Work Shown:
[tex]g(x) = -x\\\\g(f(x)) = -f(x)\\\\g(f(x)) = -(3x-3)\\\\g(f(x)) = -3x+3\\\\g(f(x)) = \boldsymbol{3-3x}\\\\[/tex]
Explanation: We start with the outer function g(x). In the second step, we replace every copy of x with f(x). From there we plug in f(x) = 3x-3 and simplify using the distribution rule.
The notation [tex]g(f(x))[/tex] is the same as writing [tex](g \circ f)(x)[/tex]
In the diagram below, \overline{ST} ST is parallel to \overline{PQ} PQ. If STST is 55 more than QTQT, RT=10RT=10, and PQ=15PQ=15, find the length of \overline{QT} QT. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.PQRTS
The length of the [tex]\overline{QT}[/tex] can be determined using the given information and
the relationship between corresponding sides of similar triangles.
[tex]\underline{\overline{QT} = 5}[/tex]Reasons:
The given parameters are;
[tex]\overline{ST} \parallel \overline{PQ}[/tex]
ST = QT + 5
RT = 10
PQ = 15
Required: The length of [tex]\overline{QT}[/tex]
Solution:
Using the relationship between corresponding sides of similar triangles, ΔRST and ΔRPQ, we have;
[tex]\displaystyle \frac{\overline{ST}}{\overline{RT}} = \mathbf{\frac{\overline{PQ}}{\overline{RQ}}}[/tex]RQ = QT + RT
Therefore;
[tex]\displaystyle \frac{\overline{ST}}{\overline{RT}} = \mathbf{\frac{\overline{PQ}}{\overline{QT} + \overline{RT}}}[/tex]Which gives;
[tex]\displaystyle \frac{\overline{QT} + 5}{\overline{RT}} = \frac{\overline{PQ}}{\overline{QT} + \overline{RT}}[/tex]
Plugging in the known values gives;
[tex]\displaystyle \frac{\overline{QT} + 5}{10} = \mathbf{\frac{15}{\overline{QT} + 10}}[/tex]
[tex](\overline{QT} + 5) \times (\overline{QT} + 10) = 10 \times 15[/tex]
[tex]\overline{QT}^2 + 10\cdot \overline{QT} + 5\cdot \overline{QT} + 50 = 10 \times 15[/tex]
[tex]\overline{QT}^2 + 15\cdot \overline{QT} + 50 - 150= 0[/tex]
[tex]\mathbf{\overline{QT}^2 + 15\cdot \overline{QT} -100} = 0[/tex]
Factorizing with a graphing calculator gives;
[tex](\overline{QT} -5) \cdot (\overline{QT} + 20)= 0[/tex]
[tex]\mathbf{\overline{QT} = 5} \ or \ \overline{QT} = -20[/tex]
Therefore, given that [tex]\overline{QT}[/tex] is a natural number, we have;
[tex]\underline{\overline{QT} = 5}[/tex]
Learn more about similar triangles here:
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What is the area of the following triangle in square meters? Do not round your answer. A =
WITH THE RIGHT ANSWER WILL RECEIVE BRAINLIEST
Answer:
0.324 m²
Step-by-step explanation:
To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2
54 cm is the base, dashed is the height which is 1.2 m, we convert 54 cm into meters (54 cm = 0.54 m)
and we apply the formula
1.2 * 0.54 : 2 =
0.324 m²
Answer:
32.4? or 0.324 m²
Step-by-step explanation:
Which elements are involved in physical weathering?
Air, salt, rivers, sand, and ice
Air, water, ice, temperature, and plants
Animals, water, pressure, sediment, and gravity
Temperature, animals, ice, gravity, and plants
Answer:
heat, water, ice, or other agents
Step-by-step explanation:
Find the measure of the exterior angle.
Answer:
125
Step-by-step explanation:
75 + 50
What is 9 ¼ percent of $485.95 ?
Jamie and Raul both work at the Pizza House. Together, they work a total of 15 hours per week. Raul works 3 more than twice the hours as Jamie. How many hours does Jamie work per week?
Enter your answer in the box.
Answer:
Step-by-step explanation:
List the facts phrase by phrase.
Total = 15 hours
Let Raul's hours = x
Let Jamie's hours = y
Total = x + y = 15
x = 3 + 2y
From total, find x
x+ y = 15 Subtract y from both sides.
x = 15 - y Put the value for x in x = 3+ 2y
3 + 2y = 15 - y Subtract 3 from both sides
2y = 15 - 3-y Combine
2y = 12 - y Add y to both sides.
