Answers
Answer:
The value of x is 3
The value of m is 5.25
The value of a is 1.75
Step-by-step explanation:
I attached the picture with labels to can solve
In the 2 Δs ADE and ACF
∵ DE // CF
∴ m∠ADE = m∠ACF ⇒ corresponding angles
∴ m∠AED = m∠AFC ⇒ corresponding angles
→ By using the AA postulate of similarity
∴ The two triangles are similar
∴ Their corresponding sides have the same ratio
∴ [tex]\frac{AD}{AC}[/tex] = [tex]\frac{EA}{FA}[/tex] = [tex]\frac{DE}{CF}[/tex]
∵ AD = AB + BC + CD
∵ AB = 3, BC = 6, CD = x
∴ AD = 3 + 6 + x
∴ AD = 9 + x
∵ AC = AB + BC = 3 + 6
∴ AC = 9
∵ AE = AG + GF + FE
∵ AG = 4, GF = 8, FE = 4
∴ AE = 4 + 8 + 4
∴ AE = 16
∵ FA = AG + GF = 4 + 8
∴ FA = 12
∵ DE = 7 and CF = m
→ Substitute them in the ratio above
∴ [tex]\frac{9+x}{9}[/tex] = [tex]\frac{16}{12}[/tex] = [tex]\frac{7}{m}[/tex]
→ By using cross multiplication with the first 2 fractions
∵ 12 × (9 + x) = 9 × 16
∴ 12(9) + 12(x) = 144
∴ 108 + 12x = 144
→ Subtract 108 from both sides
∴ 108 - 108 + 12x = 144 - 108
∴ 12x = 36
→ Divide both sides by 12 to find x
∴ x = 3
→ By using cross multiplication with the second 2 fractions
∵ 16 × m = 12 × 7
∴ 16m = 84
→ Divide both sides by 16
∴ m = 5.25
In the 2 Δs ABG and ACF
∵ BG // CF
∴ m∠ABG = m∠ACF ⇒ Corresponding angles
∴ m∠AGB = m∠AFC ⇒ corresponding angles
→ By using the AA postulate of similarity
∴ The two triangles are similar
∴ Their corresponding sides have the same ratio
∴ [tex]\frac{AB}{AC}[/tex] = [tex]\frac{GA}{FA}[/tex] = [tex]\frac{BG}{CF}[/tex]
∵ AB = 3 and AC = 9
∵ GA = 4 and FA = 12
∵ BG = a and CF = m = 5.25
→ Substitute them in the ratio above
∴ [tex]\frac{3}{6}[/tex] = [tex]\frac{4}{12}[/tex] = [tex]\frac{a}{5.25}[/tex]
→ By using cross multiplication with the second 2 fractions
∵ 12 × a = 4 × 5.25
∴ 12a = 21
→ Divide both sides by 12 to find a
∴ a = 1.75
Related Questions
Darla can do a job in eight hours while Lonnie can do the same job in six hours. Both Darla and Lonnie work three hours on the job. How much of the job is left to be finished
Answers
Answer:
Look below ⏬
Step-by-step explanation:
Darla 8h
Lonnie 6h
They both worked 3 hours now
subtract
8-3=5
6-3=3
Darla have 5 hours to finish
and...
Lonnie has 3 hours to finish
all together is 8 hours in all
1/8 part of the job is left to be finished if both Darla and Lonnie works for three hours on the job.
What is Fractions?Fractions are the part or portion of a whole.
For example, fraction 1/2 means 1 part of the 2.
Time taken by Darla to do the job = 8 hours
Time taken by Lonnie to do the job = 6 hours
Let J represent the job.
In 8 hours, Darla completes J.
In 3 hours, Darla completes 3/8 J
In 6 hours Lonnie completes J.
In 3 hours, Lonnie completes 3/6 J.
The work completed = 3/8 J + 3/6 J
= J [ 3/8 + 3/6]
= J [3/8 + 1/2]
= 7/8 J
7/8 parts of the job is completed.
Job left to finished = J - 7/8 J = 1/8 J
Hence 1/8 part of the job is left to be finished.
