Please answer & explain how the answer was found

Answer:

The width of Tyrone's actual patio is 16 feet

Step-by-step explanation:

[tex]\frac{2ft}{1in}[/tex] =  [tex]\frac{x}{8}[/tex]   If we look at what we know, we see that the scale tells us that 1 inch is proportional to 2 ft.  What do we need to multiple 1 inch by to get 8 inches?  8.  So, we multiply 2 feet by 8 to get the actual size of the patio which is 16 feet.

Answer:

-13, -7.9, -7.7, -3.3, 0.1, 2.4

Step-by-step explanation:

You can add and subtract radicals by ensuring that they have same radical parts.

It should be noted that a radical expression is an expression that contains the radical symbol which is ✓.

The necessary steps to add or subtract radicals include:

Identify the radical parts.

Add them together.

If there's unlike radical parts, one will manipulate the parts involved before solving.

Example: Add ✓63 + 5✓7

It should be noted that ✓63 = ✓9 × ✓7 = 3✓7

Therefore, ✓63 + 5✓7 will be:

= 3✓7 + 5✓7

= 8✓7.

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The value of expression using PEMDAS rule is 28 .

Given : expression [ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )

To find : value of expression

Calculation : Using V-BODMAS

[ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )

= [ ( 8 * 2 ) - ( 4 * 4 ) ] + ( 7 * 4 )

= [ 16 - ( 4 * 4 ) ] + ( 7 * 4 )

= [ 16 - 16 ] + ( 28 )

= [ 0 ] + ( 28 )

= 28

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Answer:

Step-by-step explanation:

The answer is 110

hope this helps :)

The right triangle that shows the length of the two sides is 5.2 and 3.1.

It is required to find the triangle.

The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

Given:

In trigonometry function, in a right triangle, a tangent of an angle x is equal to the ratio of the opposite side to angle x to the adjacent side to angle x.

According to given question we have:

Given that angle x will be:

[tex]x=tan^{-} \frac{3.1}{5.2}[/tex]

The opposite to angle x or perpendicular = 3.1 units

The adjacent side to angle x or base angle  = 5.2 units

Therefore, the right triangle that shows the length of the two sides is 5.2 and 3.1.

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Answer:

b

Step-by-step explanation:

If the total cost before tax was $11.5, then the cost of each bottle of juice j= $1.6 which can be found by the equation 5j + $3.50 = $11.50.

The cost of each bottle can be determined by using an algebraic expression.

An algebraic expression can be defined as the use of both numerals and letters in a mathematical equation.

To find the cost of each bottle, an algebraic expression can be given as,

Cost of a 5-pack of juice bottles + Cost of popcorn = Total cost before tax

5j + $3.50 = $11.50

Solving for j,

5j = 11.50 - 3.50

5j = 8

j = 8/5

j = $1.6

Hence, the cost of each bottle from a 5-pack of juice bottles is calculated to be $1.6

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Answer:

Step-by-step explanation:

it should be Venus

hmmm. im thinking its venus

It looks like the system of ODEs is

[tex]\begin{cases} 2x' + y' - 4x - 4y = e^{-t} \\ x' + y' + 2x + y = e^{4t} \end{cases}[/tex]

Differentiate both sides of both equations with respect to [tex]t[/tex].

[tex]\begin{cases} 2x'' + y'' - 4x' - 4y' = -e^{-t} \\ x'' + y'' + 2x' + y' = 4e^{4t} \end{cases}[/tex]

Eliminating the exponential terms, we have

[tex](2x' + y' - 4x - 4y) + (2x'' + y'' - 4x' - 4y') = e^{-t} + (-e^{-t}) \\\\ \implies (2x'' - 2x' - 4x) + (y'' - 3y' - 4y) = 0[/tex]

[tex](x'' + y'' + 2x' + y') - 4 (x' + y' + 2x + y) = 4e^{4t} - 4\cdot e^{4t} \\\\ \implies (x'' - 2x' - 8x) + (y'' - 3y' - 4y) = 0[/tex]

Now we can eliminate [tex]y[/tex] and it derivatives.

[tex]\bigg((2x'' - 2x' - 4x) + (y'' - 3y' - 4y)\bigg) - \bigg((x'' - 2x' - 8x) + (y'' - 3y' - 4y)\bigg) = 0 - 0 \\\\ \implies x'' + 4x = 0[/tex]

Solve for [tex]x[/tex]. The characteristic equation is [tex]r^2 + 4 = 0[/tex] with roots at [tex]r=\pm2i[/tex], hence the characteristic solution is

[tex]\boxed{x(t) = C_1 \cos(2t) + C_2 \sin(2t)}[/tex]

Solve for [tex]y[/tex]. Substituting [tex]x[/tex] into the second ODE gives

[tex]x' + y' + 2x + y = e^{4t} \\\\ \implies y' + y = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t)[/tex]

