lengths of corresponding side of 2 similar right ratio is 4:5 and hypotenuse of the smaller triangle is 24 inches long. How many inches long is the hypotenuse of the larger triangle?

When two straight lines or rays intersect at a shared endpoint, an angle is generated. The measure of ∠3 is 31°.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

Given that ∠2 and ∠3 are supplementary angles. Therefore, the sum of the two angles will be 180°. Thus, we can write the sum of the two angles as,

∠2 + ∠3 = 180°

Also, it is mentioned in the question that the measure of ∠2 is 149°. Therefore, substitute the value of ∠2 in the above equation.

149° + ∠3 = 180°

∠3 = 180° - 149°

∠3 = 31°

Hence, the measure of ∠3 is 31°.

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The largest area that can be enclosed will be 2812.5 square meters.

The perimeter of a rectangle is given as:

2L + 2W  ∴ L = length and W = width

As the farmer does not want to fence the side along the river, then the formula will be:

P = L + 2w

Now

150 = L + 2w

L = 150 - 2w

Here the area is LW

Area = (150 - 2W)(W)

After solving we get

150 - 2W = 0 or W = 0

150 - 2W = 0

2W = 150

W = 75

Now, there are two solutions whether 0 or 75

Let's find their average 0+75 / 2 = 37.5

Now L = 150 - 2(37.5)

L = 150 - 75

L = 75

As the dimensions are L = 75 and W = 37.5

Area = L x W = 75 x 37.5 = 2812.5 square meters

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The complete question is:

Farmer Ed has 150 meters of fencing and wants to enclose a rectangular play that borders a river. If farmer Ed does not fence in the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?

The next fraction in this sequence is 1/5

Arithmetic sequence are sequence that are separated by a common difference.

Given the sequence below:

4/5, 13/20, 1/2, 7/20,....

The fractions expressed as percentage is given as:

80, 65, 50, 35...

The nth term of the sequence is Tn = a+(n-1)d

T5 = 80+(5-1)(-15)

T5 = 80+(4)(-15)

T5 = 80 - 60

T5 = 20

Express 20% as a fraction

20% = 20/100 = 1/5

Hence the next fraction in this sequence is 1/5

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( - ∞ , + ∞) is  the possible domain and range for this situation.

What is the domain function?

Because C(s) = 8s + 15  one off function.

So,   s ∈ R

80 the domain is defined as ( - ∞ , + ∞)

b)  because s ∈ R

So ,  C(s) ∈   ( - ∞ , + ∞)

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The complete question is -

Consider the U.S. Shirts function, C(s) = 8s + 15. What expression in the function equation represents: a. the domain of the function? b. the range of the function? 5. Describe the possible domain and range for this situation.

Answer:

after 4 years her salary would be $48,000

salary after t years: y=2000t+40000

Answer:mhmm cool b

Step-by-step explanation:

The given situation presents a word problem and can be solved by converting the word problem into an equation.

Word problem is a few sentences representing a real-life scenario where a problem needs to be solved by method of a mathematical calculation.

According to the given situation:

Total number of bags – number of bags emptied=number of bags left

Total number of bags filled= b

Number of bags emptied=4

Number of bags left=6

Hence,

b-4=6

Solving the equation,

b=6+4

b=10

Note: The provided question does not include the options of equation. Possible options are:

4b=6; b+4=6; b/4=6; b-4=6

Hence, the equation used to determine the numbers of bags initially filled is b-4=6 and number of bags are 10 bags.

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false, reflection

Rotation symmetry is also called mirror symmetry.

false, reflection

Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.

Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated at 90°, however, the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles, and other spheroids

Rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation.

Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations.

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The equation of the circle x^2 + (y - 4)^2 = 11 has a radius of √11 and a center located at (0 , 4).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, x^2 + (y - 4)^2 = 11, is in standard form, then

h = 0

k = 4

r = √11

Hence, the equation of the circle x^2 + (y - 4)^2 = 11 has a radius of √11 and a center located at (0 , 4).

