The length of a rectangle is three times the width. the parameter is 240 inches. find the length and width​

Answer:

Area of trapezoid = 32√3

Step-by-step explanation:

Using Pythagoras theorem

8² = (4√3)² + x²

64 = 48 + x²

x² = 64 - 48

x² = 16

x = √16

x = 4

Area of trapezoid = ½(a + b) h

Where a = 10 - 4 = 6

b = 10

h = 4√3

Area of trapezoid = ½(6 + 10) × 4√3

= ½ × 16 × 4√3

= 8 × 4√3

= 32√3

Step-by-step explanation:

Let ABCD be a rhombus. So, AC (AC = 14 cm) and BD (BD=48 cm) will be its diagonals. Let us assume that diagonals are intersecting at point O.

Since, diagonals of a rhombus are perpendicular bisector.

[tex] \because \: OA = \frac{1}{2} \times AC \\ \\

\therefore \: OA = \frac{1}{2} \times 14

\\ \\ \huge \red{ \boxed{\therefore \: OA = 7 \: cm}} \\ \\ \because \: OB = \frac{1}{2} \times BD \\ \\ \therefore \: OB = \frac{1}{2} \times 48 \\ \\ \huge \red{ \boxed{\therefore \: OB = 24 \: cm}} \\ \\ In \: \triangle OAB, \: \: \angle AOB=90° \\ \therefore \: by \: Pythagoras \: Theorem \\ AB= \sqrt{OA^2 +OB^2 } \\ = \sqrt{7^2 +24^2 } \\ = \sqrt{49+576 } \\ = \sqrt{625 } \\ \huge \orange{ \boxed{\ \therefore \:AB= 25 \: cm.}}[/tex]

Hence, length of a side (or all) is 25 cm.

Final answer:

To find the length of a side of a rhombus with diagonals measuring 14 cm and 48 cm, one can use Pythagoras' theorem on the right-angled triangles formed by half the diagonals. The length of the side of the rhombus is calculated to be 25 cm.

Explanation:

The question involves finding the length of a side of a rhombus given the lengths of its diagonals. According to the properties of a rhombus, the diagonals bisect each other at right angles. In this case, the diagonals are 14 cm and 48 cm long. Therefore, we have two right-angled triangles formed by the diagonals, with each triangle having legs of 7 cm (half of 14 cm) and 24 cm (half of 48 cm).

To find the length of a side of the rhombus, we can use Pythagoras' theorem, which states that in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

Applying Pythagoras' theorem:

Let the length of each side of the rhombus be s.

Use the right-angled triangle with sides 7 cm and 24 cm to solve for s (hypotenuse).

Calculate s² = 7² + 24².

So, s² = 49 + 576.

s² = 625.

Therefore, s = [tex]\sqrt{625}[/tex] = 25 cm.

Hence, the length of a side of the rhombus is 25 cm.

Answer:

20+4+0.02

Step-by-step explanation:

The height of a puffin in expanded form is [tex]\(2 \times 10^1 + 4 \times 10^0 + 0 \times 10^{-1} + 2 \times 10^{-2}\) cm[/tex].

To write the height of a puffin, which is 24.02 cm, in expanded form, we need to express each digit as a product of the digit and its corresponding power of 10. Starting with the leftmost digit:

- The first digit is 2, and it is in the tens place, so it is [tex]\(2 \times 10^1\)[/tex].

- The second digit is 4, and it is in the ones place, so it is [tex]\(4 \times 10^0\)[/tex] (since any number to the power of 0 is 1).

- The third digit is 0, and it is in the tenths place, so it is [tex]\(0 \times 10^{-1}\)[/tex]. Since it is multiplied by 0, this term contributes nothing to the total and can be omitted.

- The fourth digit is 2, and it is in the hundredths place, so it is [tex]\(2 \times 10^{-2}\)[/tex].

