In triangle FGH, if the measure of angle G is five less than twice the measure of angle F and the measure of angle H is eighteen less than four times the measure of angle F, find the measure of angle G.

Answers

Answer 1

Answer:

The measure of angle G is [tex]53\°[/tex]

Step-by-step explanation:

Let

F ----> the measure of interior angle F of the triangle FGH

G ---> the measure of interior angle G of the triangle FGH

H ---> the measure of interior angle H of the triangle FGH

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

[tex]F+G+H=180\°[/tex] ----> equation A

[tex]G=2F-5[/tex] ----> equation B

[tex]H=4F-18[/tex] ----> equation C

Solve the system of equations by substitution

substitute equation B and equation C in equation A

[tex]F\°+(2F-5)\°+(4F-18)\°=180\°[/tex]

Solve for F

[tex]7F-23=180[/tex]

[tex]7F=180+23[/tex]

[tex]F=29\°[/tex]

Find the measure of angle G

[tex]G=2F-5[/tex]

substitute the value of F

[tex]G=2(29)-5=53\°[/tex]

Answer 2

The measure of angle G in triangle FGH is [tex]\( 53^\circ \).[/tex]

1. Define Variables:

  - Let the measure of angle F be [tex]\( x \).[/tex]

  - The measure of angle G is given as "five less than twice the measure of angle F," so [tex]\( G = 2x - 5 \)[/tex].

  - The measure of angle H is given as "eighteen less than four times the measure of angle F," so [tex]\( H = 4x - 18 \).[/tex]

2. Use the Triangle Angle Sum Property:

  - The sum of the angles in a triangle is always [tex]\( 180^\circ \)[/tex]. Therefore:

  [tex]\[ F + G + H = 180^\circ \][/tex]

3. Substitute the Expressions:

  - Substitute F = x , G = 2x - 5 , and  H = 4x - 18  into the equation:

  x + (2x - 5) + (4x - 18) = 180

4. Combine Like Terms:

  x + 2x - 5 + 4x - 18 = 180

  7x - 23 = 180

5. Solve for x :

  - Add 23 to both sides of the equation:

  7x = 203

  - Divide by 7:

  x = 29

6. Calculate the Measure of Angle G:

  - Use the expression G = 2x - 5 :

  G = 2(29) - 5 = 58 - 5 = 53°

7. Verify the Measures:

  - Calculate F  and H  using x = 29 :

  F = 29°

  H = 4(29) - 18 = 116 - 18 = 98°

  - Check the sum:

  F + G + H = 29 + 53 + 98 = 180°

  The sum is correct, confirming the calculations.

Thus, the measure of angle G in triangle FGH is [tex]\( 53^\circ \).[/tex]


Related Questions

Nancy can type 240 words in 6 minutes. How many words can she type in 1 minute?

Answers

Answer:

The answer is 40

Step-by-step explanation:

Divide 240 by 6 and you'll get 40 as your answer

Answer:

She can type 40 words in 1 minute

Step-by-step explanation:

Just do 240/6 equals 40 so that means every 1 minute is 40 words 40 words times 6 minutes is 240 words

7. Use mental math
28% of 100

Answers

Answer:

28/100 x 100= 28

Answer:

28% divided by 100 = 28

Brainly please?

Leona purchased a $1,000 bond having a quoted price of 99.875. She had to pay a 5.5% brokerage fee (of the selling price). What was the total cost of the bond (to the nearest whole cent)?

$943.82
$1,064.44
$534.77
$2,054.22
None of these choices are correct.

Answers

Final answer:

The total cost of Leona's bond is $1,053.68 when accounting for the quoted price and the 5.5% brokerage fee. Consequently, the option that correctly represents the total cost is 'None of these choices are correct.'

Explanation:

Leona purchased a $1,000 bond having a quoted price of 99.875. To calculate the purchase price of the bond, we multiply the face value of the bond by the quoted price percentage:

Purchase Price = Face Value × (Quoted Price / 100) = $1,000 × (99.875 / 100) = $998.75

Next, we need to calculate the brokerage fee, which is 5.5% of the selling price. We will use the purchase price to calculate this:

Brokerage Fee = Purchase Price × (Brokerage Fee Percentage / 100) = $998.75 × (5.5 / 100) = $54.93

Lastly, we add the brokerage fee to the purchase price to find the total cost of the bond:

Total Cost = Purchase Price + Brokerage Fee = $998.75 + $54.93 = $1,053.68

Therefore, Leona's total cost for the bond is $1,053.68, which to the nearest whole cent is $1,053.68. The correct answer is 'None of these choices are correct.'