The characteristic equation this time is [tex]r + 1 = 0[/tex] with a root at [tex]r=-1[/tex], hence the characteristic solution is

[tex]y(t) = C_3 e^{-t}[/tex]

Assume a particular solution with unknown coefficients [tex]a,b,c[/tex] of the form

[tex]y_p = ae^{4t} + b \cos(2t) + c \sin(2t) \\\\ \implies {y_p}' = 4ae^{4t} - 2b\sin(2t) + 2c\cos(2t)[/tex]

Substituting into the ODE gives

[tex]5ae^{4t} + (b+2c) \cos(2t) + (-2b+c) \sin(2t) = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t) \\\\ \implies \begin{cases}5a = 1 \\ b+2c = C_1 \\ -2b+c = C_2\end{cases} \\\\ \implies a=\dfrac15, b=\dfrac{C_1-2C_2}5, c=\dfrac{2C_1+C_2}5[/tex]

so that the general solution is

[tex]\boxed{y(t) = \dfrac15 e^{4t} + \dfrac{C_1-2C_2}5 \cos(2t) + \dfrac{2C_1+C_2}5 \sin(2t) + C_3 e^{-t}}[/tex]

Using the mean concept, it is found that LeBron scored 10 more points per game on his last two games than on his first two.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For his first two games, he scored 20 + 15 = 35 points, hence the mean is:

35/2 = 17.5 points per game.

For his last two games, he scored 25 + 30 = 55 points, hence the mean is:

55/2 = 27.5 points per game.

The difference is:

27.5 - 17.5 = 10.

On average, LeBron scored 10 more points per game on his last two games than on his first two.

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Answer:

Step-by-step explanation:

#1 Number of ways picking 2 from 6 = 6C2 = 15

#2 Arranging them in a circle (consider 1 pair AB)

can be done

1,5  (ABBBBB)   or (5,1)

2,4 ( AABBBB) or (4,2)

3,3

1,1 (ABABAB)

all up = 7 ways

#3 = product of #1 and #2 = 15x7 = 105

There are 60 different ways the students can place the beads on the necklace using exactly two colors.

To find the number of different ways the students can place the beads on the necklace using exactly two colors, we need to consider the different arrangements that can be made.

We can first choose the two colors to be used, which can be done in C(6, 2) = 15 ways (where C(n, r) represents the combination of n items taken r at a time).

Once the colors are chosen, we can arrange the beads on the necklace in two ways: either clockwise or counterclockwise.

We can also flip the necklace to get a different arrangement.

Therefore, for each combination of colors, there are 2 x 2 = 4 different arrangements possible.

Thus, the total number of different ways the students can place the beads on the necklace is 15 x 4 = 60.

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The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

Luis has $420 to spend at a bicycle store for some new gear and biking outfits.

Therefore,

x = maximum number of outfits Luis can purchase while staying within his budget.

Hence, the inequality that can be used to represent the situation is as follows;

209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420

235.44 + 12.08 + 37.16x ≤ 420

247.52 +  37.16x ≤ 420

37.16x ≤ 420 - 247.52

37.16x ≤ 172.48

divide both sides by 37.16

x ≤ 4.64155005382

x ≤ 4

Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

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The equation that can be used to find the coldest temperature recorded in Key west is 3T - 25°F = 98°F and the coldest temperature recorded is 41°F.

The equation represents the relationship of two expressions on either side of the sign.

We have,

The hottest temperature = 98°F.

And that this was 25°F colder than 3 times the coldest temperature.

If we let the coldest temperature be denoted by T

We can write an equation as:

98°F + 25°F = 3T

Subtracting 25° on both sides.

98°F = 3T - 25°F

3T - 25°F = 98°F

The coldest temperature recorded in key west:

3°T - 25°T = 98°F

3°T = 123°F

T = 103°F / 3

T = 41°F

Thus the equation that can be used to find the coldest temperature recorded in Key west is 3T - 25°F = 98°F and the coldest temperature recorded is 41°F.

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Answer:

A.

B.✅

C.✅

D.✅

E.

F.✅

Step-by-step explanation:

[tex](4x-1)² = 11 \\ 4x-1 = \sqrt{11 } \\ 4x = \sqrt{11} + 1 \\ x = \frac{ \sqrt{11} + 1 }{4} [/tex]

The width of rectangle is 5 feet.

Let us assume the length of rectangle to be x. So, the width of rectangle will be (x - 3).

