The three angles of a triangle measure x,y and 39. What is the equation to solve ?

The statement that best describes the relationship between the two triangles is the option;

Two triangles are similar if they satisfy the following conditions.

The length of the sides of the triangles are;

First triangle, a₁ = 3, b₁ = 5. c₁ = 15

Second triangle. a₂ = 9, b₂ = 6, c₂ = 18

The ratio of the corresponding sides is therefore;

[tex]\dfrac{a_1}{a_2} = \dfrac{3}{9} =\dfrac{1}{3}[/tex]

[tex]\dfrac{b_1}{b_2} = \dfrac{5}{6}[/tex]

[tex]\dfrac{c_1}{c_2} = \dfrac{15}{18} =\dfrac{5}{6}[/tex]

The ratio of the three corresponding sides of the triangles are not the same such that the corresponding sides of the triangles are not constantly  proportional.

Therefore the two triangles are not similar because all the corresponding sides are not proportional.

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Answer:

3x-3:

(1/3)(9x-9)

(9/2x - 2) -(3/2x +1)

(3/2x-2) + (3/2x-1)

2x-1:

(7/2 x -2) - (3/2 x - 1)

1/2(4x-2)

Step-by-step explanation:

(7/2 x -2) - (3/2 x - 1)

7/2 x -2 -3/2 x +1 Distribute the negative sign to both terms

4/2 x -1 Combine like terms

2x-1

(1/3)(9x-9)

3x-3 Distributive property

(9/2x - 2) -(3/2x +1)

9/2x -2 -3/2x -1 Distribute negative sign

6/2x -3

3x-3

(3/2x-2) + (3/2x-1)

3/2x -2 +3/2x -1 Can just get rid of parenthesis since everything is added.

6/2x -3

3x-3

1/2(4x-2)

2x-1 Distribute the 1/2 to both numbers

Answer:

z = 4

Step-by-step explanation:

7z - 4 = 12 + 3z

1) We want to first move the z values to one side of the equation. This means we would subtract 3z from both sides to move it to the left side. This would give us 4z - 4 = 12.

2) We then want to isolate the z value. This means we want to move the -4 to the right side. We would add 4 to both sides and get 4z = 16.

3) We can then divide both sides by 4 and get the value for z.

This gives us z = 4.

The length of each factory worker on average is 25.57 lengths

From the question, we have the following parameters that can be used in our computation:

Total length of the pool = 179 lengths

Number of workers = 7

The length of each on average is calculated as

Average length = Total length of the pool/Number of workers

Substitute the known values in the above equation

So, we have the following equation

Average length = 179/7

Evaluate the quotient

Average length = 25.57

Hence, the average length is 25.57 lengths

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The expanded form of  7(7a + 4b) + 10a - 10b and 6(2x+6y) will be 59x+18b and 12x+12y.

The expanding form can be used to indicate the value of each digit in a number in arithmetic. Numbers that are expressed as the sum of each digit multiplied by its place value are known as expanded numbers.

It is given that,

a) 7(7a + 4b) + 10a - 10b

b) 6(2x+6y) -

a)

[tex]=7(7a + 4b) + 10a - 10b \\\\ =49a+28b+10a-10b \\\\ =49a+10a+28b-10b \\\\ =59a+28b-10b \\\\ =59a+18b[/tex]

b)

= 6(2x+6y) -

=12x+12y

Thus, the expanded form of  7(7a + 4b) + 10a - 10b and 6(2x+6y) will be 59x+18b and 12x+12y.

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Answer:

for 20 miles per hour

Step-by-step explanation:

.

Answer:

x = 12

Step-by-step explanation:

if l and m are parallel that means that since the two angles are consecutive interior they add to 180

so add them both and set that to 180

9x - 4 + 5x + 16 = 180

now combine like terms

14x + 12 = 180

subtract 12 from both sides

14x = 168

divide everything by 14

x = 12

that is the answer

Answer:

Step-by-step explanation:

Let's find x:-

[tex]\sf 9x-4+5x+16=180^o[/tex]

Combine like terms:-

[tex]\sf 9x+5x-4+16=180[/tex]

[tex]\sf 14x-4+16=180[/tex]

[tex]\sf 14x+12=180[/tex]

Add/Subtract numbers:-

[tex]\sf 14x+12-12=180-12[/tex]

[tex]\sf 14x=168[/tex]

Divide both sides by 14:-

[tex]\sf \cfrac{14x}{14}=\cfrac{168}{14}[/tex]

[tex]\sf x=12^o[/tex]

__________________

Hope this helps!

Have a great day!

Answer:

19 liters

Step-by-step explanation:

a) The value  sets of n(A) = 5, n(B) = 8

b)  33 ∈ A is false, -4 ∈ B is true, 25 ∈ A is true, 5 ∉ B is true.