Final answer:

Leona's total cost for a $1,000 bond with a quoted price of 99.875 and a 5.5% brokerage fee is $1,053.68. Option E.

Explanation:

To calculate the total cost of the bond that Leona purchased, we need to consider both the quoted price of the bond and the brokerage fee. The quoted price of the bond is 99.875% of the face value, which means the price before the brokerage fee is 99.875/100 * $1,000 = $998.75. Then, we must calculate the brokerage fee, which is 5.5% of the selling price. Therefore, the brokerage fee equals 5.5/100 * $998.75 = $54.93.

To find the total cost of the bond, we add the price of the bond to the brokerage fee: $998.75 + $54.93 = $1,053.68. Hence, the correct answer to the nearest whole cent is $1,053.68, and the given options do not list this correct amount.

(4,7) and (5,1) as an equation

Answers

Answer:

y = -6x + 31

Step-by-step explanation:

In order for us to make this an equation of the form y = mx + b we have to find the slope.

The formula for slope is rise/ run. The rise is 6 and the run is -1.

So, the slope is 6/-1 or -6.

Our equation is now: y = -6x + b

Substituting 4,7 into the equation we get 7 = -24 + b

So, b = 31.

To check out answers we substitute 5,1 in and it works.

What sum is represented by the following number line?

Answers

Answer:

Step-by-step explanation:

B

Answer:

It Is B guys

Step-by-step explanation:

Robert's father is 4 times as old as Robert.After 5 years ,father will be three times as old as Robert. What is their present ages of Robert and his father respectively .​

Answers

Answer:  

Their present ages are:

Robert is 10 years old and his father is 40 years old.

Step-by-step explanation:

Let be "r" Robert's present age and "f" his father's present age.

Based on the information given in the exercise, you can set up the following system of equations:

[tex]\left \{ {{f=4r} \atop {f+5=3(r+5)}} \right.[/tex]

Use the Substitution Method and substitute the first equation into the second one and then solve for "r":

[tex]4r+5=3(r+5)}\\\\4r+5=3r+15\\\\4r-3r=15-5\\\\r=10[/tex]

Substitute the value of "r" into the first equation and evaluate:

[tex]f=4(10)\\\\f=40[/tex]

hot air balloon is in the shape of a sphere .find the volume of a hot air balloon that is 32 ft in diameter​

Answers

Answer:

Search Results

Sphere

Solve for volume

V≈17157.28

Step-by-step explanation:

three sister are getting new outfits. shirts cost 11 each,skirts coat 25 each and shows cost 44 a pair what is the total coast of the new outfits for all of the sisters​

Answers

Answer:

240.

Step-by-step explanation:

Here is the correct question: Three sister are getting new outfits. shirts cost 11 each,skirts coat 25 each and shoes cost 44 a pair. what is the total cost of the new outfits for all of the sisters​?

Given: Cost of each shirt is 11

           Cost of each skirts coat is 25

           Cost of each pair of shoes cost is 44.

Now, finding total cost of shirt, skirt coat and shoes as cost of one new outfit.

= [tex]11+25+44 = 80[/tex]

∴ Total cost of one new outfit is 80.

Next, finding cost of new outfit for all, three sisters.

Cost of new outfit for three sister = [tex]\textrm { cost of one outfit}\times \textrm{ number of sisters}[/tex]

∴ Cost of new outfit for three sister = [tex]80\times 3= 240[/tex]

240 is the total cost of new outfit for all the sisters.

         

A fair coin is tossed in the air four times. If the experimental probability of landing on tails is 1/4, then what is the difference between the experimental and theoretical probability?

Answers

Answer: 1/4

Explanation:

You flipped the coin 4 times and got only one tail in those four flips. So that's where the 1/4 comes from when you state the experimental probability of tails is 1/4.

The theoretical probability of tails is 1/2 assuming it's a fair coin, as each side is likely to land on. The theoretical probability is one that can be calculated without having to do the experimental trials.

Subtract the two fractions: 1/2 - 1/4 = 2/4 - 1/4 = (2-1)/4 = 1/4

Final answer:

The difference between the experimental (1/4 or 0.25) and theoretical (0.5) probability of a coin landing on tails after four tosses is 0.5 - 0.25, which equals to 0.25 or 25%.

