The adjacent sides of a parallelogram measure 14 centimeters and 20 centimeters, and one angle measures 57 degrees. Find the area of the parallelogram

Answer:

5

Step-by-step explanation:

A little trick: the imaginary part ([tex]i[/tex]) in the coordinates of complex numbers act same as the y-coordinate in a rectangular plane.

So we want the distance between the coordinate points (4,2) and (7,-2).

How do we get the distance between 2 points? We use the distance formula.

Distance Formula = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Where [tex](x_1,y_1)=(4,2)[/tex]  and  [tex](x_2,y_2)=(7,-2)[/tex]

Let's solve for distance:

[tex]\sqrt{(-2-2)^2+(7-4)^2}\\ =\sqrt{(-4)^2+(3)^2} \\=\sqrt{16+9} \\=\sqrt{25} \\=5[/tex]

Hence, the length of the segment in the complex plane with endpoints at 4 + 2i and 7 – 2i is 5.

Answer:

240 divided by 3 = c

Step-by-step explanation:

Tricky...it is $240 for all 3 nights....not $240 per night.  So it is division NOT multiplication.

Answer:

Naomi earns $8 per hour.

Step-by-step explanation:

Naomi has earned$54 mowing lawns the past two days.

She worked 2.5 hours yesterday and 4.25 hours today.

Suppose she earns x dollars per hour and is paid the same amount every hour she works.

We get the equation;

[tex]2.5x+4.25x=54[/tex]

[tex]6.75x=54[/tex]

x = 8

Hence, she gets $8 per hour.

Answer:

7

Step-by-step explanation:

Answer:

[tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Given expression 1/4 divided by 5/7

For any division [tex]\frac{a}{b}[/tex]

'a' is the dividend and 'b' is the divisor

Denominator is the divisor

[tex]\frac{\frac{1}{4} }{\frac{5}{7}}[/tex]

Here, the denominator is 5/7

So the divisor is [tex]\frac{5}{7}[/tex]

Each term in the sequence is obtained by dividing the previous term by 2. Therefore, the rule for the pattern in the given sequence is to halve each term to obtain the next term.

The pattern in the given sequence is a halving pattern.

The rule for the pattern:

1. The first term in the sequence is 128.

2. Each subsequent term is obtained by dividing the previous term by 2.

Let's see how this rule applies to the given sequence:

128 / 2 = 64

64 / 2 = 32

32 / 2 = 16

Every term in the series is created by dividing the one before it by two. The rule for the pattern in the above sequence is to divide each phrase in half to produce the following term.

To know more about the series follow

https://brainly.com/question/1862223

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Answer:

[tex]-1.5[/tex]

Step-by-step explanation:

We have been given that Beth's score is 3/4 of Trevon's score.

[tex]\text{Beth's score}=-8\times \frac{3}{4}[/tex]

[tex]\text{Beth's score}=-2*3[/tex]

[tex]\text{Beth's score}=-6[/tex]

We are also told that Leah’s score was 1/4 of Beth’s score.

[tex]\text{Leah's score}=-6\times \frac{1}{4}[/tex]

[tex]\text{Leah's score}=-\frac{3}{2}[/tex]

[tex]\text{Leah's score}=-1.5[/tex]

Therefore, Leah score was [tex]-1.5[/tex].

a. The lowest total number of cars is ( x = 3 ) Fiats and ( y = 7 ) Rolls Royces, totaling 10 cars.

b. the cheapest solution is to use 3 Fiats and 7 Rolls Royces, costing £240.

To solve this problem, we need to use a system of linear equations and optimization techniques.

Let's define ( x ) as the number of Fiats and ( y ) as the number of Rolls Royces.

The constraints are:

1. People constraint: [tex]\( 2x + 2y \geq 20 \)[/tex] (at least 20 people)

2. Sheep constraint: [tex]\( x + 4y \geq 32 \)[/tex] (at least 32 sheep)

3. Car constraint: [tex]\( x + y \leq 15 \)[/tex] (no more than 15 cars)

We also want to minimize the total number of cars, so the objective function is simply ( x + y ).

(a) To find the lowest total number of cars, we'll solve the system of equations:

[tex]\[\begin{cases}2x + 2y \geq 20 \\x + 4y \geq 32 \\x + y \leq 15\end{cases}\][/tex]

We solve these inequalities by  algebraically:

1. Solve the first two equations simultaneously:

 [tex]\[ \begin{cases} 2x + 2y = 20 \\ x + 4y = 32 \end{cases} \][/tex]

  Multiply the second equation by 2 to match coefficients with the first equation:

 [tex]\[ \begin{cases} 2x + 2y = 20 \\ 2x + 8y = 64 \end{cases} \][/tex]

Subtract the first equation from the second:

[tex]\[ \begin{aligned} (2x + 8y) - (2x + 2y) &= 64 - 20 \\ 6y &= 44 \\ y &= \frac{44}{6} \\ y &= 7.33 \end{aligned} \][/tex]

However, ( y ) must be a whole number, so we take ( y = 7).

Substitute ( y = 7 ) into the first equation:

  [tex]\[ \begin{aligned} 2x + 2(7) &= 20 \\ 2x + 14 &= 20 \\ 2x &= 6 \\ x &= 3 \end{aligned} \][/tex]

Therefore, the lowest total number of cars is ( x = 3 ) Fiats and ( y = 7 ) Rolls Royces, totaling 10 cars.

(b) To find the cheapest solution, we calculate the cost for each option:

Cost of Fiats: £10 x 3 = £30

Cost of Rolls Royces:  £30 x 7 = £210

Total cost:  £30 + £210 = £240

So, the cheapest solution is to use 3 Fiats and 7 Rolls Royces, costing £240.

Complete Question:

A farmer has to transport 20 people and 32 sheep to a market. He can use either Fiats (x) which take 2 people and 1 sheep, or Rolls Royces ( y) which take 2 people and 4 sheep. He must not use more than 15 cars altogether.

(a) What is the lowest total numbers of cars he could use?

(b) If it costs £10 to hire each Fiat and £30 for each Rolls Royce, what is the cheapest solution?

The scale factor is 3.5 and the length of the banner is 84 inches. Then the correct option is A.

Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.

A picture of a school’s mascot is 18 in. wide and 24 in. long.

It is enlarged proportionally to banner size.

If the width is enlarged to 63 in.

Then the scale factor will be

[tex]\rm S.F. = \dfrac{63}{18}\\\\S.F. = 3.5[/tex]

Then the length of the banner will be

[tex]\rm Banner \ length = S.F. \times 24\\\\Banner \ length = 3.5 \times 24\\\\Banner \ length = 84[/tex]

The length of the banner is 84 inches.

More about the dilation link is given below.

https://brainly.com/question/2856466

Answer: Richard has 5 7/12 rolls left.

Step-by-step explanation:

Hi to answer this question, first, we have to sum the amount of rolls Richard bought for the bbq:

4 1/4 + 5 2/3 = 4 3/12 + 5 8/12 = 9 11/12

Finally we have to subtract the amount of rolls eaten at the bbq to the previous number.

9 11/12 - 4 1/3 = 9 11/12 - 4 4/12= 5 7/12  

So, Richard has 5 7/12 rolls left.

Feel free to ask for more if needed or if you did not understand something.