The difference of the expression is 6x² - 15x - 4.
What is Expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
(Number/variable, Math Operator, Number/variable) is an expression.
We have the Expression as
(4x² - 12x + 6) and (10 + 3x -2x²)
Now, simplifying the expression
= 4x² - 12x +6 - (10 + 3x -2x²)
= 4x² -12x+ 6 -10 -3x + 2x²
= 6x² - 15x - 4
Thus, the simplified expression is 6x² - 15x - 4.
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Part (a)
Focus on triangle PSQ. We have
angle P = 52
side PQ = 6.8
side SQ = 5.4
Use of the law of sines to determine angle S
sin(S)/PQ = sin(P)/SQ
sin(S)/(6.8) = sin(52)/(5.4)
sin(S) = 6.8*sin(52)/(5.4)
sin(S) = 0.99230983787513
S = arcsin(0.99230983787513)
S = 82.889762826274
Which is approximate
------------
Use this to find angle Q. Again we're only focusing on triangle PSQ.
P+S+Q = 180
Q = 180-P-S
Q = 180-52-82.889762826274
Q = 45.110237173726
Which is also approximate.
A more specific name for this angle is angle PQS, which will be useful later in part (b).
------------
Now find the area of triangle PSQ
area of triangle = 0.5*(side1)*(side2)*sin(included angle)
area of triangle PSQ = 0.5*(PQ)*(SQ)*sin(angle Q)
area of triangle PSQ = 0.5*(6.8)*(5.4)*sin(45.110237173726)
area of triangle PSQ = 13.0074347717966
------------
Next we'll use the fact that RS:SP is 2:1.
This means RS is twice as long as SP. Consequently, this means the area of triangle RSQ is twice that of the area of triangle PSQ. It might help to rotate the diagram so that line PSR is horizontal and Q is above this horizontal line.
We found
area of triangle PSQ = 13.0074347717966
So,
area of triangle RSQ = 2*(area of triangle PSQ)
area of triangle RSQ = 2*13.0074347717966
area of triangle RSQ = 26.0148695435932
------------
We're onto the last step. Add up the smaller triangular areas we found
area of triangle PQR = (area of triangle PSQ)+(area of triangle RSQ)
area of triangle PQR = (13.0074347717966)+(26.0148695435932)
area of triangle PQR = 39.0223043153899
------------
Answer: 39.0223043153899This value is approximate. Round however you need to.
===========================================
Part (b)
Focus on triangle PSQ. Let's find the length of PS.
We'll use the value of angle Q to determine this length.
We'll use the law of sines
sin(Q)/(PS) = sin(P)/(SQ)
sin(45.110237173726)/(PS) = sin(52)/(5.4)
5.4*sin(45.110237173726) = PS*sin(52)
PS = 5.4*sin(45.110237173726)/sin(52)
PS = 4.8549034284642
Because RS is twice as long as PS, we know that
RS = 2*PS = 2*4.8549034284642 = 9.7098068569284
So,
PR = RS+PS
PR = 9.7098068569284 + 4.8549034284642
PR = 14.5647102853927
-------------
Next we use the law of cosines to find RQ
Focus on triangle PQR
c^2 = a^2 + b^2 - 2ab*cos(C)
(RQ)^2 = (PR)^2 + (PQ)^2 - 2(PR)*(PQ)*cos(P)
(RQ)^2 = (14.5647102853927)^2 + (6.8)^2 - 2(14.5647102853927)*(6.8)*cos(52)
(RQ)^2 = 136.420523798282
RQ = sqrt(136.420523798282)
RQ = 11.6799196828694
--------------
We'll use the law of sines to find angle R of triangle PQR
sin(R)/PQ = sin(P)/RQ
sin(R)/6.8 = sin(52)/11.6799196828694
sin(R) = 6.8*sin(52)/11.6799196828694
sin(R) = 0.4587765387107
R = arcsin(0.4587765387107)
R = 27.3081879220073
--------------
This leads to
P+Q+R = 180
Q = 180-P-R
Q = 180-52-27.3081879220073
Q = 100.691812077992
This is the measure of angle PQR
subtract off angle PQS found back in part (a)
angle SQR = (anglePQR) - (anglePQS)
angle SQR = (100.691812077992) - (45.110237173726)
angle SQR = 55.581574904266
--------------
Answer: 55.581574904266This value is approximate. Round however you need to.
f(x) = 3x2 + 5x – 14
Find f(-3)
i need the answer for now
Step-by-step explanation:
3 ( _3 ) 2 + 5 ( -3 ) - 14 = _2
.........
