Describe the given translation: T(0, 7)

Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

Okay, let's break this down step-by-step:

1) We need to choose a slope within 6 to 8 feet of vertical change for every 100 feet of horizontal change.

Let's choose a slope of 7 feet of vertical change for every 100 feet of horizontal change.

2) So for every 100 feet horizontally, the zip line will drop 7 feet vertically.

3) We know the ending point height, but we need to calculate the starting point height.

4) If the ending point height is 100 feet above the ground, then for every 100 feet of horizontal distance, the line drops 7 feet.

So to drop 100 feet vertically, the line would have to travel 100 / 7 = 14.29 ~ 15 100-foot segments.

5) So if the ending point is 100 feet above the ground,

the starting point will be 100 + (15 * 7) = 100 + 105 = 205 feet above the ground.

6) Therefore, the difference between the starting and ending point heights is 205 - 100 = 105 feet.

So the difference between the starting and ending point heights of the zip line is 105 feet.

Please let me know if any of the steps are unclear or if you have any other questions! I'm happy to explain further.

Answer:

The zip line needs to be 35 feet higher than the ending point.

Step-by-step explanation:

Assuming that we want to build a zip line with a slope of between 6 to 8 feet of vertical change for every 100 feet of horizontal change, we can choose a slope of 7 feet of vertical change for every 100 feet of horizontal change. This slope is within the given constraint of 6 to 8 feet of vertical change for every 100 feet of horizontal change.

To determine how much higher the starting point of the zip line needs to be than the ending point, we need to know the horizontal distance between the two points. Let's assume that the horizontal distance between the two points is 500 feet.

Using the slope of 7 feet of vertical change for every 100 feet of horizontal change, we can calculate the vertical change as follows:

Vertical change = slope * horizontal change

Vertical change = 7/100 * 500

Vertical change = 35 feet

Therefore, the starting point of the zip line needs to be 35 feet higher than the ending point.

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

13 triangles can be formed.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

In triangle ABC, if only one letter is used in each angle.

Then there are only three possible letters to choose from A, B, and C.

Now,

Let's start with the case where all three angles are different.

There are three ways to choose the first angle, two ways to choose the second angle, and one way to choose the third angle.

i.e

3 x 2 x 1 = 6 possible triangles.

Let's consider the case where two of the angles are the same.

There are three ways to choose the repeated angle and two ways to choose the other angle.

i.w

3 x 2 = 6 possible triangles.

When all three angles are the same.

There is only one possible triangle.

Now,

The total number of possible triangles that can be formed if in triangle ABC only a letter in each angle.

= 6 + 6 + 1

= 13 possible triangles.

Thus,

13 triangles can be formed.

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Answer:

[1;1;1]

Step-by-step explanation:

try this option; all the details are in the attachment.

Answer:

x = 26/yz

Step-by-step explanation:

Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

Answer:

6

Step-by-step explanation:

\(\sum 2(X-3)=2(3-3)+2(7-3)+2(2-3)=0+8-2=6\)

Answer: (1, 3)

Step-by-step explanation:

There are two ways to solve this problem, 1 without the pythagorean theorem, and 1 with it.  For the sake of simplicity, I will solve it without the pythagorean theorem.

As is visually evident from the graph, the line segment spans 6 units horizontally, and 3 units vertically.  Because the ratio between AP and PB is 1:2, simply divide both the domain and range by 3, to get 2 horizontally, and 1 vertically.  

Then, simply go to point A and respectively add and subtract the horizontal and vertical values to get point A(-1, 4) --> P(1,3)

Hope it helps, and let me know if you want me to solve it an alternate way or go more in depth as to the way it is know.

Answer:

Step-by-step explanation:

Coordinates of A and B:

The partition ratio:

Coordinates of P are:

Answer:

Second and third option.

Step-by-step explanation:

The initial cost is $20 with an additional $3 per class, so:

20 + 3 * each class

In equation for this is:

20 + 3x

This means that the second and third option are both correct.

Hope this helps!

The equation represents the relationship is y = 3x +20

The amount that Lucy paid to join the fitness class represents her fixed cost. Fixed cost is the cost that does not change with he number of classes she takes.

The amount Lucy pays per class is her variable cost. Variable cost increases with the number of classes she attends.

Her variable cost can be presented with the expression : $3 × x. Where x represents the number of classes she takes.

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Lucy's total cost = fixed cost + Variable cost

y = 3x +20

1. <C= 90 degree

AC =  13.25 unit

<B= 60 degree

2.  <C= 90 degree

AC =  13.