Explanation:

The difference between the experimental and theoretical probability of landing on tails when a fair coin is tossed four times is sought after. The theoretical probability of a coin landing on tails is 0.5 for each toss. If a student conducts an experiment where the coin lands on tails with a probability of 1/4, we first convert this to a decimal to compare it to the theoretical value, which is 0.25.

To find the difference, subtract the experimental probability from the theoretical probability:

Theoretical Probability: 0.5 (or 1/2)
Experimental Probability: 0.25 (or 1/4)

Difference = Theoretical Probability - Experimental Probability

Difference = 0.5 - 0.25

Difference = 0.25

Thus, the difference between the experimental and theoretical probability is 0.25, or 25%.

Which function represents the graph of y=10(4)x ? PLEASE HELP! :)



f
g
h
j

Answers

Answer:

The answer is g.

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: 40

y-intercept: 0

x : 0, 0

y : 0, 0

Hope this helps!

Answer:

Answer:

The answer is g.

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: 40

y-intercept: 0

x : 0, 0

y : 0, 0

Hope this helps

Step-by-step explanation:

This was tuff but i managed to get the answer ur welcome

Scientists have discovered a new substance with a hydrogen ion concentration of 0.095811180 M. Determine the corresponding pH level for this new substance. Round your final answer 3 decimal places

Answers

Answer: 1.018

Step-by-step explanation:

The pH level of a substance indicates the concentration of hydrogen ions ([tex]H^{+}[/tex]) in a solution and is calculated by:

[tex]pH=-log(H^{+})[/tex]

In this case the hydrogen ion concentration is [tex]0.095811180 M[/tex], where

[tex]M=\frac{moles}{volume}[/tex]. Hence:

[tex]pH=-log(0.095811180 M)[/tex]

[tex]pH=1.018[/tex] This means this new substance is acid


Which system of equations has infinitely many solutions?
A)6x + 3y = 12
3x + y = 9
B)2x + 3y = 6
4x + y = 8
C)12x +9y = 6
4x + 3y = 6
D)5x + 10y = 20
2x+4y=8​

Answers

The answer is D.

Divide the first equation by 5 to get
x + 2y = 4

Divide the second equation by 2 to also get
x + 2y = 4

Since they are the same equation it results in an answer that has infinitely many solutions.
D)
If you multiply 5x+10y=20 by 2 and 2x+4y=8 by 5 that are equal

24 tenths minus 1 one and 3 tenths?

Answers

Answer:   " 1. 1 "  ;  or,  write as:  " 1 [tex]\frac{1}{10}[/tex] "  .

________________________________________________

Step-by-step explanation:

________________________________________________

(24/10) -  1  3/10  =

2 4/10 -  1  3/10 =

2.4  -  1.3  =

_______________________

   

    2. 4

 -  1.  3

___________

    ?  

______________________________

    2. 4

 -  1.  3

___________

   1 .  1

______________________________

The answer is:   " 1. 1 "  ;  or,  write as:  " 1 [tex]\frac{1}{10}[/tex] "  .

_______________________________

An ice cream store sells 2drinks, in 5 sizes, and 5 flavors. In how many ways can a customer order a drink?  

Answers

Answer:

2*5*5= 50 because for each drink (2) there’s (5) different sizes and (5) flavors.

Step-by-step explanation:

Final answer:

A customer at an ice cream store can order a drink in 50 different ways by choosing from 2 drinks, 5 sizes, and 5 flavors, as calculated by the fundamental counting principle.

Explanation:

To determine the number of ways a customer can order a drink at an ice cream store with 2 drinks, 5 sizes, and 5 flavors, we need to calculate the combinations of these options. Since each choice is independent of the others, we use the concept of the fundamental counting principle, where we multiply the number of options for each category together.

For drinks, there are 2 options. For sizes, there are 5 options, and for flavors, there are 5 options.

We multiply these options together: 2 drinks * 5 sizes * 5 flavors = 50 combinations.

Therefore, a customer can order a drink in 50 different ways.

what is the surface area of a cylinder with the hight of 7 and the diameter of 9​

Answers

Answer:

Step-by-step explanation:

for this, you need to remember a formula for the curved bit of the cylinder. The top and the bottom circles are easy since you only need to find their areas which are πr^2 therefore to find the radius you half 9. So 4.5^2 x π =63.62 then times two as there are two parts.

63.62 x 2 =127.24

For the curved, long bit use formula of 2πhr.