Plzz answer this question properly step by step
Answer:
54°
Step-by-step explanation:
∠A = 2x + 10, ∠C = 3x - 14
∠E + 266 = 360 (sum of angles around a point)
∠E = 360 - 266
∠E = 94°
AB is parallel to line BD. Lets draw a line cuts line AB and line BD to form ∠B and ∠D. Hence:
∠B + ∠D = 180° (sum of interior angles on the same side)
∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angles in a pentagon)
2x + 10 + 3x - 14 + 94 + 180 = 540
5x + 270 = 540
5x = 540 - 270
5x = 270
x = 54°
What is the slope of this line: y=10
The slope of this line is 0. If you graph the line y=10, for any x value, the y-value remains 10 (denoted because x is equal to 0 in the actual equation shown, which means that x will not be shown in the equation). The graph would basically just be a straight horizontal line, neither curving up or down.
please help fast will mark brainliest
Answer:
X=7
Step-by-step explanation:
Hope this helps, have a good day
5)
How many solutions can be found for the linear equation?
3(x + 4) = 3x + 4
A)
no solution
B)
one solution
C)
two solutions
D)
infinitely many solutions
Which equation represents a linear function?
equation 1: y=2x^2+1
equation 2: y=8x+1
equation 3:y=5x^3-1
equation 4: y^2=4x-1
a. equation 1
b. equation 2
c. equation 3
d. equation 4
I need an answer by today ASAP! please!
Answer:
Equation 2
Step-by-step explanation:
Equation 2 is the only one possible to be linear. All of the other answers have an exponents. For instance, say you have y=x^3. For 1, it is 1*1*1. (1,1). For 2, it is 2*2*2. (2,8). For 3, 3*3*3. (3,27) It escalates into a curve and is non-linear.
what are 5 triangle congruence theorems
Which pattern can we use to factor the expression? (x-1)2+(x-1)+4
how do you write 7/10 as a decimal Can someone please help me!!
Answer:
0.7
Step-by-step explanation:
To get 7/10 as a decimal you simply divide 7 by 10 which gets you 0.7.
help me please I dont know the answer and I am cleaning the house for my mom
17/20 = t + (- 13/20)
t = 17/20 + 13/20
t = 30/20
t = 1.5
Need help on this one. Which knot is the correct one that would be able to unknot itself
Answer:
7 6
Step-by-step explanation:
Answer:
i think it 7 6
Step-by-step explanation:
please help asap ill give brainliest if youre correct!!!
Answer: its B
Step-by-step explanation: i've done this test before
Answer:
the answer is b
Step-by-step explanation:
because i have done this question before
The sphere shown has a radius of 3.5
inches. Find the volume
Answer:
V
≈
179.59in³
Step-by-step explanation:
can you figure out the answer please
Answer:
h = — 10.071
Step-by-step explanation:
Look at the picture for my work.
PLZ HELP THAI IS DUE IN AN HOUR
Mrs. Brown asked four students how to find the perimeter of a rectangle where l = length and w = width. Their answers are below. Which would NOT find the perimeter of a rectangle?
A. P = l + w + l + w
B. P = 2 x l + 2 x w
C. P = 2(l + w)
D. P = 2(l x w)
Answer:
i think its B but i'm not 100 percent sure sorry if im not but i think i am
Step-by-step explanation:
Answer:
It's D
Step-by-step explanation:
You l*w is the area.
Determine the equations you would use to represent the situation.
You sold 27 tickets total. Some of the tickets were student tickets and the rest were adult tickers.
You collected $170 selling the tickets. If the student tickets cost $5 and the adult tickets cost $10.
how many student tickets did you sell?
Answer:
You sold 20 student tickets.
Step-by-step explanation:
Given that:
Total tickets sold = 27
Total amount collected = $170
Cost of student ticket = $5
Cost of adult ticket = $10
Let,
x be the number of students tickets sold
y be the number of adult tickets sold
x+y = 27 Eqn 1
5x+10y=170 Eqn 2
Multiplying Eqn 1 by 10
10(x+y=27)
10x+10y=270 Eqn 3
Subtracting Eqn 2 from Eqn 3
(10x+10y)-(5x+10y)=270-170
10x+10y-5x-10y=100
5x=100
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{100}{5}\\x=20[/tex]
Hence,
You sold 20 student tickets.
mallory and meg attend the physics day for their school. their favorite rides were splash mountain and the centrifugal chamber. here are their stamped tickets at the end of the day. find the cost of each ride
Answer:
Splash Mountain = $7.25
Centrifugal Chamber= $5.25
Step-by-step explanation:
Click On Link For Work
A business trip will be reimbursed $0.55 per mile. Mr. Jackson has a budget of $70 for the round trip. If he is traveling to a town 61 miles away, then will he be under or over? Prove your thinking.
Answer:
We know Mr. Jackson will have to pay 0.55 dollars per mile and that he's traveling 61 miles, so, if we want to know. how much will he pay, we can multiply the quantity of miles (61) per the cost of these:
0.55 * 61 = 33.55
So we know he will have to pay 33.55 dollars, and, as the travel is round, considering he will travell the same quantity of miles, he will pay twice
33.55 * 2 = $67.10
He has more budget than the needed for the travel
Answer:
Mr. Jackson will be under his budget.
