Use a substitution strategy to solve the following problem.
Two isosceles triangles have the same base length. The equal sides of one of the triangles
are 3 times as long as the equal sides of the other. Find the lengths of the sides of the triangles when
their perimeters are 34 cm and 82 cm.

Answers

Answer 1

Answer:

The length of the equal sides of the isosceles triangle with a perimeter of 34 cm perimeter is 12 cm

The length of the equal sides of the isosceles triangle with a perimeter of 82 cm perimeter is 36 cm

The base length of both triangles is 10 cm

Step-by-step explanation:

The given parameters are;

The base length of the triangles are equal

The base length of one of the triangle = The base length of the other triangle

The equal sides of one of the triangles = 3 × The length of the equal sides of the other

The perimeter of the triangles are; 34 cm and 82 cm

Let 'b' represent the base length of each triangle, let 'a' represent the length of an equal side of the smaller triangle with a perimeter of 34 cm and let 'c' represent the length of an equal side of the larger triangle with a perimeter of 82 cm

For the smaller triangle, we have;

b + 2·a = 34..(1)

For the other triangle;

b + 2·c = 82...(2)

Given that the side length of the larger triangle are larger than those of the smaller triangle, and that the side length of the larger triangle is 3 times the side length of the smaller triangle, we get;

c = 3·a

By the substitution method, from equation (2) we get;

b + 2·c = b + 2 × 3·a = b + 6·a = 82

∴ b + 6·a = 82...(3)

Subtracting equation (1) from equation (3) gives;

b + 6·a - (b + 2·a) = 82 - 34 = 48

b - b + 6·a - 2·a = 48

4·a = 48

a = 48/4 = 12

The length of the equal sides of the 34 cm perimeter (smaller) isosceles triangle, a = 12 cm

From c = 3·a, and a = 12, we get;

c = 3 × 12 = 36

The length of the equal sides of the 82 cm perimeter (larger) isosceles triangle, c = 36 cm

From equation (1), we get;

b + 2·a = 34

∴ b + 2 × 12 = 34

b = 34 - 2 × 12 = 10

The base length of both triangles, b = 10 cm


Related Questions

PLEASE ANSWER ASAP
expand and simplify the following:
a) (√6+√3)(√6-√3)
b)(√5-√2)(√2+√5)

Answers

Answer:

I've attached the Answer

Step-by-step explanation:

here it is

Answer:

[tex](\sqrt{6}+\sqrt{3})(\sqrt{6}-\sqrt{3})=3[/tex]

[tex](\sqrt{5}-\sqrt{2})(\sqrt{2}+\sqrt{5})=3[/tex]

Step-by-step explanation:

We want to simplify the expression:

[tex](\sqrt{6}+\sqrt{3})(\sqrt{6}-\sqrt{3})[/tex]

Notice that this is the difference of two squares pattern. Namely:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

If we let a = √6 and b  =√3, we acquire:

[tex](a+b)(a-b)[/tex]

Expand accordingly:

[tex]=a^2-b^2[/tex]

Back-substitute:

[tex]=(\sqrt{6})^2-(\sqrt{3})^2[/tex]

Simplify:

[tex]=6-3=3[/tex]

For the second expression, we have a similar pattern:

[tex](\sqrt{5}-\sqrt{2})(\sqrt{2}+\sqrt{5})[/tex]

We can first rewrite the expression (commutative property):

[tex]=(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})[/tex]

And if we let a = √5 and b = √2:

[tex]=(a-b)(a+b)[/tex]

Expand accordingly:

[tex]=a^2-b^2[/tex]

Back-substitute and simplify:

[tex]=(\sqrt{5})^2-(\sqrt{2})^2=5-2=3[/tex]

I don’t understand this equation please help me

Answers

Answer:

Evaluated, you get 4x^4

Step-by-step explanation:

Differentiated, you get 16x^3

It all depends on what you're looking for, really

PLWASE HELP PLEASE PLEASE

Answers

Answer:

66 in^2

Step-by-step explanation:

Imagine that the figure is a whole square, where the space between is filled in.