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Answer:

W=12cm

L=36cm

Step-by-step explanation:

We are told L=3W

and P=96

so 96=2⋅W+2⋅3⋅W

8W=96

so W=968=12cm

and L=3⋅12=36cm

hope this helps :)

Answer:

what are the given options? :)

The question's payroll (FICA) taxes total 0.2295.

Considering the information provided,

7.65% of payroll (FICA) taxes

Boss promises a minimum of 3 hours each week and not more than 18 hours.

We have, 3 × 0.0765

= 0.2295

Amount of payroll taxes that will be taken out of your paycheck.

= 0.2295

FICA Taxes: The Federal Income Contributions Act, also known as FICA, is the name of the payroll tax deduction used in the United States to pay for Social Security and Medicare. Tens of millions of seniors, Americans with disabilities, and children receive financial and medical benefits from those well-known government programs. Both employees and the employers they work for are jointly liable for FICA taxes.

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If the cost of renting a pool at an aquatic center is either 30 per hour or 20 per hour with a 40 non-refundable deposit, then the cost of renting the pool is the same for both plans for 4 hours.

The number of hours for which the cost of renting the pool will be the same for both plans can be calculated by using an algebraic expression.

An algebraic expression is a type of equation that consists of both numbers and letters.

An algebraic expression for this problem can be given as,

30(x) = 20(x) + 40

Where x is equal to the number of hours.

The value of x can be calculated by rearranging the equation,

30(x) - 20(x) = 40

10(x) = 40

x = 40 ÷ 10

x = 4

Thus, the number of hours for which the cost of renting the pool same for both plans is 4 hours.

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If there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.

Given that the element X decays radioactively with a half life of 15 minutes.

We are required to find the time that would take the 420 grams of element X would take the element to decay to 4 grams.

Radioactive decay is basically the emission of energy in the form of ionizing radiation.

4=420*[tex](1/2)^{x/15}[/tex]

x=15* [tex]log_{2}[/tex] (105)

x=15*log (105)/log (2)

x=15*2.0212/0.3010

x=30.318/0.3010

x=100.72

After rounding it will be 100.7 of a minute.

Hence if there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.

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Answer:

1/3 n = n - 12  Cross multiply

n = 3(n - 12)

n = 3n -36

2n = 36

n = 36/2

n = 18

Check:

1/3 (18) = 18 - 12

6 = 6

Hope this helps

Answer:

10^2 . . . . see below for additional information or versions of the answer(s)

Step-by-step explanation:

You seem to want 10^exponent, where exponent is an even single digit, not zero.

We choose exponent = 2, so your expression is ...

10^2

__

There are several versions of expanded form. One uses exponents. In that form, the expression above is the expanded form.

Another uses multipliers of 1, 10, 100, 1000, and so on. In that form, the expression expands as ...

10^2 = 1×100

Another expanded form uses individual digits of the expanded form with others set to zero

10^2 = 100

The standard form is ...

10^2 = 100.

_____

We suppose your exponential expression might have another multiplier, such as 2.98:

exponential expression: 2.98×10^2

standard form: 298

expanded form 1: 2×10^2 + 9×10^1 +8×10^0

expanded form 2: 2×100 +9×10 +8×1

expanded form 3: 200 + 90 + 8

  The algebraic expression or sigma (summation) notation is given by:

∑ = 10(100 + 10)/2

And its value is ∑ = 550

 The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.

  The equation for this type of problem is:

∑ = n(a1 + an)/2

  Our values are:

100+90+80+ . . . . . . +10

∑ = 10(100 + 10)/2

∑ = 10(110)/2 = 5(110)

∑ = 550

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Answer:

You could measure the distance from both of the lasers and divide by 2 to know the middle of the line. Then draw a straight line from the middle of the line joining the lasers, to you.

The cost of renting equipment is sometimes, always, or never proportional based on the prices attached.