To learn more about Fractions, click :
https://brainly.com/question/10354322
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The elevation of a city is positive if the city is above sea level and negative if below sea level. The elevation of New Orleans is -0.3 \text{ m}−0.3 mminus, 0, point, 3, start text, space, m, end text. What does an elevation of -0.3 \text{ m}−0.3 mminus, 0, point, 3, start text, space, m, end text represent in this situation? Choose 1 answer: Choose 1 answer: (Choice A) A New Orleans is 0.3 \text{ m}0.3 m0, point, 3, start text, space, m, end text above sea level. (Choice B) B New Orleans is at sea level. (Choice C) C New Orleans is 0.3 \text{ m}0.3 m0, point, 3, start text, space, m, end text below sea level.
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
the anwser is below sea level
Step-by-step explanation:
Someone plz help me fast plz
Answers
Answer:
Yes, it said of a mile and so that states since there are two numbers of a mile...
Step-by-step explanation:
(need help ASAP!) A moving truck has 10 feet ramp that is used to put furniture in the truck. The ramp touches the ground 8 feet from the back of the truck. How high off the ground is the ramp meet the back of the moving truck?
Answers
5. 0384748939
Step-by-step explanation:
let's take the ramp, if u draw a diagram 8, 10 and the unknown value makes a right angled triangle
So according to pythogaraos(dnot care the spelling) theorem a square + b square = c square
Now 10 is the hypothenuse, so let's rearrange them as c square - b square = a square
now apply the values, 10 square - 8 square = X square
100 - 64 = X square
36 = X square
now root of 32 is-------
I MESSED UP I GUESS
HELPPP PLS
James is tossing a counting cube numbered 1 to 6 to see how many times he gets a 3 or a 6. If he tosses the cube 36 times, predict how many times he will roll a 3 ora 6.
A. 6 times
B. 12 times
C. 9 times
D. 18 times
Answers
6+6= 12
In a math game, Bradley was supposed to find the square root of a number. Instead the squared the number and said "81."
What number should Bradley have given?
Answers
Answer:
The square root of 81 is 9, the square root of 9 is 3, your answer is 3
Step-by-step explanation:
3x3=9, 9x9=81
The required squared number that Bradley should give is 9.
Given that,
In a math game, Bradley was supposed to find the square root of a number. Instead, they squared the number and said "81."
To determine the number that should Bradley have given.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the number be x,
Bradley said it is 81
Now accoding to the question,
x = √81
x = √9*9
x = 9
Thus, the required squared number that Bradley should give is 9.
Learn more about simplification here:
brainly.com/question/12501526
#SPJ2
Which of the following equations are true? Select three that apply.
A (2x−1) (x2+4x+3)= 2x3+7x2+2x−3
B (4x2−3x+6)+(5x2−8)=9x2−3x−2
C (8x−4x2)+(2x2−5x)=−2x4+3x
D (4x2+4x−5)−(6x2−5x−3)=−2x2−x−8
E (3x3−5+2x)−(5x−6+x3)=2x3−3x+1
Answers
______________________________
a.) [tex]\bold{(2x-1) (x^2+4x+3)= 2x^3+7x^2+2x-3}[/tex]:
Use the distributive property to multiply [tex]2x-1[/tex] by [tex]x^2+4x+3[/tex] and combine like terms:
[tex]=2x^3+7x^2+2x-3[/tex]
- So this is True.
b.) [tex]\bold{(4x^2-3x+6)+(5x^2-8)=9x^2-3x-2}[/tex]:Combine like terms and subtract 8 from 6 to get −2:
[tex]=9x^2-3x-2[/tex]
- So this is True.
c.) [tex]\bold{(8x-4x^2)+(2x^2-5x)=-2x^4+3x}[/tex]:Combine like terms:
[tex]=3x-2x^2[/tex]
- So this is False.
d.) [tex]\bold{(4x^2+4x-5)-(6x^2-5x-3)=-2x^2-x-8}[/tex]:Combine like terms and add -5 and 3 to get -2:
[tex]=-2x^2+9x-2[/tex]
- So this is False.
e.) [tex]\bold{(3x^3-5+2x)-(5x-6+x^3)=2x^3-3x+1}[/tex]:Combine like terms and add -5 and 6 to get 1:
[tex]=2x^3-3x+1[/tex]
- So this is True.
______________________________
Someone please help!!