2y + y = 12 Combine
3y = 12
y = 12 / 3
y = 4
Jamie worked 4 hours
Raul worked 11
AYOOOO HELP!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Value of x= `
4x+5y-6z =2
x= (2-5y+6z) divided by 4
For example : if x is 2.5
2.5 = 2 - 5x2 + 6x3
If I add 60 to 325 and then subtract 40, the answer I get will be equal to
Answer:
345
Step-by-step explanation:
On adding 60 to 325 and then subtracting 40 the answer will be 345.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given numbers 60, 325, and 40. The expression will be formed as below:-
E = 60 + 325 - 40
E = 385 - 40
E = 345
Therefore, on adding 60 to 325 and then subtracting 40 the answer will be 345.
To know more about an expression follow
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Which expression has a value equal to 28 divided by 4
There are 4 options.
7x4
4x28
28/4
4/28
Answer:
28/4
Step-by-step explanation:
the slash is also a division sign.
Answer:
B: 28/4 should be the correct answer, correct me if I'm wrong.
Please help I need the answer quickly.
Answer:
r = ± [tex]\sqrt{q^2-p^4[/tex]
Step-by-step explanation:
p² = [tex]\sqrt{q^2-r^2}[/tex] ( square both sides )
(p² )² = q² - r²
[tex]p^{4}[/tex] = q² - r² ( subtract q² from both sides )
[tex]p^{4}[/tex] - q² = - r² ( multiply through by - 1 )
q² - [tex]p^{4}[/tex] = r² ( take square root of both sides )
± [tex]\sqrt{q^2-p^4}[/tex] = r
What type of angle is 19 degrees
Answer:
Obtuse Angle
Step-by-step explanation:
Answer:
Acute
Step-by-step explanation:
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS PLS ANSWER
Answer:
4
Step-by-step explanation:
I think if not sorry
Your friend solved the equation 4x+12x−6=4(4x+7) and got x=34. What error did your friend make? What is the correct solution?
Answer:
=34
Step-by-step explanation:
4x+12x-6=4(4x+7) ur question
using BODMAS
4x+12x-6=16x+28
16x-6=16x+28
16x-16x=28+6
0=34
but make sure your question is right, can you go through it again
7 2/9 + -5 1/5 =
show your work, show me how you got this answer
Answer:
Step-by-step explanation:
Convert mixed fraction to improper fraction.
Find LCM of the denominators and find equivalent fraction.
Now, subtract
[tex]7\dfrac{2}{9}=\dfrac{(7*9)+2}{9}=\dfrac{63+2}{9}=\dfrac{65}{9}[/tex]
[tex]5\dfrac{1}{5}=\dfrac{26}{5}[/tex]
LCM of 9 and 5 = 45
[tex]\dfrac{65}{9}*\dfrac{5}{5}=\dfrac{325}{45}[/tex]
[tex]\dfrac{26}{5}*\dfrac{9}{9}=\dfrac{234}{45}[/tex]
[tex]7\dfrac{2}{9}- 5\dfrac{1}{5}=\dfrac{65}{9}-\dfrac{26}{5}\\\\ =\dfrac{65*5}{9*5}-\dfrac{26*9}{5*9}\\\\\\=\dfrac{325}{45}-\dfrac{234}{45}\\\\\\=\dfrac{325-234}{45}\\\\\\=\dfrac{91}{45}\\\\\\=2\dfrac{1}{45}[/tex]
what are the reasons?
Answer:
Step-by-step explanation:
1. ∠WVX , ∠YZX are right angled triangles 1.Given
2. WV ≅ YZ 2. Given
3. X is the midpoint of WY 3. Given
4. WX ≅ YX 4. definition of midpoint
5. ΔWVX ≅ ΔYZX 5. RH congruent
Joyce buys a bus pass for the month of march for $32.55.How much does the bus pass cost per day?
Answer 1.085
dd
sa
d
sd
a
ds
d
The bus pass cost per day will be $1.05 per day.
What is the rate?The rate is the ratio of the amount of something to a certain unit.
For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Parenthesis, Exponent, Multiplier, Division, Adding, and Subtraction is referred to as the PEMDAS rule. To answer the problem properly and accurately, this rule is applied.
Joyce buys a bus pass for the month of March for $32.55.
In March month, there are 31 days. Then the bus pass cost per day is given by dividing the cost of $32.55 by 31.
⇒ $32.55 / 31
⇒ $1.05 per day
The bus pass cost per day will be $1.05 per day.
More about the rate link is given below.
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Consider the following proportion:
2
7
=
12
x
Use cross products to write the equation: 2x = 84.
What is the value of x?
