Use the Pythagorean theorem and the following diagram to help you find the area and perimeter of the following triangle. Please show your work and steps, so partial credit may be given:

Use The Pythagorean Theorem And The Following Diagram To Help You Find The Area And Perimeter Of The

Answers

Answer 1

Answer:

Perimeter = 30

Area = 30

Step-by-step explanation:

[tex](x+8)^2 -x^2 = 12^2[/tex]

[tex]x^2 +16x +64 - x^2 = 144[/tex]

[tex]16x+64=144[/tex]

[tex]16x = 80[/tex]

[tex]x = 5[/tex]

Double check:

[tex]\sqrt{12^2 + 5^2} = (5+8)\\\sqrt{12^2 + 5^2} = 13\\13 = 13[/tex]

Perimeter:

[tex]12+5+13=30[/tex]

Area([tex]\frac{1}{2}bh[/tex]):

[tex]\frac{1}{2}[/tex] × 12 × 5 = 30

Answer 2

According to Pythagorean theorem,

Δ  (Hypotenuse)² = (1st Leg)² + (2nd Leg)²

⇒  (x + 8)² = x² + 12²

⇒  x² + 64 + 16x = x² + 144

⇒  16x = 80

x = 5

Hypotenuse = (x + 8) = (5 + 8) = 13

1st Leg = 5

2nd Leg = 12

We know that : Perimeter is the Sum of all sides of the Triangle

⇒  Perimeter = Hypotenuse + 1st Leg + 2nd Leg

⇒  Perimeter = 13 + 5 + 12

⇒  Perimeter = 30

We know that :

[tex]\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : \dfrac{1}{2} \times Base \times Height}}[/tex]

Base = 1st Leg

Height = 2nd Leg

[tex]\implies \sf{\textsf{Area of the Triangle} = \dfrac{1}{2} \times 5 \times 12}[/tex]

[tex]\implies \sf{\textsf{Area of the Triangle} = 30}[/tex]


Related Questions

Circle o centered at the origin that passes through (9,-2)

Answers

Answer:

Step-by-step explanation:

center at the origin means

x^2 + y^2 = r^2

9^2 + (-2)^2 = 81+4 = 85, so the circle is

x^2 + y^2 = 85

center at (0,-2) means

x^2 + (y+2)^2 = r^2

(-6)^2 + (0+2)^2 = 36+4 = 40

x^2 + (y+2)^2 = 40

The equation of circle which is centered at the origin that passes through (9,-2) is,

⇒ x² + y² = 85

What is mean by Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Circle o centered at the origin that passes through (9,-2).

Now, We can find the radius of circle as;

Radius of circle is distance between (0, 0) and point (9, - 2).

⇒ r = √ (- 2 - 0)² + (9 - 0)²

⇒ r = √4 + 81

⇒ r = √85

Thus, The equation of circle which is centered at the origin that passes through (9,-2) is,

⇒ x² + y² = (√85)²

⇒ x² + y² = 85

Learn more about the circle visit:

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help appreciated!!!!!

Answers

Answer:

Step-by-step explanation:

the given equation is in the form of quadratic formula i.e.ax^2+bx+c=0.

So ,here a=-1 ,b=-6 and c=-9

b^2=(-6)^2

=36

4ac=4*(-1)*(-9)

=4*9

=36

b^2-4ac=36-36

=0

number of solutions =1

Hope this helps u !!

At a pet store, Rhonda paid $55 for 8 dog bowls and 6 bones. Kelly paid $32.50 for 2 dog bowls and 9 bones. Determine the cost of one dog bowl (x) and one bone (y). Write a system of linear equations that models this situation.
please don't leave a link just answer

Answers

Answer:

y is 8/5 when x = -4.

Step-by-step explanation:

If the value of "Y" varies directly with "X", we can write y = kx, where k is the constant of proportionality.

If "y=-8,when x=20," then we can find k:    -8 = 20k, or k = -2/5.

Then y = (-2/5)x.

If x = -4, then y = (-2/5)(-4) = 8/5

y is 8/5 when x = -4.