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.

A = { 25, 26, 27, 28, 29}

B ( is greater or equal to -6 and equal to 1) = { -6, -5, -4, -3, -2, -1, 0, 1}

n(A) = number of elements in A which is 5 and n(B) = 8

33 ∈ A The symbol ∈ means element of. so 33 is not an element of A.

-4 is an element of B so it is true, -4 ∈ B is true

25 ∈ A is true because 25 is an element of A

5 ∉ B is true because 5 is not an element of B

In conclusion, n(A) = 5, n(B) = 8

-4 is an element of B so it is true, -4 ∈ B is true

25 ∈ A is true because 25 is an element of A

5 ∉ B is true because 5 is not an element of B

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Answer:

x = -11

Step-by-step explanation:

2x - 7 = 3x - 2x - 18

2x - 7 = x - 18

collect like terms

2x - x = 7 - 18

x = -11

Answer:

60 ways;

GOOD LUCK!

Step-by-step explanation:

The word CHEWY has 5 letters, Therefore, it can be arranged in 5!/2! = 120/2 = 60 ways.

Answer:

v = 99

Step-by-step explanation:

given v varies directly as g then the equation relating them is

v = kg ← k is the constant of variation

to find k use the condition v = 36 when g = 4 , then

36 = 4k ( divide both sides by 4 )

9 = k

v = 9g ← equation of variation

when g = 11 , then

v = 9 × 11 = 99

Answer:

[tex] \sf Root \: of \: x \: are \: \dfrac{3}{2} \: and \: \dfrac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]

Step-by-step explanation:

[tex] \rm \implies 8 {x}^{3} - 27 = 0 \\ \\ \rm \implies (2 \times 2 \times 2) {x}^{3} - (3 \times 3 \times 3) = 0 \\ \\ \rm \implies {(2x)}^{3} - {3}^{3} = 0 \\ \\ \boxed{ \rm {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )} \\ \\ \rm \implies (2x - 3)( {(2x)}^{2} + (2x)(3) + {3}^{2} ) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: and \: 4 {x}^{2} + 6x + 9 = 0 \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{36 - 144} }{8} \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]

Two times or Twice the sum of a number and 3 is 8. The value of the number will be 1.

Let the value of the unknown number or variable be c.

Given,

"Two times the sum of a number and 3 is equal to 8", which means when you add the unknown number with 3 and then multiply it by 2, then the final answer will come as 8.

If we form the statement into an equation, then finding the value of the unknown variable will be a lot easier.

The equation will be:

    2(c + 3) = 8

=> 2c + 6 = 8

=> 2c = 8- 6

=> 2c = 2

=> c = 2/2

=> c = 1.

Hence, the value of the unknown number c will be 1.

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1) Option 3 had the least amount invested. The investment plan was to invest a certain amount in the beginning and let it grow at an interest of 6.25% APR compounded monthly for 30 years.

2) Option 2 yielded the highest amount at the end of 30 years. The plan was to invest $75/quarterly i.e, $25/monthly at an interest of 4.00% APR compounded monthly for 30 years.

3) Difference in principle is $8000 and the difference is interest is $2976.83

4) It is better to invest more at the end of 30 years.

Define interest.

When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The loan's interest rate is denoted by this proportion.

Solution Explained:

First, let's calculate the amount after adding the compound interest using

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex], where P is principal, r = interest rate, n = number of times interest is compounded monthly, and t = time

After calculation (For Op 1 and 2, the principal is $9000 and 3 is $1000)

Option 1 has $15275.50
Option 2 has $17467
Option 3 has $6489.17

Interest for Option 1 = $6275.50
Interest for Option 2 = $8466
Interest for Option 3 = $5489.17

After this solving the questions will be easy to understand.

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Answer:

contributions:
1 $25/ month at a rate of 3.25% APR
2 $75/ quarter at a rate of 4.00%
3 $1,000 at a rate of 6.25% APR

total interest rate:

1 $6275.50

2 $8466

3 $5489.17

final balances:

1 $15275.50

2 $17467

3 $6489.17

questions 1-4

1: Option 3 had the least amount invested

2: option 2
3: Difference is $8000 – and interest difference in $2976.83

4: it’s better to invest more at the end of 30 years

Step-by-step explanation:

i did the assignment

The amount of money that Katelyn’s brother borrowed for school would be = $ 2,000.

Interest in the amount of money that an individual pays in extra with a borrowed amount of money either from an individual or from the bank.