Step-by-step explanation:
We know that Mr. Jackson has a budget of only $70 for the trip. We know that the trip will be reimbursed $0.55 per mile. Mr. Jackson is traveling 61 miles. Therefore, we need to multiply $0.55 by 61.
61 x 0.55 = $35.55
Since $35.55 is less than $70, he will be under his budget.
Hope this helps! :D
Evaluate the expression for x = 2 and y = 4. Enter your answer in the box.
16x0 + 2x2 • y –1
Answer:
31
Step-by-step explanation:
PEMDAS
16(2) * 0.
32 * 0
=0
2(2) * 2
=8
8 * 4 - 1
32 - 1 = 31
Answer:
Its 6. Trust me.
Step-by-step explanation:
What is the y-intercept of -x + 4 = y? *
Answer:
y intercept: (0,4)
Step-by-step explanation:
PLEASEEE HELPPP!!!!
Which of the following relations is NOT a function?
A. ((0, 1), (1, 1), (2, 1), (3, 1))
B. {(0, 1), (0.2), (0, 3), (0,4)}
C. (0,0), (3, 4), (5, 6), (8, 9)}
D. {(0, 0), (2, 2), (4,4), (6, 6))
Answer:The answer is B cause the 0 repeats multiple times
Step-by-step explanation:
3(x + 10) + 6 = 3(x + 12)
Answer:
x = infinite amount of solutions
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
3(x + 10) + 6 = 3(x + 12)
Step 2: Solve for x
Distribute 3: 3x + 30 + 6 = 3x + 36Combine like terms: 3x + 36 = 3x + 36Subtract 36 on both sides: 3x = 3xDivide 3 on both sides: x = xHere we see that x does indeed equal x. We can plug in any number x and it would render the equation true.
∴ x = infinite amount of solutions
Answer:
infinitely many solutions / all solutions
Step-by-step explanation:
you distribute 3x+30+6 = 3x+36combine like terms 3x+36 = 3x+36realise the 2 terms are the same so x can be anythingRead the following prompt and type your response in the space provided.
Write an inequality that could be used to solve the following problem. Do not solve.
Sall's Pizza charges $12 for a large cheese pizza and $2 for each additional topping.
Brian only has $18 to spend on pizza. How many toppings can he get on a large
pizza?
Answer:
equation form: 12 + 2x = 18
x = 3
lets check the work see if its true
12 + 2(3) = 18
12 + 6 = 18
It Checks!
therefore your answer is 3. He can get 3 different toppings
Step-by-step explanation:
10) It takes a sloth to 14 seconds to move 2 centimeters. How many centimeters does the sloth move per second? SHOW YOUR WORK. A) 7 B) C) 2 DJ 7 5
Answer:
A (7)
Step-by-step explanation:
14/2=7
Answer:
i think its a) 7
Step-by-step explanation:
From what i learned, to find the unit rate/slope you must do y/x or rise/run. In this case 14 is y and 2 is x. You divide 14 by 2 and get 7! Hope this helps! Brainliest would be much appreciated! <3
Each of the numbers 1 through 7 is written on a small piece of paper and placed in a box. What is the probability of picking a paper with an odd number?
A. 12
B. 47
C. 37
D. 14
I NEED ASAP PLS 20 pnts!
Answer:
Either C or B I’m not quite sure which one. I’m sorry
Step-by-step explanation:
y
What is the equation of the graphed line written in
standard form?
3
2+
1
X=-3
y=-3
O x + y = -3
Ox-y=-3
1 2 3 4 5 X
54-3-2-14
2
-3
N
4
Answer:
A) x = -3
the line is undefined
The equation of the graphed line written in slope-intercept form is x = -3
What is the Slope-Intercept form?The graphed line in slope-intercept form, y = mx + b
To Convert it into the standard form of the equation, ax + by = c.
Consider that the points be (0, 3) and (5,0).
A Slope exists how many units it brought to go vertically or horizontally.
Which Slope doesn't exist.
The y-intercept in slope-intercept form, y = mx + b
where, m = undefined
x = -3
Therefore, the correct answer is option (A), x = -3 because the line is undefined.
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2x+5=11 two step equations
Answer:
x=3
Explanation: 11-5=6
6/2= 3
Plug 3 into the equation and you get 2x3+5=11 which 2x3=6 and 6+5=11
The length of a rectangle is 1 7/9in and its width is 3/4 of its length Find the area of this rectangle
Answer:
l = 16/9 inches and w = 3/4 * 16/9, which equals 4/3
Step-by-step explanation:
A=l*w
16/9 * 4/3 = 64/27 = 2 10/27 sq in