = 36

If the first inequality is written as:

3x ≤ -12

Then the correct option is D.

If it is written as it is in the problem, then neither of the graphs is the correct option.

Here we have the inequalities:

3x ≤ 12

2x + 3 > 11

(notice that in all the options, the first inequality has a negative sign, while in the two given inequalities there are no negative sign. This means that you will never get the correct answer if you use the given information, as the problem is incorrectly written).

First, we need to isolate x on both inequalities, we will get:

3x ≤ 12

x ≤ 12/3

x ≤ 4

(As you can see, because we don't have the negative sign, this inequality is different to all the ones in the options).

And for the other:

2x + 3 > 11

2x > 11 - 3

x > 8/2

x > 4

So neither of the options is actually correct.

If we instead write the first inequality as:

3x ≤ -12

We would solve this as:

x ≤ -4

And in that case, our two inequalities are:

x ≤ -4

x > 4

So the correct graph is graph D.

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Step-by-step explanation:

hope this help you the result is In square

The inequality which shows the graph is [tex]y\le\ 4x+2[/tex].

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

As, from the inequalities the graph is representing the fourth inequality.

The graph attached below show the graph corresponding to  

[tex]y\le\ 4x+2[/tex] is shown.

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Answer:

2.865.

Step-by-step explanation:

first get to know the place value of each digit is you move on you will realise that there's no digit for tens of thousands that means that you can add a zero which which will be counted as tens of thousands and since it's not past 5 it can't change the other number. I mean it can't add 1 to 5 so the number remains 2.865 good day.

Answer:

its most likley graph 4

Step-by-step explanation:

hope this helps and if its wrong im very sorry

The range of the given function will lie from ( -0.333,0) to ( 0,1).

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given that:-

When we plot the graph of the function we will see that the straight line will cut the x-axis at point (-0.333 ) and the y-axis cut at ( 0,1 ) the points between the two points will be the solutions of the equation.

Therefore range of the given function will lie from ( -0.333,0) to ( 0,1).

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Answer:i think the answer is B

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

Well you just plug in the value 3 for x. This will give you the following equation: [tex]\frac{4(3+3)(3+1)}{(3+5)(3-5)}[/tex] which simplifies to [tex]\frac{4(6)(4)}{(8)(-2)}[/tex] which further simplifies to [tex]-\frac{96}{16}[/tex] which can further be simplified by dividing the two numbers and that results in -6

Answer:

A

Step-by-step explanation:

it really only means to replace every x by 3 and then simply calculate.

4(3+3)(3+1) / ((3+5)(3-5)) =

= 4×6×4 / (8×-2) = 96/-16 = -6

Answer:

24/x-8 = 4

Multiplying both the sides with x-8

24 = (x-8)*4

24 = 4x - 32

24 + 32 = 4x

56 = 4x

56/4 = X

14= X

The area of a 2D form is the amount of space within its perimeter. The area of the rectangle is 12 units². Thus, the correct option is A.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

As per the given information, the graph of the rectangle can be made as shown below. It can be observed from the graph that the length of the rectangle and width of the rectangle are 4 units and 3 units, respectively. Therefore, the area of the rectangle is,

Area = 4 units × 3 units = 12 units²

Hence, the area of the rectangle is 12 units². Thus, the correct option is A.

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Answer:

t=4+6n

Step-by-step explanation:

a = 10

d=6

in general

tn = a + (n-1)*d

tn = 10 + (n-1)*6

tn = 10 + 6n - 6

tn = 4 + 6n

So if n = 5 then

t5= 4+6*5

t5= 4 + 30

t5 = 34 which agrees with your givens.