The height of the trap is 30 inches, the length is 12 inches, and the width is 10 inches. What is the surface area that you need to coat with glue? Remember there is no top or bottom to this trap and you are just coating the outsides of it.

Answers

Answer:

Surface area of four outer sides = 1,320 inch²

Step-by-step explanation:

Given:

Height of trap = 30 inches

Length of trap = 12 inches

Width of trap = 10 inches

Find:

Surface area of four outer sides

Computation:

Lateral Surface area of cuboid = 2h[l + b]

Surface area of four outer sides = Lateral Surface area of cuboid

Surface area of four outer sides = 2h[l + b]

Surface area of four outer sides = 2(30)[12 + 10]

Surface area of four outer sides = 2(30)[22]

Surface area of four outer sides = 1,320 inch²

∆ABC has coordinates A(3, 1), B(5, 5) and C(4, 1). After a translation, the coordinates of A' are (0,0). What are the coordinates of B' and C'?

Answers

Answer:

B'(2,4) & C'(1,0)

Step-by-step explanation:

According To the Question,

Given, We have an ∆ABC that has coordinates A(3, 1), B(5, 5) and C(4, 1).

Now, After a translation, the coordinates of A' are (0,0) .

Then, the coordinate of B' & C' Also changes the same as like A' .

A(3,1) ⇒ A'(0,0)      {here from x-axis it reduce 3 and from y-axis it reduce 1}

Same as Above,

B(5,5) ⇒ B'(2,4)

&, C(4,1) ⇒ C'(1,0) .

PLEASE I NEED THE ANSWER DON'T IGNORE MY QUESTION!!!

Answers

Answer:

Step-by-step explanation:

x+y=94 degree(sum of two interior opposite angles is equal to the exterior angle formed)

 let third angle be y because the base of an isosceles triangle are always equal.

y+x+y=180 degree (sum of interior angles of a triangle)

y+94=180

y=180-94

y=86 degree

for angle x

substitute the value of x

x+y=94

x+86=94

x=8 degree

What is the value of the expression, written in standard form?

Answers

Answer:

200

Step-by-step explanation:

6.6/3.3 = 2

10^-2 / 10^-4 = 10^2

10^2 = 100

2 x 100 = 200

A bus is traveling between two cities that
are in neighboring states. The graph of
the function d(t) = 60|t − 1.25| shows the
distance of the bus in miles from the state line,
where t represents time in hours.
a. What does the graph tell you about the bus ride?
b. What is the average rate of change from 1.5 h to 2 h? What does the
average rate of change represent?

Answers

Answer:

(a). The bus decelerated to rest through 75 miles for 1.25 hours and accelerated through same distance for 1.25 hours.

b.

[tex]s _{1} = \frac{d _{1} }{t _{1} } \\ = \frac{15}{1.5} \\ s _{1} = 10 \: miles \: per \: hour \\ \\ s _{2} = \frac{d _{2} }{t _{2}} = \frac{45}{2} \\ = 22.5 \: miles \: per \: hour \\ average = \frac{22.5 + 10}{2} \\ = 16.25 \: miles \: per \: hour[/tex]

a) The bus decelerated to rest through 75 miles for 1.25 hours and accelerated through same distance for 1.25 hours.

b)The average rate of change represent is 16.25 miles per hour.

What is a function rule? A functional rule is the relationship between an input or domain and an output or scope.A relation is a function only if it has a value within each domain value.Functions are written like where is the input value. The general form of the function is:A vertical test is run graphically to determine if the relationship is a function.A formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable).Functions are ubiquitous in mathematics and essential in the natural sciences for formulating physical relationships.A formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable).

a) The bus decelerated to rest through 75 miles for 1.25 hours and accelerated through same distance for 1.25 hours.

b)

s1 = d1/t1

15/1.5

s1 = 10 miles per hour

s2 = d2/t2

22.5 miles per hour

Average = 16.25 miles per hour.

To learn more about functions, refer

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I need help with math 2 on gradpoint I’ll literally pay anyone because I need the class to graduate.

Answers

hey there, i might be interested in this deal. how much will i be getting paid?