Now, as per the known fact, perimeter, length and width of rectangle are related by the formula -

Perimeter = 2 × (length + width)

Keep the values in formula to find the value of width

26 = 2 × (x + x - 3)

Performing addition of variables inside the bracket

26 = 2 × (2x - 3)

Shifting 2 to other side of equation to find the value of x

2x - 3 = [tex]\frac{26}{2}[/tex]

Performing division to find the value of x

2x - 3 = 13

Shifting 3 to other side of equation to find the value of x

2x = 13 + 3

Performing addition to find the value of x

2x = 16

Shifting 2 as denominator to other side of equation to find the value of x

x = [tex]\frac{16}{2}[/tex]

Performing division to find the value of x

x = 8

So, length of rectangle is 8 feet

Width of rectangle = x - 3

Width of rectangle = 8 - 3

Width of rectangle = 5 feet

Hence, the width of rectangle is 5 feet.

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P= 3

b=4

By using pythagorus therom,

h^2=p^2+b^2

=3^2+4^2

=9+16

=25

h =5

now,

sin(theta)= p÷h

=3÷5

Answer:

$31.44

Step-by-step explanation:

$125.76 ÷ 4 = $31.44

Lauren $31.44

Friend 1 $31.44

Friend 2 $31.44

Friend 3 $31.44

+ ________

$125.76

Answer:

the anser in 60

Step-by-step explanation:

Let the original number be x.

According to the question we can write as (2/3)x+20x

On rearranging x−(2/3)x=20

Now taking the L.C.M od 1 and 3 is 3

(3x−2x)/3=20

x/3=20

Again by transposing x=60

So the original number is 60

Answer:  C, I think is correct

The formula for the general term and of the sequence is ±8.

To find the formula for the given sequence:

Therefore, the formula for the general term and of the sequence is ±8.

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Answer: f(k)=4k² - 6k +7

Step-by-step explanation:

f(x)=4x² - 6x +7

f(k)=4k² - 6k +7

The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week, regular pay $14 per hour and double time pay for overtime.

As given,

Regular pay per hour = $14

Overtime work payment= 2 × ($14)

Total hours work done last week = 44hours

Let regular timing be 8 hours per day 5 days a week

Total regular working hours = 8 × 5

                                           = 40 hours

Over time = 44-40

                = 4 hours

Payment check = (40 × 14)+ (4 × 28)

                         = $672

Therefore, The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week.

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1) d - c is calculated as; -4

2) Simplifying ³/₄ - ²/₅ gives; 7/20

1) We are given;

c = 12 and d = 8. Thus;

d - c is calculated as;

8 - 12 = -4

2) We want to simplify ³/₄ - ²/₅

Factoring out 1/20 gives;

1/20(15 - 8) = 7/20

3) Number of pencils purchased = 888 pencils

Number of pencils in a box = 12

Thus;

Number of boxes purchased = 888/12 = 74 boxes

4) An integer is a whole number (not a fractional number) that can be positive, negative, or zero. The only one that is not an integer here is; 20/6

5) √64 = 8

6) (30 - 4 * 2)/(2 * 2²)

= (30 - 8)/8

= 22/8 = 11/4

7) 11 = x + 19

x = 11 - 19

x = -8

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Answer:

1) 60 miles per hour (60.00, if rounded)

2) 152 customers per day (150, if rounded)

3) 3.5 meters per second (3.50, if rounded)

4) 1.48 dollars per pound (1.48, if rounded)

5)  0.4825 dollars per pair (0.48, if rounded)

( shown work in screenshots, 1-5; magnify it to see better :D )

Answer: p - 1 > 6, or p > 7

Step-by-step explanation:

   We will write an expression from the sentence given.

difference of a number (p) and 1 ➜ p - 1

is greater than ➜ >

    The difference of a number p and 1 is greater than 6​ ➜ p - 1 > 6

   To solve for the possible values of p, we will add 1 to both sides of the equation;

p > 7

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The number that contains digits where the hundreds digit is 1/10 the value of the thousand's digit is: 748917.

Firstly, refer to the image attached for the complete question.

Now,

Given: The value of the digit in the hundreds place in 653,841 is: 800

Now, the following cases arise for the given options:

Value of digit in the thousands place = 8000

=> 1/10 the value of the digit =  [tex]\frac{1}{10}(8000) = 800[/tex]

Value of digit in the thousands place = 9000

=> 1/10 the value of the digit = [tex]\frac{1}{10}(9000) = 900[/tex]

Value of digit in the thousands place = 4000

=> 1/10 the value of the digit = [tex]\frac{1}{10}(4000) = 400[/tex]

Value of digit in the thousands place = 7000

=> 1/10 the value of the digit = [tex]\frac{1}{10}(7000) = 700[/tex]

Out of all the options, as shown above, only Option A satisfies the given condition.

Hence, the correct Option is A, i.e., The number that contains digits where the hundreds digit is 1/10 the value of the thousand's digit is: 748917.

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Answer:

Step-by-step explanation:

It is asking for the "mode" which is the data element you see the most, therefore it is 2.

Answer:

5X - 2 = 18

Step-by-step explanation:

5 x 4 = 20

20 - 2 = 18