Putting it all together, we get the expanded form as:

[tex]\(2 \times 10^1 + 4 \times 10^0 + 0 \times 10^{-1} + 2 \times 10^{-2}\) cm.[/tex]

Answer:

x = 3

Step-by-step explanation:

[tex]\\4x^2-2x=30\\\\x=3\\4(3)^2-2(3)=30\\4(9) - 6 =30\\36 - 6 = 30\\30 = 30 \\\\x=4\\4(4)^2-2(4)=30\\4(16) - 8 =30\\64 - 8 = 30\\56\neq 30[/tex]

56  is not equal to 30

Answer:

1/5

Step-by-step explanation:

Answer:

[tex]\frac{1}{15}[/tex]

Step-by-step explanation:

[tex]\frac{1}{5}[/tex]÷[tex]\frac{3}{1}[/tex]

[tex]\frac{1}{5}[/tex]·[tex]\frac{1}{3}[/tex]

[tex]\frac{1}{15}[/tex]

Answer:

y= 4x-6

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is its gradient and c is its y-intercept.

Let's find the gradient, m, first.

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Using the above formula,

[tex]m = \frac{10 - ( - 6)}{4 - 0} \\ m = \frac{10 + 6}{4} \\ m = \frac{16}{4} \\ m = 4[/tex]

Subst. the value of m into the equation.

y=4x+c

To find c, substitute a coordinate into the equation.

When x=0, y= -6,

-6= 4(0) +c

c= -6

Thus, the equation of the line is y= 4x -6.

Answer:

$449.8

Step-by-step explanation: 450-0.2

The question is about calculating the new price of a Hamilton multitouch watch which was priced originally at $450, and is reduced by 20%. The new selling price of the watch is $360.

The problem at hand is telling us that a Hamilton multitouch watch, which originally costs $450, is experiencing a price reduction of 0.2 or 20%. To calculate the new selling price, we need to multiply the original price of $450 by the reduction rate of 0.2 and then subtract that value from the original price.

The calculation would look like this: $450 * 0.2 = $90. This suggests that the watch is being discounted by $90.

Following, to calculate the new selling price, subtract the discount from the original price: $450 - $90 = $360. Thus, the new selling price of the Hamilton multitouch watch is $360.

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Answer:

y = -3/2 x.

Step-by-step explanation:

y = kx where k is a constant.

6 = -4k

k = 6/-4 =  -3/2

So the equation is y = -3/2 x.

so the right ans is of option C

Answer:

  yes

Step-by-step explanation:

The ratio between the present value and the future value will be the same for any present or future date, provided that the discount/interest rate is the same in each case.

Alternative cash flows projected to the same date will have the same ratio, regardless of the chosen date — again, provided that the discount/interest rate is the same in each case.

Answer:

No

Step-by-step explanation:

Because in a function for every one x there is one y.

Answer:

YES.

Step-by-step explanation:

f(x) = 3x^2.

This is a parabola which opens upwards ( roughly U shaped) so it will pass the vertical line test and is a function.

A square root can’t be a negative value, so the root would be greater than or equal to zero.

Range:

Y>=O

[O, infinity)

24h=d.

if you multiply 24 by the number of hours than you will get the distance.

if you traveled for 2hours than you would have traveled 48miles because if you multiply 24 by 2 you get 48.

In the equation 24 is distance traveled in 1 hour.

Answer:

24h=d

Step-by-step explanation:

0=0

2=48

4=96

7=168

its just multiples of 24 :)

Answer:

option 3

Step-by-step explanation:

Using the Sine rule in Δ ABC, that is

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex], that is

[tex]\frac{20}{sin30}[/tex] = [tex]\frac{CA}{sin45}[/tex] ( cross- multiply )

CA × sin30° = 20 × sin45° ( divide both sides by sin30° )

CA = [tex]\frac{20sin45}{sin30}[/tex] → (3)

following expression  [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] is equal to  [tex]-4x[/tex] . Kindly match with your options!

