For a dinner , a caterer charges $150 plus $19 per person. This function represents the relationship between n, the number of people at the dinnerand T(n) , the total cost. T(n) = 150 + 19n Determine the total cost, in dollars, for the caterer to serve dinner to 90 people
a -42+(-17)
b 8-(-9)
c 8(-9)
D
E
F
G
Answer:
.A -42+(-17)
Step-by-step explanation:
Please help me to prove this!
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π → A + B = π - C
→ B + C = π - A
→ C + A = π - B
→ C = π - (B + C)
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]
Use the Sum/Difference Identity: cos (A - B) = cos A · cos B + sin A · sin B
Use the Double Angle Identity: sin 2A = 2 sin A · cos A
Use the Cofunction Identity: cos (π/2 - A) = sin A
Proof LHS → Middle:
[tex]\text{LHS:}\qquad \qquad \cos \bigg(\dfrac{A}{2}\bigg)+\cos \bigg(\dfrac{B}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)[/tex]
[tex]\text{Sum to Product:}\qquad 2\cos \bigg(\dfrac{\frac{A}{2}+\frac{B}{2}}{2}\bigg)\cdot \cos \bigg(\dfrac{\frac{A}{2}-\frac{B}{2}}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)[/tex]
[tex]\text{Given:}\qquad \quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{\pi -(A+B)}{2}\bigg)[/tex]
[tex]\text{Sum/Difference:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\sin \bigg(\dfrac{A+B}{2}\bigg)[/tex]
[tex]\text{Double Angle:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\sin \bigg(\dfrac{2(A+B)}{2(2)}\bigg)\\\\\\.\qquad \qquad \qquad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+2\sin \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A+B}{4}\bigg)[/tex]
[tex]\text{Factor:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\bigg[ \cos \bigg(\dfrac{A-B}{4}\bigg)+\sin \bigg(\dfrac{A+B}{4}\bigg)\bigg][/tex]
[tex]\text{Cofunction:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\bigg[ \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{\pi}{2}-\dfrac{A+B}{4}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{2\pi-(A+B)}{4}\bigg)\bigg][/tex]
[tex]\text{Sum to Product:}\ 2\cos \bigg(\dfrac{A+B}{4}\bigg)\bigg[2 \cos \bigg(\dfrac{2\pi-2B}{2\cdot 4}\bigg)\cdot \cos \bigg(\dfrac{2A-2\pi}{2\cdot 4}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =4\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -A}{4}\bigg)[/tex]
[tex]\text{Given:}\qquad \qquad 4\cos \bigg(\dfrac{\pi -C}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -A}{4}\bigg)\\\\\\.\qquad \qquad \qquad =4\cos \bigg(\dfrac{\pi -A}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -C}{4}\bigg)[/tex]
LHS = Middle [tex]\checkmark[/tex]
Proof Middle → RHS:
[tex]\text{Middle:}\qquad 4\cos \bigg(\dfrac{\pi -A}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -C}{4}\bigg)\\\\\\\text{Given:}\qquad \qquad 4\cos \bigg(\dfrac{B+C}{4}\bigg)\cdot \cos \bigg(\dfrac{C+A}{4}\bigg)\cdot \cos \bigg(\dfrac{A+B}{4}\bigg)\\\\\\.\qquad \qquad \qquad =4\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{B+C}{4}\bigg)\cdot \cos \bigg(\dfrac{C+A}{4}\bigg)[/tex]
Middle = RHS [tex]\checkmark[/tex]
If each interior angle of a regular polygon is 144 degrees. Find the number of sides in it.
Answer:
10
Step-by-step explanation:
In a polygon
interior angle + interior angle = 180°, thus
exterior angle = 180° - 144° = 36°
The sum of the exterior angles in a polygon = 360°, thus
number of sides = [tex]\frac{360}{36}[/tex] = 10
Answer:
10 sides
Step-by-step explanation:
A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144° and they all add up to 1,440°.
83.63 - 2.89 × (4.9 - 2.9)2 A. 72.07 B. 50.43 C. 1,046.56 D. 49.31 Please help
Answer:
A would be the anwser
Step-by-step explanation:
Answer: A. 72.07
Step-by-step explanation: Plato
x²y + 2 xy² + 3x²y=?