Help,anyone can help me do quetion​

Answers

geckos sundry cheri suffering augusto

Answer;

B3 = 72°

C3 = 84°

Solution

B3: x = 180° - 55° - [ 180° - 127° ] = 127°- 55° = 72°

C3: x = 180° - 133°+ [ 180°-143° ] = 47°+37°= 84°

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hope it helps you. thank you.

Find the value of x.

Answers

Answer:

x=9

Step-by-step explanation:

so the angles of a triangle add up to 180 and since it shows two angles of 60 which makes 120, you have 60 more degrees which means A has to be 60 degrees. so if all of the angles are the same then the side lengths are the same so since it already shows one side =9 then x=9

Answer:

x=9

Step-by-step explanation:

missing angle + 60 + 60=180 degree (sum of interior angles of a triangle

missing angle + 120 =180

missing angle =180 -120

missing angle =60 degree

since all angles are 60 degree it is an equilateral triangle and all sides of a equailateral triangle are equal .So, x is also 9

Need help with this math

Answers

Here is all of my work from answering the question. I’ll put pictures too, my handwriting is pretty good so it should be easy to see. ;)

Part A-

1) 4x-3 = -2x+9

2) 4x+2x -3 = -2x+2x + 9

3) 6x -3 = 9

4) 6x -3+3 = 9+3

5) 6x = 12

6) 6x/6 = 12/6

7) x = 2

Part B-

1) y=4x-3

2) y=4(2)-3

3) y=8-3

4) y= 5

Therefore, x = 2 and y = 5.

I used substitution in Part B. 4x and x = 2.

I really hope this is right and helps, good luck! ;)

Anna is cutting several lengths of twine. The length of the first piece is 4 inches. She cuts the second piece one inch longer than 3 times the length of the first piece. If Anna continues the pattern, which sequence shows the lengths of the first four pieces?

Answers

Answer:

the pattern is 4, 13, 4, 13. I dont know what the answer choices are, but the first 4 legths put together are 34 inches.

Step-by-step explanation:

look above, hope this helps...

brainliest...

Answer:

The order of the first four strings is 1: 4in 2: 13in 3: 40in 4: 121in

a) How many possible outcomes are there when 3 coins are tossed? b) What is the probability of getting 3 heads? c) What is the probability of getting exactly one heads?

Answers

Answer:

a) there are 6 possible outcomes. b) the probability of getting 3 heads would be 3/6. c) the probability of getting 1 head is 1/6.

What is the product?

(2y +3)(3y^2+ 4y +5)

Answers

Answer:

6y^3 + 17y^2 +22y + 15

Step-by-step explanation:

Multiply each term in the first expression by each term in the second expression and combine like terms.

in the function f(x) is translated 3 units

Answers

Answer: Choice D.   -f(x-3)

==========================================================

Explanation:

Imagine that we're able to move the xy grid freely but keep the f(x) curve fixed in place. Now imagine that we move the xy grid 3 units to the left. This would give the illusion the f(x) curve moves 3 units to the right.

If we replace each input x with x-3, then that will effectively move the xy grid 3 units to the left. So that's why f(x-3) is a translation of 3 units to the right.

The negative out front will reflect the curve over the x axis. Points of the form (x,y) become (x,-y). For example, if (1,2) is on the curve then (1,-2) is on the reflected curve.

Putting this all together and it leads us to -f(x-3) which is choice D.

X-3 is the correct answers

How many dolls can Julie and Erin make with the amount of black velvet they have? Complete the model to represent the problem.​

Answers

what’s the problem? show a picture of it 15

Evaluate 5c−3d+115c-3d+115c−3d+115, c, minus, 3, d, plus, 11 when c=7c=7c=7c, equals, 7 and d=8d=8d=8d, equals, 8.

Answers

Answer:

use substitution

(5 x 7) - (3 x 8) + 11= 35 - 24 + 11= 22

Answer:

22

Step-by-step explanation:

Please help me on this problem, im struggling

Answers

Answer:

a

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

in fact if we look at the graph we can see that sausages are 7.5 % and mushrooms 5%, while in the table this datas are inverted.