Step-by-step explanation:

Here we have , following expression to evaluate . 1/3(9 - 18x) + 1/4(8x - 12 or , [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] :

⇒ [tex]\frac{1}{3}(9 - 18x) + \frac{1}{4}(8x - 12)[/tex]

⇒ [tex]\frac{1(4)}{3(4)}(9 - 18x) + \frac{1(3)}{4(3)}(8x - 12)[/tex]

⇒ [tex]\frac{(9 - 18x)(4)}{3(4)} + \frac{(8x - 12)(3)}{4(3)}[/tex]           { Making denominator of both terms same ! }

⇒ [tex]\frac{(9 - 18x)(4)+(8x - 12)(3)}{12}[/tex]

⇒ [tex]\frac{9(4) - 18(4)x+8(3)x - 12(3)}{12}[/tex]

⇒ [tex]\frac{36- 72x+24x - 36}{12}[/tex]

⇒ [tex]\frac{ -48x}{12}[/tex]           { Simplifying even further }

⇒ [tex]-4x[/tex]

Therefore , following expression  [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] is equal to  [tex]-4x[/tex] . Kindly match with your options!

Final answer:

The equivalent expression for 1/3(9 - 18x) + 1/4(8x - 12) is -4x.

Explanation:

The given expression is 1/3(9 - 18x) + 1/4(8x - 12).

We need to distribute the fractions across the terms inside the parentheses:

Therefore, the equivalent expression is -4x.

The range of Ervin's scores is 55.

Range is the difference between the largest number and the smallest number.

To find the range of a set of values, first sort the values numerically (smallest to largest). With this set, it would look like this: 138, 142, 155, 165, 172, 193. Lastly, subtract 138 from 193 to find the range. By doing so, you will get 55 as an answer.

I hope this helps!

The range of ErvIn's scores is 55.

The range of ErvIn's scores is calculated by finding the difference between the highest and lowest scores.

Arrange the scores in numerical order: 138, 142, 155, 165, 172, 193.

Find the highest score: 193.

Find the lowest score: 138.

Subtract the lowest score from the highest score to find the range: 193 - 138 = 55.

Answer:

The probability that he chooses a yellow ball is 5/14. If he removes all the orange balls, the probability that he will choose a red ball is 2/10.

Step-by-step explanation:

Simple logic.

Answer:

Column 1:

Positive infinity

Negative infinity

Column 2:

Negative infinity

Positive infinity

h = -16t^2 + 64t

When the ball reaches the ground, h will equal zero.

0 = -16t^2 + 64t

16t^2 = 64t

16t = 64

t = 4 seconds

Answer:

the first answer the other person put is the correct one

Step-by-step explanation:

just Dubble checked it

Answer:81

Step-by-step explanation:

3x3x3x3

Answer:81

Step-by-step explanation:

3.3.3.3=81

Answer:

Vertical angles

Step-by-step explanation:

Two non-adjacent angles formed by the intersection of two lines are called vertical angles.

There is 20% error in zookeeper's calculations.

Step-by-step explanation:

Given,

Approx weight of newborn lion = Approx value =2.8 pounds

Exact weight of newborn lion = Exact value = 3.5 pounds

Percent error = [tex]\frac{|approx-exact|}{exact}*100[/tex]

Percent error = [tex]\frac{|2.8-3.5|}{3.5}*100\\[/tex]

Percent error = [tex]\frac{|-0.7|}{3.5}*100[/tex]

Percent error = [tex]\frac{70}{3.5}[/tex]

Percent error = 20%

There is 20% error in zookeeper's calculations.

Final answer:

To find the zookeeper's percent error, subtract the predicted weight from the actual weight to find the absolute error, divide by the actual weight, multiply by 100, and round to the nearest percent. The percent error in predicting the weight of the newborn lion is 20 percent.

Explanation:

To calculate the zookeeper's percent error in predicting the weight of a newborn lion, we follow these steps:

Round to the nearest percent.