Find the area of the imaginary square (l x w):

9 in. x 9 in. = 81 in^2

Lets make that whole square the original figure it used to be (take away the space we “filled in”)

Lets find the area of the space we filled in:

5 in x 3 in= 15 in^2

Subtract the imaginary square’s area by the area of the space that was originally blank:

81 in^2 - 15 in^2 = 66 in^2

66 in^2 IS YOUR FINAL ANSWER, that is the real area of the composite figure you have.

Hope this helps!

Find the exact arc length of the given arc. show all work and leave terms of pi and reduce your fraction.

Answers

Answer:

20/3pi

Step-by-step explanation:

[tex] \frac{75}{360} \times 2\pi \times 16 \\ = \frac{2400}{360} \pi\\ = \frac{20}{3} \pi\\ = 20.94 \: cm[/tex]

Please give brainliest if it helps

Write an in Standard Folm given the following points:
(-2, 6), (9,8)

Answers

Answer:

2/11 x + 70/11

Step-by-step explanation:

Given the coordinate (-2, 6), (9,8), the equation in standard form is of the form y = mx+b

m is the slope = 8-6/9-(-2)

m = 2/11

Get the y-intercept

Substitute m = 2/11 and (-2, 6) into the expression y = mx+b

6 = 2/11(-2)+b

6 = -4/11 + b

b = 6 + 4/11

b = (66+4)/11

b = 70/11

Get the required equation

y = 2/11 x + 70/11

Hence the required equation is 2/11 x + 70/11

How to find the slope of a line passing through (-3,3) , (-5,9)

Answers

Answer:

slope = - 3

Step-by-step explanation:

[tex]slope, m = \frac{y_2 - y_1}{x_2 - x_ 1}[/tex]    ,    [tex][ \ (x_ 1 , y_ 1 ) = ( -3 , 3 ) , \ (x_2 , y _ 2 ) = ( - 5 , 9 ) \ ][/tex]

[tex]slope = \frac{9 - 3}{-4 - ( -3 )} = \frac{6}{-5 + 3} = \frac{6}{-2} = -3[/tex]

2 extra large chocolate shakes contain 85 ounces of ice cream. How many ounces of ice cream are there in 12 extra large chocolate shakes?

plz show work ​

Answers

Answer:

It will be 1020

Step-by-step explanation:

2 extra large = 85 ounces

multiply by 6 to get to 12 cups

85*12=1020

8p²-18p² need help from brainliest​

Answers

Answer:

- 10p2

Step-by-step explanation:

p(8p - 18 p)

p x -10p

ans = -10p2

Answer:  -10p²

This is the same as saying -10p^2

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

Explanation:

Both terms 8p² and -18p² are like terms.

We combine them in much the same way as 8-18 = -10, just with a p² attached to everything.

So 8p² - 18p²  = (8-18)p² = -10p²

The coefficient -10 is negative because we're subtracting small minus big. If it was the other way around, then we'd get a positive value.

I need to draw also no files just type it in and tell me what to draw

Answers

Answer:

Draw 8 boxes with 8 cupcakes in each one of them.

Step-by-step explanation:

34+30=64, and 64/8 also equals 64.

what is the answer
Which inequality represents the graph?

Answers

Answer:

y ≤ x - 2

Step-by-step explanation:

Using the coordinate points on the graph (0, -2) and (2,0)

The general equation of the line will be y = mx+b

Slope m = 0-(-2)/2-0

m = 2/2

m = 1

From the coordinate (0, -2), this shows that the y intercept is -3

Get the equation

y = 1x + (-2)

y = x - 2

Since the line is a thick line and shaded towards the negative y-axis, the required inequality expression will be y ≤ x - 2

The given equation has been solved in the table.
Step
Statement
1
fr – 9 = -13
RO
2
2
31
et – 9 + 9 = -13
+ 9
2
ਤੇ
3
3 = -4
3 2
3
3 .(-4)
2.32
5
6
in which step was the addition property of equality applied?

Answers

Answer:

Step 3

Step-by-step explanation:

how. to know if your data is numerical or categorical​

Answers

Answer:

See in details.