It should be noted tha two sequences of numbers are proportional or directly proportional when their corresponding elements have a constant ratio. It should be noted that this is the coefficient of proportionality.

In this case, the reasoning here is that if all the items have different prices it won't be, however, if the items you are ordering all have the same price they will be proportional.

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The greatest number of comparisons each operation in the method add needs, given a binary search tree with n nodes and height h, is O. (h).

Computer scientists utilize the search method known as binary search to locate a target value within a sorted array. Binary chop, logarithmic search, and half-interval search are other names for it. The binary search compares the target value to the array's center member. If not, the half where the target cannot lie is eliminated, and the search is then carried out on the remaining half while once again comparing the center element's value to the target value. Up till the goal value is found, this process is repeated. if, at the end of the search, the remaining half is empty.

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Answer:

256

Step-by-step explanation:

According to the rule of exponents: 16 to the power of 2 can be written as 162.

........................................................................................

Answer:

Options 3 and 6

[tex]3i\sqrt{3} \\-3i\sqrt{3}[/tex]

Step-by-step explanation:

hope this helps

Answer:

y

=

1

2

x

−

5

Step-by-step explanation:

Answer:

y=x+5

Step-by-step explanation:

divide by 2 on each side

The equation in slope-intercept form is y = 4x + 1

Given,

Points (x, y) = (-1, 5)

Parallel to y = 4x - 5

Now,

Recall that a parallel line to the one given has to have the same slope. The slope of the line given is "4" (the coefficient that accompanies "x").

Therefore the equation of a parallel line has to be of the form:

y = 4x - b

5 = 4(-1) - b

5 = -4 - b

b = -4 - (-5)

b = -4 + 5

b = 1

So the equation now becomes:

y = 4x + 1

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Answer:

−2322q−6945

Step-by-step explanation:

Simplify  129(2q+6) * 9 to 1161(2q + 6)

Expand by Distributing terms

21 - (2322q + 6966)

Remove parentheses.

21 - 2322q - 6966

Collect like terms.

-2322q + (21−6966)

Simplify

-2322q - 6945

Done

Answer:

Mind you that the average rate of change is the gradient. Commonly we get it by using the formula that requires us to have also the y coordinates.

we can find them by plugging in the x-values in the function g(x)

x=1

[tex]g(1)=-2(1^{2} )-1\\g(1)=-3\\\\g(6)=-2(6^{2})-1\\ g(6)=-73[/tex]

now we have the points (1,-3) and (6,-73)

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

that is the formula we will use

[tex]=\frac{-73-(-3)}{6-1} \\=\frac{-70}{5} \\=-14[/tex]

You can solve this by isolating the variable.

1.

30 + a = 40

You can isolate a by subtracting 30 from each side

30 + a - 30 = 40 - 30

a = 10

2.

500 + b = 200

Subtract 500 from each side

500 + b - 500 = 200 - 500

b = -300

3.

-1 + c = -2

Add 1 to each side

-1 + c + 1 = -2 + 1

c = -1

4.

d + 3567 = 0

Subtract 3567 from each side

d + 3567 - 3567 = -3567

d = -3567

The cost for x rides is modeled by the linear function:

c(x) = $15 + $2.50*x

A table and a graph for that function are provided below.

Here we know that the entrance fee to the fair is $15, and the cost of each ride on the fair is $2.50

So, if you go to the fair and enter in x rides, the total cost for that will be modeled by the linear function:

c(x) = $15 + $2.50*x

Now let's find a table, to do that we just need to evaluate the function in some values of x, I will use x = 0, x = 1 and x = 2, we will get:

C(0) = $15 + $2.50*0 = $15

C(1) = $15 + $2.50*1 = $17.50

c(2) = $15 + $2.50*2 = $20.00

Then we can write the table:

Number of rides |||    Cost

      0                          $15

       1                          $17.50

       2                         $20.00

Now that we have the table, we just need to graph these 3 points on a coordinate axis, and connect them with a line.

The graph can be seen below.

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