2 x π x 7 x 4.5 =63π =197.92

help me solve this please​

Answers

Answer:

x= -6

Step-by-step explanation:

First, you would write down the equation how it is shown first.

1) -x/3=2

Second, you would naturally multiply both sides by -3. To solve the equation, you need to use the inverse operation in the inverted order of PEMDAS. (Parentheses, exponent, multiplication, division, addition, and subtraction.)

2) -3(-x/3)=-3* 2

Lastly, you are going to reduce and simplify your new equation. This last step will achieve you your desired answer.

3) x= -6

6/3=2

Step-by-step explanation:

I know because 2×3=6 so 6/3 would have to equal 2.

I’m not sure how to graph linear equations on a graph. We are learning slope and linear equations and I’m so confused. Could someone help me understand or give a resource that will help me?

Answers

Answer:

Step-by-step explanation:

Desmos is a great online calculator, and when you put in a line, you can personalize it to the way you like it, making learning much easier, plus it gets your homework done quicker! the url is desmos . com

What is the slope of this line?

15

−15

5

−5

Answers

Answer:

the slope is 1/5 which is none of these. y=1/5x+3 is the equation

Step-by-step explanation:

for every single y value that the graph goes up, it travels 5 units on the x axis.

rise over run is the way i remeber slope, rise is one for every 5 run. This has a slope of positive 1/5x.

The slope of the line is [tex]\dfrac{1}{5}[/tex]. So, the correct option is A.

Given:

The graph of the line.

To find:

The slope of the given line.

Explanation:

Slope formula: If a line passes through the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of the line is:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the given graph it is clear that the line passes through the points [tex](0,2)[/tex] and [tex](5,3)[/tex]. So, the slope of the line is:

[tex]m=\dfrac{3-2}{5-0}[/tex]

[tex]m=\dfrac{1}{5}[/tex]

Therefore, the slope of the line is [tex]\dfrac{1}{5}[/tex] and the correct option is A.

Learn more:

https://brainly.com/question/19227805

Complete the solution of the equation. Find the
value of y when x equals 24.
-2x + 2y = -56

Answers

Answer:

For x = 24, y = -4.

Step-by-step explanation:

[tex]Put\ x=24\ to\ the\ equation\ -2x+2y=-56,\ and\ solve\ it\ for\ y:\\\\-2(24)+2y=-56\\\\-48+2y=-56\qquad\text{add 48 to both sides}\\\\-48+48+2y=-56+48\\\\2y=-8\qquad\text{divide both sides by 2}\\\\\dfrac{2y}{2}=\dfrac{-8}{2}\\\\y=-4[/tex]

Jon borrows $6.50 from his friends to pay for snacks, and $11.75 from his sister to go to the movies. how much money does he need to repay

Answers

Answer:

Step-by-step explanation:

You need to add $6.50 and $11.75 and you get $18.25.

That’s easy you add 11.75 + 6.50 first do 5 + 0=5 then 5 + 7 = 12 regroup 6 +1 = 7 +1= 8 and nothing plus 1 is 1 so the answer is $ 18.25

John walks 3 miles in 5 hours
for his exercise routine. Find
the Unit rate​

Answers

John walks 0.6 miles in 1 hour.

Step-by-step explanation:

Distance walked by John = 3 miles

Time period = 5 hours

5 hours = 3 miles

Unit rate is the ratio of two measurements, in which one measurement is one, therefore,

1 hour = [tex]\frac{3}{5}\ miles[/tex]

[tex]1\ hour=0.6\ miles[/tex]

John walks 0.6 miles in 1 hour.

Keywords: ratio, distance

Learn more about distances at:

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#LearnwithBrainly

Find the average rate if change in the function f(x) = x^2 +2 over the interval x= -5 to x= -2

Answers

If f(x) = x^2 +2 and 5<= x <= -2 :

F(-5)=(-5)^2+2=25+2=27

F(-4)=(-4)^2+2=16+2=18

F(-3)=(-3)^2+2=9+2=11

F(-2)=(-2)^2+2=4+2=6

Average =

(27+18+11+6)/4

=62/4

=15.5

Hope this helps

What is the image of (-9, -1) after a dilation by a scale factor of 2 centered at the
origin?

