The points F, G, H and I all lie on the same line segment, in that order, such that the
ratio of FG : GH: HI is equal to 3 : 2: 4. If FI = 18, find FH.

Answer:

x = 60 degrees, y = 120 degrees, z = 30 degrees

Step-by-step explanation:

To solve this problem, we must first recognize that the triangle on the left is an equilateral triangle.  This means that all of its side lengths are equal, which in turn means that all of its angles have the same measure.  Since we know the sum of the interior angles of a triangle must be 180, we can write and solve the following:

x + x + x = 180

3x = 180

x = 60 degrees

Next, we should notice that one of the 60 degree angles is supplementary with angle y, which means that their sum should equal 180 degrees.  This lets us write the following equation:

y + 60 = 180

When we subtract 60 from both sides to solve, we get:

y = 120 degrees

Finally, we should notice that the triangle on the right is isosceles.  This means that two of the side lengths (and thus two of the angles) are equal.  This means that the unmarked angle must also measure z degrees since the side lengths corresponding to these two side lengths are equal.  From this information we can write the following equation:

y + z + z = 180

If we substitute the value for y and solve, we get:

120 + 2z = 180

2z = 60

z = 30 degrees

Therefore, the correct answer is x = 60 degrees, y = 120 degrees, and z = 30 degrees.

Hope this helps!

Answer:

Step-by-step explanation:

espera y termino y te ayudo vale que me falta poco vale

Answer:

1. A is congruent to C

2. Given

3. I think line ac is congruent to line ce, don't know the options

4. angle ABC is congruent to angle DCE

5. Possibly vertical angles

Answer: D) It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

Step-by-step explanation:

slope is y2-y1/x2-x1

20-10/7-7

10/0

denominator can't be 0

Answer:

D

Step-by-step explanation:

cause i said so

Answer:

Step-by-step explanation:

[tex]a_1=35\\d=8\\\\a_n=a_1+d(n-1)\\\\a_n=35+8(n-1)\\a_n=35+8n-8\\a_n=8n+27[/tex]

Answer:

The value of f(1 + g(2)) is 5

Step-by-step explanation:

Let us solve the question

∵ f(x) = 2x - 3

∵ g(x) = x + 1

We need to find the value of f(1 + g(2))

That means we will replace x in f(x) by 1 + g(2)

→ g(2) means substitute x in g by 2

∵ g(x) = x + 1

∵ x = 2

∴ g(2) = 2 + 1

∴ g(2) = 3

∵ x of f = 1 + g(2)

∵ g(2) = 3

∴ x of f = 1 + 3

∵ x of f = 4

→ To find f(1 + g(2)) substitute 1 + g(2) by 4

∵ f(x) = 2x - 3

∵ x = 4

∴ f(4) = 2(4) - 3

∴ f(4) = 8 - 3

∴ f(4) = 5

∴ f(1 + g(2)) = 5

Answer:

27/2 or 13.5

Step-by-step explanation:

use PEMDAS

Divide the 18 by 2 then multiply by 3

Subtract 3 from 5 then divide the top 27 by the bottom 2

Answer:

the answer is 9

Step-by-step explanation:

18 divided by 2 equals 9. then 9 times 3 equals 27. 27 divides by 3 (5-2 =3) which equals 9

Answer:

graph #x

Step-by-step explanation:

where are the graphs

Given:

A number line going from negative 2.5 to positive 2.5 in increments of 0.5.

To find:

The inequality which is true.

Solution:

Consider the number line as shown in the below figure.

We know that, on a line as we go to the left direction, the number become smaller and as we go right, the numbers become larger.

From the number line it is clear that -1.5 is on the left side of 0.5. So,

[tex]-1.5<0.5[/tex]

Hence, option A is incorrect.

-0.5 is on the left side of 0. So,

[tex]-0.5<0[/tex]

Hence, option B is incorrect.

-1.5 is on the left side of -0.5. So,

[tex]-1.5<-0.5[/tex]

Hence, option C is correct.

One half is equal to 0.5.

[tex]\dfrac{1}{2}=0.5[/tex]

Hence, option D is incorrect.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the decimal number 7.7592

The value of the 7 in the ones place is 7 tens i.e 10

The value of 7 in the tenths place is 7 tenth i.e 7/10 = 7 * 1/10. The value of 7 in the tenths place is 1/10 = 0.1

Comparing both values

We will compare both values by finding their ratios as shown;

ratio = value of the 7 in the ones place/value of the 7 in the tenth place

ratio = 10/0.1

ratio = 100

Since the ratio is 100, this means that "the value of the 7 in the ones place is 100 times the value of the 7 in the tenths place"

Answer

Given the decimal number 7.7592

The value of the 7 in the ones place is 7 tens i.e 10

The value of 7 in the tenths place is 7 tenth i.e 7/10 = 7 * 1/10. The value of 7 in the tenths place is 1/10 = 0.1

Comparing both values

We will compare both values by finding their ratios as shown;

ratio = value of the 7 in the ones place/value of the 7 in the tenth place

ratio = 10/0.1

ratio = 100

Since the ratio is 100, this means that "the value of the 7 in the ones place is 100 times the value of the 7 in the tenths place"

Answer: $581

Step-by-step explanation:

given data:

Hours worked weekly(hrs) = 40

wages = $14/hr

Amount earned for overtime = 1.5 times of his hourly pay.