<B= 60 degree

1. Using Sine law

sin C/4 = sin 30/2 = sin B/ AC

so, sin C/4 = 1/4

sin C = 1

C= 90 degree

and, <B= 180 - 30- 90= 60 degree

So, sin 30/2 = sin 60/ AC

1/4 AC = √3/2

AC = 2√3

2. Using Sine law

sin 30/ 7.65 = sin B / 15.3

1/15.3 = sin B/15.3

sin B= 1

B = 90 degree

and, <C= 180 - 90 - 30 = 60

So, 1/15.3 = sin 60/ C

C = 13.25

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Answer:

Step-by-step explanation:

(y/10)^2+(x/30)^2=1

y^2/100+x^2/900=1

9y^2+x^2=900

9y^2=900-x^2

y^2=(900-x^2)/9, when x=8 we have

y^2=(900-8^2)/9

y^2=(900-64)/9

y^2=836/9

y=9.6 meters

The arch is 9.6 meters above the river at a distance of 8 meters from the center.

Answer:

\(\frac{1}{2}\) of the garden will be radishes.

Step-by-step explanation:

Given a rectangular garden which grows cucumbers in \(\frac{2}{3}\) of the garden.

\(\frac{3}{4}\) of the cucumber section to grow radishes.

To find:

How much of the whole garden will be radishes?

Solution:

Let the total area of the garden = \(x\) sq units

Then as per our assumption, total area to grow cucumbers:

\(\frac{2x}{3}\) sq units

Cucumber area to grow radishes = \(\frac{3}{4}\) of cucumber area

\(= \dfrac{3}{4}\times \dfrac{2x}{3}\\\Rightarrow \dfrac{x}{2}\ sq\ units\)

Fraction of whole garden to grow radishes = Area to grow radishes divided by whole area of garden

\(\Rightarrow \dfrac{\frac{x}{2}}{x}\\\\\Rightarrow \bold{\dfrac{1}{2}}\)

Therefore, \(\frac{1}{2}\) of the garden will be radishes.

Answer:

The answer is x/12>10 and Turner made more than 120 fluid oz of apple cider

Step-by-step explanation:

They each mug had more than 10 not 10 so it is x/12 > 10 then to remove the 12 multiply 12 on both sides so you you get x>120 so Turner made more than 120 fluid oz of apple cider.

Answer:

A 2-column table with 3 rows. Column 1 is labeled x with entries 12, 18, 22. Column 2 is labeled y with entries 2, 3, 4.

Step-by-step explanation:

cv

Answer:

67% discounted

26

555.2

Step-by-step explanation:

39 - 13 = 26

48 x 1.15 = 55.2

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

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The sum of the angles of the triangle expressed in two ways are x + 1/2x + 3/2x and 2x + x + 3x/2

It is important to note that the sum of the angles of a triangle is equal or equivalent to 180 degrees.

We have the angle measurements as;

Substitute the values

x + 1/2 x + 3/2x = 180

Find the lowest common multiple

2x + x + 3x /2 = 180

Add the numerators

6x/2 = 180

cross multiply

6x = 360

x = 60

Hence, the expression is x + 1/2x + 3/2x and 2x + x + 3x/2

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Answer:

I believe your missing part of the question.

Answer:

Domain

Step-by-step explanation:

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

Answer:

B. 33

Step-by-step explanation:

The average of the terms of a contiguous subsequence of any arithmetic progression is the average of the first and last terms.

To see this, notice that if you remove  25  and  41 from your sequence, then the average of the remaining terms is still given by the average of the extreme terms

The weight of the male that has a body surface area of 2.3 would be = 108kg

The body surface area (BSA) is defined as the parameter that can be used to estimate the surface area of a person's body based on body weight and height.

The formula for BSA = √w×h/3600

The weight of the male = X

The height of the male = 176cm

The BSA = 2.3

From the formula, make w the subject of formula;

w = BSA²× 3600/h

w = 2.3²× 3600/176

w= 5.29×3600 /176

w = 19044/176

w = 108kg

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The missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

The equation of the function is given as:

y = 5^x

And the x value is given as

x = 2

To determine the missing value, we start by substituting 2 for x in the function y = 5^x

So, we have:

y = 5^2

Evaluate the exponent

y = 25

So, the complete coordinate is (2, 25)

Hence, the missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

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The value of the given expression = 2

The given expression is:

30 + z - 1.33

x = 8

y = 14

z = -0.67

Substitute the values of z into the given expression:

30 + (-0.67) - 1.33

30 - 0.67 - 1.33

30 - 2 = 28

Answer:

6.50x

Step-by-step explanation:

To form an arithmetic sequence with this information, you take the rate (6.50) and you multiply it by the hours (x). This can help you determine how many hours one has to work to acquire a certain amount of money.

The result can be shown in multiple forms.

Exact Form:

15/7

Decimal Form:

2.142857

Mixed Number Form:

2   1/7

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Usually I try to explain what to do, but it's been a hot second from when I learned this. I uploaded a picture that might help.
This is a free tool for solving math problems if you ever need help: (no spaces or exclamation point) mat h way . co!m

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much love <333 good bye!!

Answer:

o minutes5.10.15.20.25.30.35.40.45.50 minutes