Laura has a set of 16 books. Each book in the set weighs the same. One book has a weight of 0.8 kilograms (kg). Laura wants to find the total weight, w, of the set of books.Which equation and solution shows the total weight of the set of books A.
w=16×0.8w=12.8 kg, B.w=16−0.8w=15.2 kg
c.w=16+0.8w=16.8 kg D.w=16÷0.8w=20.0 kg

Answers

b will be ur answer bc the weight of set of books

find the inverse of the given function h(x) = 2x-4/3

Answers

Answer:

[tex]h^-^1(x)=0.5x+1.5[/tex]

Step-by-step explanation:

Finding the inverse of a function is similar to solving for the complete opposite of a function. An easy trick to do so is the think of the resulting value (h(x)) as another variable. Solve the equation for (x) in terms of (h(x)). Finally, switch the variable and evalutator so that one has the funciton in inverse function notation.

[tex]h(x) = 2x - \frac{4}{3}[/tex]

Inverse operations,

[tex]h(x)=2x-\frac{4}{3}\\\\h(x)+\frac{4}{3}=2x\\\\\frac{h(x)+\frac{3}{4}}{2}=x[/tex]

Simplify,

[tex]0.5(h(x))+1.5=x[/tex]

Write in inverse function notation,

[tex]h^-^1(x)=0.5x+1.5[/tex]

No files just type it in please and thank you<3

Answers

Answer:

Option C is correct

Step-by-step explanation:

[tex]8 + 8 + 8 + 8 + 8 + 8 = 48[/tex]

[tex]6 \times 8 = 48[/tex]

Hope it is helpful...

What is the value of x in the equation x-ty= 30, when y = 15?
4
8
80
200

Answers

Answer:

2

Step-by-step explanation:

Assuming that you mean x is t, then the answer is 2.

You plug in 15 for y, and you have this: 15t=30

Divided both sides by 15, and you get t = 2

35 and 50 (make a chart, list all factors, and make factor tree)

Answers

Answer:

35          50

1             2

5            5

7            10

35         25

             50

Factor Trees are in the images!

Acri invested $500 for 3 years at the rate of 2.8% per year compound interest. Calculate the final amount he has after 3 years

Answers

Answer:

[tex]A=P (1 + \frac{r}n)} ^{nt}[/tex]

A = 500(1 + .028/1)^ (3*1)

$543.19

Step-by-step explanation:

3. Find the measure of each indicated arc or the measure of an inscribed angle.

b. Find the measure of Arc BAD

Answers

Answer:

Step-by-step explanation:

Arc BAD is intercepted by inscribed angle BCD which measures 110. The rule is that an intercepted arc is twice the measure of the angle that intercepts it. Therefore, arc BAD is 110(2) which is 220.

What is the measurements for me b ?

Answers

Answer:

Step-by-step explanation:

Angle b and the one that measures 76 are vertical angles. That means that they also have the same exact angle values. Therefore, b = 76 degrees

At Mike’s Pet shop there are 300 total animals and the ratio of cats to dogs is 7:3. At Pets R Us there are 150 total animals and the ratio of cats to dogs is 6:4. What fraction of the total animals at both stores are cats? Show your work

Answers

Mikes pet shop: add the ratio: 7+ 3 = 10

Divide total animals by the sum:

300/10 = 30

The ratio of cats is 7

Total cats = 30 x 7 =210

Do the same for Pets R Us:

Ratio: 6 + 4 = 10

150/10 = 15

Cats = 15 x 6 = 90

Total cats = 210 + 90 =300

Total animals = 300 + 150 = 450

Fraction that are cats = 300/450 = 2/3

2/3 of the animals are cats

A set of weights includes an 8 lb. barbell and 6 pairs of weight plates. Each pair of plates weighs 15 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f(x) = 15x + 8. What is the range of the function for this situation?

Answers

Answer

8,98

Step-by-step explanation:

the minimum amount of weight you can use is the barbell alone which is 8lbs by itself and the maximum is 98 because there are 6 15lb plates which equal to 90lb total and when you add the 6 plates to the barbell you get 98lbs

Give the Solution to the System of
Equations shown below
YA
6
5
4
3
2
1
-4
-3
-2
10
1
2
3
-1
2

Answers

Answer:

Step-by-step explanation:

-10 g

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