Solution

Amount earned for overtime

= 1.5 * $14

= $21

Amount Roberts earns in a week

= $14 * 40 + $21

= $560 + $21

= $581

Answer:

Weekly earning = 560 + 21h

Step-by-step explanation:

Given the following :

Regular Pay = $14 per hour

Work hour = atleast 40 hours per week

Overtime pay = 1.5(regular pay)

If overtime hour = h

Robert's weekly earning :

Regular pay * 40 + (overtime * 1.5(regular pay))

$14 * 40 + (h * 1.5(14))

560 + 21h

Hence,

Weekly earning = 560 + 21h

Answer:

5.5

Step-by-step explanation:

-2x + 5 = -6

subtract -5 from -6 then divide by -2

i hope i explained it well.

Answer: 5.5 is your answer.

Step-by-step explanation:

1) -2x + 5 -5 = -6 -5 <------Subtract 5 from 5 and 5 from -6.

2) -2/-2 x = -11/-2 <---------------Now divide -2 by -2 and divide -2 by -11.

3) x = 5.5 <-------------And this is your answer.

Hope this helped! Have a great day! :).

Answer:

I would use associative property and the awnser should be -29+-18= -47

Step-by-step explanation:

i hope that helps im very sorry if thats not right

If a package requires 43 cents to mail, the number of 9 cent stamps that will be needed is 41cent  is the value needed.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

Identify the question that is being asked. Write the pertinent details in straightforward statements. Give values that need to be discovered symbols. Find the mathematical connections between the assertions.

The most well-known equation in the entire universe is E=mc2. Just like that. It is succinct, elegant, and expresses a phenomenon that is so important that everyone should be aware of it.

Given,

The equation will be:

7x + 9y = 43

7(2) + 9(3) =41

14+ 27 = 41

Since the value that's is gotten not equal to 43  

Therefore  The value is  41 cent  is needed to 9 cent stamps

To learn more about mathematical equation refer to:

https://brainly.com/question/2972832

#SPJ2

Answer:

50% profit

Step-by-step explanation:

Cost price = £ 5000

Selling price = £ 7500

Profit  = Selling price - cost price

        = 7500 - 5000

       = £ 2500

Profit percentage = [tex]\frac{2500}{5000}*100[/tex]

                             = 50 %

Answer:

The equation that represents the number of flyers Max made be represented as : 4(x)

Where x is the number flyers Max put in his bag.

Hence, Max made 40 flyers.

Step-by-step explanation:

Mark divides all the flyers evenly among 4 bags, one for each person.

Let the number of flyers Max put in the bag is represented by x

The equation that represents the number of flyers Max made be represented as : 4(x)

Each bag contains 10 flyers.

= 4(10 flyers)

= 40 flyers.

Answer:

Step-by-step explanation:

The three best questions to ask would be the following

Most bank checkings account charges fees and these fees may or may not be hidden. These can include maintenance fees, overdraft fees, balance fees, etc. and can stack up if not managed correctly. Therefore it is best to know beforehand.

One of the main things that set these accounts apart between banks are the bonuses and rewards. Some banks may offer a sign-up bonus which can be 200$ or higher when opening a new account. Others may offer higher interest rates for returning customers, or even a physical reward for spending money or depositing a certain amount into the account. These are features that set the different banks apart.

Lastly, would be the interest rate. This is especially important if you have a large sum of money that will be in the account as your money can generate more money with an interest rate. Banks may offer anywhere between 1% to 3% annual interest rate. This can be a deciding factor when choosing one bank over another.

Answer:

wait isn't the answer right there-

Answer:

[tex]-5\frac{1}{2}+2\frac{1}{2}=-3[/tex]

Step-by-step explanation:

[tex]-5\frac{1}{2}+2\frac{1}{2}[/tex] or [tex](-5+2)+(\frac{-1}{2}+\frac{1}{2}) =[/tex]

[tex]-3+\frac{-1+1}{2}=[/tex]

[tex]-3+\frac{0}{2} =[/tex]

[tex]-3[/tex]

I think this is right.(✿◠‿◠)

I hope this helps! (✿◕‿◕✿)

Answer:$14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

14 x 4= 56

x³ + y³ = (x + y)(x² - xy + y²)

x³ - y³ = (x - y)(x² + xy + y²).