Answer:
2xy(2x+y)
Step-by-step explanation:
Tell whether the blue figure is a translation of the red figure.
The blue figure !
I a translation of the red figure.
Answer:it is a translation
Step-by-step explanation:a translation is just a movement up down left or right not diagonal you’re just moving it up down left or right across the grid
Answer:
Yes
Step-by-step explanation:
Because a translation moves a shape up, down, or from side to side but it does not change its appearance in any other way. The translation is an example of a transformation. A transformation is a way of changing the size or position of a shape. Every point in the shape is translated at the same distance in the same direction.
Five times the sum of a number and 6 is 48
Answer:
3.6
Step-by-step explanation:
Step 1: Find out what 48 ÷ 5 is
9.6
Step 2: Subtract 6 from 9.6
3.6
Certain cooking oil has a density of 0.91 grams per milliliter. Which of the following series of calculations correctly determines the mass, in kilograms, of 15 liters of this oil?
Answer:
Step-by-step explanation:
Here is a picture of the answer, since I couldn't put into words!
The mass of 15 liters of oil is 13.65 kg.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that performs the arithmetic operations are called arithmetic operators.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
What is the density?Density is the ratio of the mass of the body to the volume of the body.
Density = Mass / Volume
Given that oil has a density of 0.91 grams per milliliter
To determines the mass, in kilograms, of 15 liters of this oil
Rearranging the equation,
Mass = Density × Volume
∵ 15 liters = 15000 milliliters (ml)
So, 0.91g/ml x 15000ml = 13650g
∵ 1 kilogram = 1000grams
⇒ 13650g / 1000g/kg
⇒ 13.65kg
Thus, the mass of 15 liters of oil is 13.65kg.
Learn more about Arithmetic operations here:
brainly.com/question/25834626
#SPJ2
When ax3 +x2 -2x +b is divided by x+1, the remainder is 10. When it is divided by x-3, the remainder is -46. What is the value of a and b?
Step-by-step explanation:
Given
X+ 2 = 0
X = -2
on putting in polynomial
-8a +2b= 0
- 8a = 2b
b = -4a
Now
when divided by x - 1 give remainder -15
so
x - 1 = -15
x = -14
on putting in polynomial
-2744a + 198 + 14b - 4 = -14
-2744a + 56a = - 208
-2688a = -208
a = 168/13
Now
b = 672/13
what is an equation of the line that passes through the points (4,-6) and (8,-4)
Answer:
[tex]y = \frac{1}{2} x - 8[/tex]
Step-by-step explanation:
The equation of a line is usually written in the form of y=mx+c, where m is the gradient (also known as slope) and c is the y-intercept (the point through which the line cuts through the y-axis).
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Using the gradient formula above,
[tex]m = \frac{ -4 - ( - 6)}{8 - 4} \\ m = \frac{ - 4 + 6}{4} \\ m = \frac{2}{4} \\ m = \frac{1}{2} [/tex]
Substitute the value of m into the equation:
y= ½x +c
To find the value of c, substitute a pair of coordinates.
When x=4, y= -6,
-6= ½(4) +c
-6= 2 +c
c= -6 -2 (-2 on both sides)
c= -8 (simplify)
Thus, the equation of the line is y= ½x -8.
Help needed ASAP will give BRAINLIEST
Answer:
177.2 i think
Step-by-step explanation:
0.001429 in scientific notation
Answer:
1.429 × 10^-3
Step-by-step explanation:
since it's below 1, you're moving the decimal to the right, which makes the 3 negative.
Evaluate each expression.
6! =
3! - 2! =
6!/3!=
Answer:
I hope it will help you :)
Answer:
6! = 720
3! - 2! = 12
6!/3!= 120
Step-by-step explanation:
just finished the assignment.
Please help lol
Answer options:
A. (2.5,4)
B. (2,3)
C. (1.5,3)
D. (2,3.5)
One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 35. Find the
lengths of all three sides, to two decimal places.
i would appreciate if you showed work so i know how you did it!
Answer:
6.68, 13.37, 14.95
Step-by-step explanation:
One of the legs is twice as long as the other.
b = 2a
The perimeter is 35.
35 = a + b + c
The triangle is a right triangle.
c² = a² + b²
Three equations, three variables. Start by plugging the first equation into the second and solving for c.