Answers

Answer:

(- 18, - 2 )

Step-by-step explanation:

Since the dilatation is centred at the origin then multiply each of the original coordinates by the scale factor for image, that is

(- 9, - 1 ) → (2 × - 9, 2 × - 1 ) → (- 18, - 2 )

Answer:

top is correct

Step-by-step explanation:

How do you use cos on the calculater in math

Answers

Answer:First make sure your calculator is on the right setting which would be a DEG. Then depending on the problem you would press COS, put whats needed inside the parentheses and close it.

Or if a different kind of problem you would press 2nd on the top of the calculator then Cos and continue the same way as the first one.

Step-by-step explanation:

Choose all the examples that describe volume.

A. the amount of shampoo in a bottle
✓ B. the amount of soap in a bar of soap
c. the amount of border around a chalkboard
D. the amount of wrapping paper covering a gift

Answers

Answer:

A, B

Step-by-step explanation:

Volume: the measure of the amount of space that a substance (such as liquid, gas, or solid) occupies in an enclosed environment (such as a container).

A fountain launches a stream of water directly out of a pool at a vertical speed of 48 feet per second. The water shoots up and then falls back into the pool. The height, h, of the water at time t, in seconds, is given by the equation h = –16t 2 + 48t. The greatest height of the water above the pool is

Answers

Answer:

36 feet.

Step-by-step explanation:

h = -16t² + 48t .......... (1)

The above equation relates the height h, in feet of the water at time t, in seconds.

Now, condition for greatest height is [tex]\frac{dh}{dt} = 0[/tex] ......... (2)

So, differentiating equation (1) with respect to t we get, -32t + 48 = 0 {From condition (2).

t = 1.5 seconds

So, the greatest height is = -16 (1.5)² + 48 (1.5) = 36 feet. (Answer)

TO TRANSMIT INFORMATION ON THE INTERNET, LARGE FILES ARE BROKEN INTO PACKETS OF SMALLER SIZES. EACH PACKET HAS 1,500 BYTES OF INFORMATION. AN EQUATION RELATING PACKETS TO BYES OF INFORMATION IS GIVEN BY B=1,500P REPRESENTS THE NUMBER OF PACKETS AND B REPRESENT THE NUMBER OF BYTES OF INFORMATION.
A. HOW MANY PACKETS WOULD BE NEEDED TO TRANSMIT 30,000BYTES OF INFORMATION
B. HOW MUCH INFORMATION COULD BE TRANSMITTED IN 30,000 PACKETS

Answers

Answer:

A. It would be needed 20 packets to transmit 30,000 bytes of information.

B. 45'000,000 (45 million) of bytes could be transmitted in 30,000 packets.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Size of each packet of information = 1,500 bytes

Number of packets = P

Number of bytes of information = B

2. Let's answer the questions:

A. How many packets would be needed to transmit 30,000 bytes of information?

P = 30,000 ÷ 1,500

P = 20

It would be needed 20 packets to transmit 30,000 bytes of information

B. How much information could be transmitted in 30,000 packets?

B = 30,000 * 1,500

B = 45'000,000

45'000,000 (45 million) of bytes could be transmitted in 30,000 packets.

Factor completely : 35 + 5x

Answers

Answer: 5(7+x) because this is how you factor

Sofia has $1.90 worth of nickels and dimes. She has a total of 25 nickels and dimes altogether. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Sofia has. Define the variables that you use to write the system.

Answers

Answer:

The number of dimes does Sofia has is 13 , and The number of dimes does nickles does Sofia has is 12

Step-by-step explanation:

Given as :

The net worth of nickels and dimes = $ 1.90

The total number of nickles and dimes altogether = 25

Let The number of nickles that Sofia has = n

And The number of dimes that Sofia has = d

Now,

Since The value of 1 nickle = [tex]\frac{1}{20}[/tex] dollar

And The value of 1 dimes =  [tex]\frac{1}{10}[/tex] dollar

So, According to question

n + d = 25          ..........1

And  $ [tex]\frac{1}{20}[/tex] × n + $ [tex]\frac{1}{10}[/tex] × d = $ 1.90

Or, n + 2 d = 38        .....2

Solving Eq 1 and 2

∵  n + 2 d = 38

or, 25 - d + 2 d = 38

or, d = 38 - 25

∴ d = 13

So, The number of dimes she has = 13

And the number of nickles = n = 25 - 13

∴  n = 12

Hence The number of dimes does Sofia has is 13 , and The number of dimes does nickles does Sofia has is 12 Answer

what is -14+5k-3= simplifying​

Answers

Answer:

5k-17

Step-by-step explanation:

-14+5k-3=5k-14-3=5k-17

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