Answers
Answer:
25 degree
Step-by-step explanation:
The sum of angles is 180
so to find angle b, subtract 155 from 180
180 - 155 = 25
b = 25 degree
On one day four gardeners and four helpers earned 360 dollars. On another day working the same number of hours and at the same rate of pay , five gardeners and six helpers earned 480 dollars how much does a gardener and how much does a helper earn each day?
Answers
They get paid 60 dollars per
Last week Mr. Wilson spent $125 on groceries. This week his spending increased by 25%. How much did he spend on groceries this week?
Answers
Answer:
$156.25
Step-by-step explanation:
$125. × 25% = $31.25
$125.00+$31.25=$156.26
Answer:
156.25
Step-by-step explanation:
(125*0.25)+125=x=156.25
What is the GCF(Greatist common factor) of 18 and 176?
Brainlist for the correct answer!
Made a mistake with the first owo
Answers
Angelica has ten pounds of jelly beans. She wants to repackage the jelly beans into bags of size 2/3pound. How many basofiel beans can she make?
Answers
Answer:
15 bagsStep-by-step explanation:
Jelly beans weight = 10 poundsEach bag = 2/3 poundNumber of bags required:
10 ÷ 2/3 = 10 × 3/2 = 30/2 = 15 bagsTotal beans:-.
10/2/3=10×3/2=5×3=15beansin a highschool, 2/5 of the boys make up 250 students. how many boys are there in the high school?
Answers
Answer:100 boys
Step-by-step explanation:
250 / 5 is 50.
50 x 2 is 100.
which coordinate grid shows the graph of y=x-2
Answers
A 40-pound bag of dog food costs $38. How much does the dog food cost per pound?
Answers
Answer: 1,520
Step-by-step explanation:
distance covered by minute hand in 1 hour is 94. 20 cm find the circumference of the circle whose radius is 12 CM
Answers
Answer:
[tex]\large\boxed{75.4cm(1 d.p)}[/tex]
Step-by-step explanation:
Important Information:
Circumference of a cirlce= [tex]\pi*diameter[/tex]
Diameter= [tex]2*radius[/tex]
Method:
The first step in working out the circumference of this cirlce is to work out the diameter. You can work this out by multiplying the radius of 12 by 2, this gives you 24cm. This is because the radius is half of the diameter.
The next step is to work out the circumference. You can do this by multiplying pi by the diameter of 24, this gives you [tex]27\pi[/tex] or 75.4cm (1 d.p).
Step by Step:
1) Multiply 12 by 2.
[tex]12*2=24cm[/tex]
2) Multiply pi by 24.
[tex]\pi*24=75.4cm(1 d.p)[/tex]
Can y’all help me with dis question
Answers
Pretty sure is A or D.
Answer for brainliest
Answers
you have to match them with the right ones
Answers
Answer:
switch inequality and equation around
Step-by-step explanation:
equation: 4j-3=j
inequality: g+h>f
expression: leave it alone
The point(0, 0) is a solution to which inequality?*
O y-9<3x - 10
Oy - 9> 3x + 10
O y-9> 3x - 10
O y + 9 > 3x + 10
Answers
Henry is flying a kite. The kite makes an angle of 43 with the ground. If henry is standing 100 feet from a point on the ground directly below the kite, find the length of the kite string
Answers
Answer:
x = 136.73 feet
Step-by-step explanation:
Given that,
Henry is flying a kite. The kite makes an angle of 43 with the ground. If henry is standing 100 feet from a point on the ground directly below the kite.
We need to find the length of the kite string. It can be calculated by using trigonometry.
The length of the string will be hypotenuse, 100 feet is the base.
The relation between the hypotenuse, base and angle with the ground is given by :
[tex]\cos\theta=\dfrac{\text{base}}{\text{Hypotenuse}}\\\\\cos(43)=\dfrac{100}{x}\\\\x=\dfrac{100}{\cos(43)}\\\\x=136.73\ \text{feet}[/tex]
So, the length of the kite string is 136.73 feet.
Find the 40th term in each arithmetic sequence.
1. 4, 8, 12, 16, ...
2. 13, 26, 39, 52, ...
3. 6, 12, 18, 24, ...