35 = a + 2a + c
c = 35 − 3a
Now plug this and the first equation into the Pythagorean theorem:
(35 − 3a)² = a² + (2a)²
1225 − 210a + 9a² = a² + 4a²
1225 − 210a + 4a² = 0
Solve with quadratic formula:
a = [ -(-210) ± √((-210)² − 4(4)(1225)) ] / 2(4)
a = (210 ± √24500) / 8
a ≈ 6.68 or 45.82
Since the perimeter is 35, a = 6.68. Therefore, the other sides are:
b ≈ 13.37
c ≈ 14.95
4x²-9y²-6x-9y Factorize
Answer:
Step-by-step explanation:
What is the value of 6x power of 2 when x=1.5
Answer:6x=
2=
X=1.5
Step-by-step explanation:
Evaluate the expression for v = 12.
Write your answer as a decimal or whole number.
–10.9 + 4v =
Answer:
1.
v = 12
-10.9 + 4v
-10.9 + 4(12)
-10.9 + 48
= 37.1
Pls help me with this question
6x10-4 in standard notation
Answer:
The Answer is 2(3x^10-2) Hope this helps :)
-by-step explanation:
50 points PLSS HELP MEE!!!! What is the value of x in the equation 5x+3 - 4x? -3
- 17
3
Answer:
-3Step-by-step explanation:
I believe it is
5x+3 = 4xAdding -4x - 3 to both sides
5x +3 - 4x - 3 = 4x - 4x - 3Simplifying
x = - 3Answer is - 3
Answer:
x + 3
Step-by-step explanation:
5x + 3 - 4x
(5x - 4x) + 3
x + 3
Best of Luck!
Don’t know the answer
Answer: The answer i think is A
Step-by-step explanation:45w stands for how much she paid each week, while 123.95 stands for a one time payment
This all should equal 753.95 which is how much they paid in total.
Segment AB is congruent to segment AB. This statement shows the ______ property. reflexive symmetric transitive substitution
Answer:
the answer is reflective
Step-by-step explanation:
Answer:
A). reflexive
Step-by-step explanation:
The correct answer is reflexive. I know because I got it right on the Edge quiz. Trust me!
Which of the following expressions is equivalent to (x + 5)2?
O A. (x + 5)(x + 5) + 10(x + 5)
OB. (x - 5)(x + 5) + 10(x + 5)
OC. (x + 5)(x + 5) + 10(x - 5)
OD. (x - 5)(x - 5) + 10(x - 5)
Please someone help me this texts is so important and I need it done by the end of today!
Answer:
B
Step-by-step explanation:
Expand (x+5)^2 through binomial expansion and you get x^2+10x+25.
Break up the problem into little pieces like (x-5)(x+5) and 10(x+5)
Solve the first piece (x-5)(x+5) by doing something like FOIL.
x^2-25
Do the second piece
10x+50
When you add them together, it becomes x^2+10x+25, and (x+5)^2=(x-5)(x+5)+10(x+5).
Evaluate the function 7(x) = 2x+8 when x = 6.
O 96
O 28
O 20
O 16
Answer:
20
Step-by-step explanation:
Substitute x = 6 into f(x), that is
f(6) = 2(6) + 8 = 12 + 8 = 20
write a calculation and a result that represents a number that is 5 greater than 3
Step-by-step explanation:
vt7vy7v fyy7ctyxt6zqDg gj
Combining Like Terms
Equation: 5x + 7y -2x + 3y
So I get why it could be simplified into 5x - 2x and 7y + 3y, but how do we get the operation to combine those two?
What I mean is what would go in the underline here -
5x - 2x _ 7y + 3y
Explanation please not just answer
Help me guys! This question is hard for me
Answer:
should be answer A
Step-by-step explanation:
Answer:
I'm pretty sure the answer is D
Step-by-step explanation:
it appears to be a reflection to the plane below it. and it is one of the only ones to remain its shape and stay rigid(the same)
Is -4 greater than -4.25?
Answer:
Yes
Step-by-step explanation:
The smaller the negative number, the greater it is. i.e., -230 < -9.
Answer:
yes
Step-by-step explanation:
it is closer to zero on a number line, therefore the value of -4 is higher even though it's negative