The formula for simple interest= Principal ×Time × Rate/100

Rate of payment= 6%

Time = 6 years

Simple interest = $720

Principal= X

From the formula above, make principal the subject of formula;

Principal = SI × 100/ T× R

= 720 × 100/ 6×6

= 72000/36

=$ 2,000

Therefore, the amount of money that Katelyn’s brother borrowed for school is $2,000.

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The function is positive and increasing from 0 to 2.5, at negative and decreasing  from 0 to -2.5,  respectively.

How to find returns to scale?

Returns to scale involves an increase in an output more than when all the inputs increase proportionately.

Using the graph, there is a line segment from the origin to a point. at the middle of the third block making 2.5.  this shows an increase which is positive and on the other hand, there is a line segment from the origin towards left hand side on the number line showing a decrease and a negative from 0 to -2.5.

In conclusion, the line pointing upwards towards right hand side shows both positive and increase while the line pointing leftward shows decrease and negative.

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Answer:

  x = 2

Step-by-step explanation:

You want x such that dividing by 5 and then adding 2 gives the same outcome as adding 22 and then dividing by 10.

  (x/5) +2 . . . . the value after dividing by 5 and adding 2

  (x +22)/10 . . . . the value after adding 22, then dividing by 10

These two outcomes are the same:

  x/5 +2 = (x +22)/10

Multiplying the equation by 10 gives ...

  2x +20 = x +22

  x = 2 . . . . . . . . . . . . subtract x+20

The number is x = 2.

__

Additional comment

The outcome in each case is 2.4.

Answer: [tex]6/(x-7) +( -5)/(x-5)[/tex]

Step-by-step explanation:

Let

   [tex](x+5)/(x-7)(x-5) = A/(x-7) +B/(x-5)[/tex]

⇒[tex](x+5)/(x-7)(x-5)=( A(x-5) +B(x-7))/(x-7)(x-5)[/tex]

Comparing both the sides

[tex](x+5)= A(x-5)+B(x-7)\\x+5=Ax-5A+Bx-7B\\x+5= (A+B)x + (-5A-7B)\\[/tex]

Comparing both sides of the equation we get,

[tex]A+B= 1[/tex]   ....eq(1)

[tex]-5A-5B=5[/tex]   ..... eq(2)

solving eq(1) and eq(2),

we get B=-5 and A=6.

Hence the solution is [tex]6/(x-7) +( -5)/(x-5)[/tex]

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Answer:

h(x)= |x-3|-4

Step-by-step explanation:

If f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4

The function is given

f(x) = |x|

Translation of the shape mean the displacement of the shape from one place  to another place. Some usually used displacements are shifted to right / left and shifted to up / down etc.

First f(x) is shifted down 4

Then the function will become

f(x) = |x| - 4

Then the function shifted right 3

Then the function will be

h(x) = |x - 3| - 4

Hence, if f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4

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The amount of interest to be charged on the note, based on the face value of the note, is $302. 22.

The amount the borrower would receive is $16, 697. 78.

The interest charged on the simple discount note can be found by the formula:

= Face value of note x discount rate x number of days / total days in a year

= 17, 000 x 4% x 160 / 360

= $302. 22

The amount that the borrower would receive is then:

= Face value of note - Interest charged on note

= 17, 000 - 302.22

= $ 16, 697. 78

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They joined together to resist the attempts of Europeans to change them.

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Answer:

2x – 4 – 1 + x

Step-by-step explanation:

Answer:

Step-by-step explanation:  -15

Answer:

y = 3x + 12

Step-by-step explanation:

y = mx + b  
The m is the slope and the b is the y intercept.

Slope:

Change in y over the change in x.  The ordered pair is written in the form (x,y)

[tex]\frac{12-3}{8-5}[/tex] = [tex]\frac{9}{3}[/tex] = 3

The slope is 3.

Use the slope of the 3 and the x and y from one of the ordered pairs given.  I am going to use the point (5,3), but either point will work

slope 3

x = 5

y=3  Plug these all in and solve for b

y = mx + b

3 = (3)5 + b

3 = 15 + b  Subtract 15 from both sides

-12 = b

This is the y intercept

y = 3x - 12

Answer:

Slope-intercept form,

→ y = 3x - 12

Step-by-step explanation:

Formula we use,

→ y = mx + b

The value of slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (12 - 3)/(8 - 5)

→ m = 9/3

→ [ m = 3 ]

Then the value of b will be,

→ y = mx + b

→ 12 = (3)8 + b

→ b + 24 = 12

→ b = 12 - 24

→ [ b = -12 ]

Now the slope-intercept form is,

→ y = mx + b

→ [ y = 3x - 12 ]

Hence, the answer is y = 3x - 12.

Step-by-step explanation:

to find the perimeter first:

13×3=39

13×3=39

5×3=15

5×3=15

39+39+15+15=108

P=108

i hope it's useful