Answers
Solve the equation using the multiplication property of equality and the reciprocal of 1 4 . 1 4 ( r − 5 2 ) = 1 8 What is r? r = one-third r = 3 r = two-thirds r = one-half
Answers
Answer:
3
Step-by-step explanation:
1/4(r - 5/2) = 1/8
1/4r - 5/8 = 1/8
1/4r = 1/8 + 5/8
1/4r = 6/8
Divide both sides by 1/4
1/4r ÷ 1/4 = 6/8 ÷ 1/4
1/4r * 4/1 = 6/8 * 4/1
r = 24/8
r = 3
Answer:
3
Step-by-step explanation:
I did it
Solve for x and y. 30-60-90 triangles
Answers
Answer:
[tex]x = 3[/tex][tex]y=3\sqrt{3}[/tex]Step-by-step explanation:
From the given right-angle triangle
The angle = ∠60°
The adjacent to the angle ∠60° is x.The opposite to the angle ∠60° is y.The hypotenuse = 6
Using the trigonometric ratio
cos 60° = adjacent / hypotenuse
substituting adjacent = x and hypotenuse = 6
cos 60° = x / 6
6 × cos 60° = x
x = 3
Thus, the value of x is:
x = 3And using the trigonometric ratio
sin 60° = opposite / hypotenuse
substituting opposite = y and hypotenuse = 6
[tex]sin\:60^{\circ }\:=\:\frac{y}{6}\:[/tex]
[tex]y=6\:\times\:sin\:60^{\circ }[/tex]
[tex]=6\times \frac{\sqrt{3}}{2}[/tex] ∵ [tex]\sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}[/tex]
[tex]=3\sqrt{3}[/tex]
Therefore, the value of y is:
[tex]y=3\sqrt{3}[/tex]Summary:
[tex]x = 3[/tex][tex]y=3\sqrt{3}[/tex]if a lady chargers $2.00 for gas and $3.00 per 1/2 hour of work . What is the amount of money she makes in 4 hours ?
Answers
Answer:
$32
Step-by-step explanation:
The lady charges $2.00 for gas which means over a 4 hour period we would do
4 x 2 = 8
She makes a total of 8 dollars
She also gains $3.00 per half hour of work
This means we would do 3 x 8
24
We add these values to get $32
Answer:
22 dollars maybe
Step-by-step explanation:
math
(06.03)
Rachel can make 3 bracelets in an hour. Oliver can make only 2 bracelets in an hour, but he already has 5 completed bracelets. Explain to Rachel how she can use a system of equations to determine when she will have the same number of bracelets as Oliver. Use complete sentences.
Answers
Answer:
I just need popints
Step-by-step explanation:
I just need points
Answer: R=3 Bracelets per HR
O=2 Bracelets per HR
Step-by-step explanation: She can go faster
Simplify the expression:
5(–5 + 3u) =
Answers
Answer:
-25+15u
Step-by-step explanation:
all you need to do is distribute the 5 to everything in the parenthesis!
Answer:
-25+15u
Step-by-step explanation:
5(-5+3u)=
-25+15u
Find the distance between the two numbers on a number line. (Hint: distance is always positive.)
-9.2, 4.5
Answers
Answer:
13.7
Step-by-step explanation:
Let us imagine that 0 on the numberline. -9.2 is to the left, and 4.5 is to the right of zero.
Since distance as positive, we can simply add the absolute values of -9.2 and 4.5 to obtain the distance:
|-9.2|+|4.5|=
9.2+4.5=
13.7
I hope this helps! :)
What professions did Nathan Hale and his brother pursue? A. farmer and teacher B. teacher and minister C. doctor and lawyer D. farmer and soldier
Answers
Answer:
B. teacher and minister
Step-by-step explanation:
Nathan Hale and Enoch Hale were two brothers who went to Yale College to complete their further studies. Among them, Nathan decided to become a school teacher and Enoch wanted to become a minister. Nathan promoted equal opportunities for the women in terms of education. He is known for his sacrifice that he made for his country. Among the colonists, he became a hero because of his thoughts for his country. He was hanged on the order of British commander, General Thomas Howe. Nathan was considered as a spy and was immediately hanged till death.
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
The table below relates the number of gallons to number of quarts.
1. Describe the relationship between gallons and quarts.
2. Is the given table proportional. if it is, what is the constant of proportionality for this relationship?
Answers
Step-by-step explanation:
1. The relationship between the galloon and quarts is that the galloons are being x4 each time. (example; 5x4 = 20, 4x3 = 12, etc...)
2. 4 quarts per gallon