The zookeeper predicted the weight would be 2.8 pounds, but the actual weight was 3.5 pounds. So the absolute error is:

|Predicted Weight - Actual Weight| = |2.8 pounds - 3.5 pounds| = 0.7 pounds

Then, divide the absolute error by the actual weight:

0.7 pounds / 3.5 pounds = 0.2

Multiply by 100 to convert to a percentage:

0.2 × 100 = 20%

Since we round to the nearest percent, the zookeeper's percent error is 20 percent.

Answer:

Step-by-step explanation:

Let r and m represent the registration fee and the monthly fee, respectively. We are told that the charges are ...

  370 = r + 4m

  530 = r + 6m

This is your system of equations.

__

Subtract the first equation from the second to start the solution.

  (530) -(370) = (r +6m) -(r +4m)

  160 = 2m . . . . . . simplify

  80 = m . . . . . . . . divide by 2

Using this value in the first equation, we find ...

  370 = r + 4(80)

  50 = r . . . . . . . . . . . . subtract 320

The registration fee is $50; the monthly fee is $80.

Answer:

36

Step-by-step explanation:

This questions tests for the fundamentals of counting.

Let's say event [tex]x_i[/tex] can be done in X ways and event [tex]y_i[/tex] can be done in Y ways, therefore the total number of ways [tex]x_i[/tex] and [tex]y_i[/tex] can be done is given as [tex]xy[/tex].

Applying this counting principle in our case, the total different sandwiches is obtained as the product of the individual sandwich types.

[tex]Total=s\times m\times b\\=3\times 4 \times 3\\=36[/tex]

36 different sandwiches can be made.

Answer:

3x + 3y

Step-by-step explanation:

X + 2X = 3X

Y + 2Y = 3Y

In this expression, we can combine the like terms to simplify it.

To simplify the expression x + 2x + y + 2y, we can combine the like terms. Like terms are terms that have the same variables raised to the same power. In this case, the terms 2x and x are like terms because they both have the variable x raised to the power of 1. Similarly, the terms 2y and y are like terms because they both have the variable y raised to the power of 1.

So, when we combine the like terms, the expression becomes 3x + 3y.

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Answer:

17 nights.

Step-by-step explanation:

The total length of the scarf that should be knitting = 34 cm

Sarah has already knit 17 centimeters of a scarf.

So, the remaining = 34 - 17 = 17 cm

Sarah can knit 1 centimeter each night.

So, the number of nights will Sarah have to spend knitting = 17/1 = 17 nights.

Answer:

x = 3

Step-by-step explanation:

(x - 1)2 = 4

how to get this solved is very simple.

first step to apply is the BODMAS RULE

B..................... bracket

O..................... of

D.....................Division

M.................... multiplication

A..................... addition

S.................... Subtraction

so (x - 1)2 = 4

we have,

2x - 2 = 4 ( by opening the bracket)

collect the like terms

2x = 4+2

divide both sides by 2

2x/2 = 6/2

x = 3

to check if your answer is correct put the value of x = 3 into the question and see if the right hand side will equal to the left handside

(x - 1)2 = 4

(3-1)2=4

2(2)=4

4=4.............................. proved

Answer:

2

Step-by-step explanation:

8+6+4+2+1 =21

Total 21 dots/observations

Centre at 11th dot which corresponds to 2

Number of Laps Around a Track. A dot plot going from 1 to 5, 1 has 8 dots, 2 has 6 dots, 3 has 4 dots, 4 has 2 dots, and 5 has 1 dot,  the center is 2.

The location is sometimes alluded to as the data collection's "core." The two metrics that are most frequently used to identify the "center" of both the data are the mean (average) and the median. To find the weighted mean of 50 people, add up all 50 weights once more and divide by 50.

Order the data and locate the number that divides the information into two equal portions to determine the median weight of both the 50 individuals. Because it is unaffected by the specific numerical values of the outliers, the median is typically a better indicator of the center if there are extreme values or outliers. The most popular way to measure the center is with the mean.

8+6+4+2+1 =21

21 dots/observations

Centre at 11th dot which corresponds to 2

Therefore, the center is 2.

To learn more about center, here:

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C. Is your answer

y=−52+8x