Step-by-step explanation:

Categorical data don't have any logical order and it can't be translated into a numerical value.

Numerical data are numbers and they represent some order and value.

Qualitative or categorical data have no logical order, and can't be translated into a numerical value. Eye colour is an example, because 'brown' is not higher or lower than 'blue'. Quantitative or numerical data are numbers, and that way they 'impose' an order. Examples are age, height, weight.

samantha recieved $500 as a graduation present and decided to invest it in an account that is compounded continuously. how much will be in the account at the end of 5 years if the interest rate is 3%​

Answers

Answer:

$2,226.20

Step-by-step explanation:

[tex]a_{5}[/tex] = 500e^5(0.03)

Help please giving brainly and points! :)​

Answers

Answer:

(8,5):

8 is x-axis

5 is y-axis

(8,5) yeeeeeettttttttttr

A Sanddune stands 5 feet above sea level the hill is eroding at a rate of 1 foot/ 20 years light wire represent the height of the Sandune after X years which represents the situation

Answers

Answer:

x is equal to 12 which represents the situation

Here is some information about a holiday.

7 night holiday
$340 per person
8% discount if you book before 31 March

On 15 February, Naseem books this holiday for 2 people.
Calculate the total cost of his holiday.

Answers

Answer:

$625.6

Step-by-step explanation:

Information about a holiday:

7 night holiday

$340 per person

8% discount if you book before 31 March

Number of people Naseem booked the holiday for = 2

Date of booking of the holiday = February 15

Total cost of the holiday per person = cost per person - discount before March 31

= $340 - 8% of $340

= 340 - 8/100 * 340

= 340 - 0.08 * 340

= 340 - 27.2

= $312.8

Total cost of the holiday for 2 persons = 2 × Total cost of the holiday per person

= 2 * $312.8

= $625.6

Question 1: Given the following expression
6 - 3w – w4
Classify the polynomial
Monomial
Binomial
Trinomial

Answers

The answer is a trinomial because there are 3 expressions

At which angle will the hexagon rotate so that it maps
onto itself?
O 60°
90°
0 120°
O 180°

Answers

Answer:

60 degress

Step-by-step explanation:

Edgen 2021

60° is the angle at which the hexagon rotate so that it maps onto itself.

What is Polygon?

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.

When a figure has a rotational symmetry, it maps onto itself under rotation about a point at the centre.

When an hexagon rotate onto itself,the vertices must cover to vertices and from sides to sides.

There are six angles in a hexagon and the sum of the angles is 360°. Therefore, each angle has a measure of 360°/6 is equal to 60°.

Rotating subsequently by 60 degree will rotate a hexagon onto itself. A hexagon has 6 rotations, that is, a hexagon has a rotational symmetry of 6 and at angle 60°, the hexagon will rotate onto itself.

Hence,  60° is the angle at which the hexagon rotate so that it maps

onto itself.

To learn more on Polygons click:

https://brainly.com/question/24464711

#SPJ7

What is the value of x?

2
3
6
7

Answers

Answer:

x = 2

Step-by-step explanation:

AE is equal to the sum of AB and BE because of segment addition postulate, we can substitute to get AE = 11 + x + 1 = x + 12

DE is equal to the sum of DC and CE because of segment addition postulate, we can substitute to get DE = 1 + x + 4 = x + 5

To solve the problem, we can use power of a point, more specifically exterior secants products scenario. In this case, we can get the equation:

AE * BE = DE * CE

Now, we can substitute and solve:

(x + 12)(x + 1) = (x + 5)(x + 4)

x^2 + 13x + 12 = x^2 + 9x + 20

13x + 12 = 9x + 20

4x + 12 = 20

4x = 8

x = 2

This is correct it would. Be 2 and. The explanation was spot on

correct answer will get brainliest.