Proof for 1st Identity :

★ x³ + y³ = x (x² - xy + y²) + y(x² - xy + y²)

⟶ x³ + y³ = x³ - x²y + xy² + x²y - xy² + y³

⟶ x³ + y³ = x³ + y³

Proof for 2nd identity :

★ x³ - y³ = x(x² + xy + y²) - y(x² + xy + y²)

⟶ x³ - y³ = x³ + x²y + xy² - x²y - xy² - y³

⟶ x³ - y³ = x³ - y³

Let us assume that,

x = 1

y = 2

So,

✯ x³ + y³ = 1³ + 2³

⟹ (x + y)(x² - xy + y²) = 1 + 8

⟹ (1 + 2)(1² - (1)(2) + 2²) = 9

⟹ 3 * (1 - 2 + 4) = 9

⟹ 3 * 3 = 9

⟹ 9 = 9

✯ x³ - y³ = 1³ - 2³

⟹ (1 - 2) * (1² + (1)(2) + 2²) = 1 - 8

⟹ ( - 1) * (1 + 2 + 4) = - 7

⟹ ( - 1) * (7) = - 7

⟹ - 7 = - 7

Thus , they can be called as identities/formulae as they are very useful in finding the value of a certain equation or an expression easily.

I hope it will help you.

Regards.

Given :

To Find :-

Solution :-

Here , 96° & 2x° are co - interior angles and we know that the sum of co - Interior angles is 180°.

⇒ 96° + 2x = 180° .

⇒ 2x = 180° - 96° .

⇒ 2x = 84° .

⇒ x = [tex]\red{\sf \dfrac{84^{\circ}}{2}}[/tex]

[tex]\bf\longmapsto x = 42^{\circ}[/tex]

Hence value of x is 42° .

Similarly , 94° & ( 3y + 44) ° are co- interior angles

⇒ 94° + ( 3y + 44)° = 180° .

⇒ ( 3y + 44 )° = 180° - 94° .

⇒ 3y + 44° = 86°.

⇒ 3y = 86° - 44° .

⇒ 3y = 42° .

⇒ y = [tex]\sf \red{\dfrac{42^{\circ}}{3}}[/tex]

[tex]\bf\longmapsto y = 14^{\circ}[/tex]

Hence the value of y is 14°.

Complete question :

Coach Right is looking at his students' running times in order to place students into running groups. He is working on forming a group that matches Jim's pace of 4 miles in 38 minutes. Which of these student times would fit into a group that runs at the exact same rate as Jim? Prax ran 6 miles in 57 minutes. Jose ran 5 miles in 45.5 minutes. Sandy ran 7 miles in 66.5 minutes. Zynep ran 3 miles in 27 minutes

Answer:

Prax and sandy

Step-by-step explanation:

Given that:

Jim's pace = 4 miles in 38 minutes

Jim's rate = Distance covered / time.

Rate = 4 / 38 = 0.1052631 miles /min

Prax ran 6 miles in 57 minutes:

Prax rate : 6miles / 57 mins = 0.1052631

Jose ran 5 miles in 45.5 minutes:

Jose's rate = 5 miles / 45.5 = 0.1098901 miles /

minute

Sandy ran 7 miles in 66.5 minutes:

Sandy's rate = 7 / 66.5 = 0.1052631 miles / minutes

Zynep ran 3 miles in 27 minutes:

Zynep's rate : 3 / 27 = 0.1111111 miles / minutes

Answer:

I believe it would be $2 per bag normally.

Step-by-step explination:

If you take $2 and subtract $.50 it is $1.50. Take that multiplied by the number of bags he bought (4), would mean he spent $6 at Wal-mart.

Now $2 subtracted my the sale of $1, is $1 per bag. If he bought 6 bags at Kroger, 1 multiplied by 6, would equal 6. Meaning he spent $6 at both stores if the price was $2.

Answer: for number one it is t=2

And for number 2 the answer is t=1

Step-by-step explanation:

Answer: B. 2x + y = 10; 5 minutes

Answer:

It would be 12 1/2. (12.5%)

Answer:

Step-by-step explanation:

a² + b² + c² = ab + bc + ca

On multiplying both sides by “2”, it becomes

2 ( a² + b² + c² ) = 2 ( ab + bc + ca)

2a² + 2b² + 2c² = 2ab + 2bc + 2ca

a² + a² + b² + b² + c² + c² – 2ab – 2bc – 2ca = 0

a² + b² – 2ab + b² + c² – 2bc + c² + a² – 2ca = 0

(a² + b² – 2ab) + (b² + c² – 2bc) + (c² + a² – 2ca) = 0

(a – b)² + (b – c)² + (c – a)² = 0

=> Since the sum of square is zero then each term should be zero

⇒ (a –b)² = 0, (b – c)² = 0, (c – a)² = 0

⇒ (a –b) = 0, (b – c) = 0, (c – a) = 0

⇒ a = b, b = c, c = a

∴ a = b = c.

hence

a+b/b​

a+a/a= (since a=b)

2a/a=

a....