Answer:
x=42
Step-by-step explanation:
divided by 2 equals 42 first you have to dive x by 2 and do the same for 80
WILL MARK BRAINLIEST, PLS INCLUDE SOLUTION
im so confused can someone help me please
Answer:
1. false
2. false
3. false
4. true
Step-by-step explanation:
a quadritilateral always has 4 sides, but it dpesnt HAVE to be a square
a parrellelogram can be any shap as long as its parrelel
a rhombus is always a square, becuase if you turn it around... VIOLA! you get a square.
HELP PLEASE ILL GIVE U BRAINLIEST
Answer:
number 3
Step-by-step explanation:
angleNGL=~angleHGF
Answer:
NG≅GF
Step-by-step explanation:
Since the side has to be in between the two angles so it from a ASA
The angles ∠N is the same as ∠F and ∠NGL is the same as ∠HGF
pls help quick :( worth 20 pts
Answer:
Answer A
Step-by-step explanation:
From the image, it looks like the answer is y<1/2x+2 because the shading of the line is below, as well as the points of interception are 4 and 2. I hope this helps!
A rectangle has an area of 1,450.8 square inches and a base of 37.2 inches. What is the height?
Answer:
39
Step-by-step explanation:
1450.8 / 37.2 = 39
In a 30 minute show 12 minutes of airtime are spent on commercials. Determine what percent of the television show air time is spent on commercial
Directions:
It’s easy for people to get stuck in their own minds or their own worlds instead of seeing the perspectives of others. Take a moment to consider the perspective of the characters listed. Choose one character. Write a short paragraph to explain the perspective of that character by putting yourself “in their shoes.” Consider these questions:
What might be his or her struggles?
How does the character see the world around himself or herself?
What decisions would you make if you were in the character’s place?
Be sure to use specific examples or textual evidence from research, the readings in this class, or your own experiences and knowledge.
Prompt:
Topic 1: Perspective of Montresor in “The Cask of Amontillado”
Topic 2: Perspective of Princess Irene in The Princess and the Goblin, Chapter 14
Answer: Montresor struggles with anger, and grudges. Montresor feels remorse at the end but excuses it as the dampness of the catacombs.
He sees the world without justice and sees to make justice for himself. In the story he talks about the misgivings and insults he receives from fortunato. He takes vengeance against him.
(haven´t read book based off summary) Princess Irene shares a friendship that is strong. I infer this based off the trust and bonding they share in the book. She struggles against goblins.
Step-by-step explanation: I really hope this helps havent read the books in a long time.!!
What is the equation of the line on the graph? Write your answer in slope-intercept form. (y = mx + b)
Don't forget to simply if you can!
Answer:
y= ⅔x -2
Step-by-step explanation:
slope-intercept form
y= mx +b, where m is the slope and b is the y-intercept.
Two given coordinates: (-3, -4) and (6, 2)
[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]
Slope
[tex] = \frac{2 - ( - 4)}{6 - ( - 3)} [/tex]
[tex] = \frac{2 + 4}{6 + 3} [/tex]
[tex] = \frac{6}{9} [/tex]
[tex] = \frac{2}{3} [/tex]
Substitute m= ⅔ into the equation:
y= ⅔x +b
From the graph, the y- intercept is -2 since the line cuts through the x-axis at (0, -2).
Alternatively, we can also substitute a pair of coordinates into the equation to find the value of b.
When x= 6, y= 2,
[tex]2 = \frac{2}{3} (6) + b[/tex]
2= 4 +b
b= 2 -4
b= -2
Thus the equation of the line is y= ⅔x -2.
(3+6i)(4-4i) simplify
Answer:
See picture
Step-by-step explanation:
Hope this helps!
Match the terms to their definition.
1. the result of a transformation on a point or figure
2. a transformation that preserves distance
the flipping of a plane about a fixed line; a transformation
3.
resulting in a mirror image over a line
the process of setting up correspondence between the
4. elements by of two sets so that every element of the first set corresponds to a unique element in the second set
Isometry
Image
Reflection
Transformation
I believe the numbers didn't fully correspond with the definitions so I tried my best to fix them and then match them.
Answer:
Isometry = 2: A transformation that preserves distance.
Image = 1: The result of a transformation on a point or figure.
Reflection = 3: The flipping of a plane about a fixed line; a transformation resulting in a mirror image over a line.
Transformation = 4: The process of setting up correspondence between the elements of two sets so that every element of the first set corresponds to a unique element in the second set.
Use angle relationships to complete the top equation. Then, solve for x and find the measure of both angles.
1.1x10^5 in standard notation
Answer:
110000
Step-by-step explanation:
first, expand 10^5, which is 100000
use a calculator (or long multiplication) to multiply 1.1*100000, which is 110000
A card game has 50 cards. After dealing 7 cards to each player, Tupi has 15 cards left over. Solve the equation 50 7p = 15 to find the number of players.