31.
At noon, the temperature at a mountaintop research center is 11 degrees. Overnight the temperature drops to -19 degrees. Which expression represents how much the temperature changed?

a. |19|

b. |-19|

c. |-30|

d. |-38|

Answers

Answer:

c. |-30|

Step-by-step explanation:

It wants the change from 11 to -19. While normally absolute value is the distance from zero, zero can be shifted. Depending on where you are in learning about absolute value, the midway point can change from zero to, say, 4. This is called a transformation and is typically represented on a graph. Simple answer is that zero is shifted to 11. Therefore, absolute value changes from distance away from zero, to distance away from 11.

I hope this helped :)

John measured two pieces of string. One piece measured 7/12 m and the other measured 4/7 m.

Select the true statement about the lengths of John's string.

Answers

1) 7/12= 0.58, 4/7= 0.57

they are about 1/2

2) 7/12 + 4/7 = 97/84= 1.15 approximately 1

which is 1m from the option

did I do this right??

Answers

Answer:

yes.

Step-by-step explanation:

it is correct

Answer: Yes, this is correct.

What is the factored form of 3x+24y?

Answers

Answer: the factored form of 3x+24y is 3(x+8y) 3(x+8y)

can you guy's help me quick!

Answers

Answer:

480,700 sets (first choice)

Step-by-step explanation:

If all 25 questions are different,

When order of selection counts:

P(25,7)

= 25!/(25-7)!

= 15511210043330985984000000/6402373705728000

= 2422728000

When order of selection does not count count:

C(25,7)

=25!/(7!*(25-7)!)

=15511210043330985984000000/(6402373705728000*5040)

= 480,700

Hope this helps, have a nice day.

What is the answer and explain why

Answers

Answer:

20

Step-by-step explanation:

Take note of the important information/key words:

60 total ornaments

3 grandchildren

Divide them evenly

Set up an equation:

60 ornaments ÷ 3 grandchildren = ornaments per grandchild

60 ÷ 3 = 20 ornaments per grandchild.

In other words, each grandchild will receive 20 ornaments.

60 PTS PLS ANSWER WILL AWARD BRAINLIEST ASAP

Answers

Answer:

9. a) 180 - (55+90) = a

b) a=35 degrees

10. a) 2w + 3w + 40 = 180

b) w=28

c) 2w=56      3w=84

Step-by-step explanation:

Answer:

the person above is 100% right trust me :)

Step-by-step explanation:

Fly the super spy is trying to unravel a secret 3 digit code. Fly knows that the first digit must be an even number, an the last must be an odd number. How many differnt combinatons of the threendigit code exist. ( Note; zeto is counted as an even number)

Answers

Answer:

250

Step-by-step explanation:

Given

[tex]n =3[/tex] --- digit code

[tex]First = Even[/tex]

[tex]Last=Odd[/tex]

Required

The different combination of codes

The set of even number is:

[tex]Even = \{0,2,4,6,8\}[/tex]

The set of odd is:

[tex]Odd = \{1,3,5,7,9\}[/tex]

This means that:

The first can be any of the 5 even digits

The last can be any of the 5 odd digits

Since there is no restriction in selection;

The [tex]second[/tex] can be [tex]any[/tex] of [tex]the[/tex] 10 digits

So, the possible combination (k) is:

[tex]k =5 * 10 * 5[/tex]

[tex]k =250[/tex]

59.73 - 21.876
can u help me​

Answers

Answer:

37.854

Step-by-step explanation:

59.73-21.876=37.854

What is the result if -8ײ +24× divided by -4×

Answers

-4x(2x-6)
-4x+2(x-3)
-4(x+2)(x-3)


Explain too please !!!!!!!!!!!!!!!!!!

Answers

Answer:

4th Option isn't a function

Step-by-step explanation:

it is because a domain can't have two images in the co domain set

Hope it helps

Please mark as brainliest

Answer:

"D" (the fourth one....(7,1),(6,2)....

a "function" is a very specific relationship in math...

for a relationship to be "a function" every possible INPUT (x-values) has to map (correspond) to a UNIQUE output value (Y-value)

a line is a function (all x's have unique y values.

A circle is NOT ..... at the center (x-value) there are two y values (one above and one below)

in your problem answer "D" the "x-value" "5" has two different "y-values"

3 and 4

Step-by-step explanation:

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