Simplify the expression 5(3u-4) +6
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Use the functions m(x) = 5x + 4 and n(x) = 6x − 9 to complete the function operations listed below.Part A: Find (m + n)(x). Show your work. Part B: Find (m ⋅ n)(x). Show your work. Part C: Find m[n(x)]. Show your work.
How do you compute two thirds of 6 ounces what is two thirds of 6 ounces
11. Quadrilateral GHJK is similar toquadrilateral RSTU. If GH = JK = 10, HJ = KG = 14, and RS = TU = 16, what is the scale factor of quadrilateral GHJK to quadrilateral RSTU?
All of the following expressions are equivalent except _____.A.2 - xB.x - 2C.-2 + xD.x + (-2)
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Answer:
14
Step-by-step explanation:
In total, Emily has yards of ribbon.
Each bow requires yards of ribbon
To figure out, we divide total amount of ribbon by amount each bow needs:
Number of bows =
So the maximum number of "complete" bows Emily can make is 14
Final answer:
Emily has a total of 27 1/4 yards of ribbon. Each bow requires 1 5/6 yards, therefore Emily can make 14 bows with the ribbon she has.
Explanation:
To solve this problem, we first need to determine the total amount of ribbon that Emily has. She has one piece that is 23 yards long and another that is 4 1/4 yards long. To find the total, we add these two lengths together:
23 yards + 4 1/4 yards = 27 1/4 yards
Each bow Emily makes needs 1 5/6 yards of ribbon. To find out how many bows she can make, we divide the total amount of ribbon by the amount needed for each bow:
27 1/4 yards ÷ 1 5/6 yards = 14.6(around)
Since Emily cannot make a fraction of a bow, we round down to the nearest whole number. So, Emily can make 14 bows.
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1/2 + 1/2 = 2/4
2/4+ 1/4= 3/4
cot (–270°) = 1
cot (–270°) = –1
cot (–270°) = 0
undefined
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Answer:
cot(-270) = 0
Step-by-step explanation:
given cot ( -270)
In trigonometry function we will use cot ( -x) = -cotx
so cot (-270) = - cot270
trigonometry table
II quadrant I quadrant ( All positive)
sin θ 90+θ 90 -θ
cosec θ 180-θ 360+θ
third quadrant fourth quadrant
tan θ 180+θ cos θ 270+θ
cot θ 270 - θ sec θ 360-θ
Given
cot (-270) = -cot ( 270)
= - cot ( 180 + 90) (third quadrant above table)
= -cot 90 =0 ( cot θ positive in third quadrant
Final answer:-
cot(-270) =0
Final answer:
The value of cot(−270°) is undefined because it involves a division by zero, as its calculation is based on the cosine and sine values at −270° on the unit circle, which are 0 and 1, respectively.
Explanation:
To find the value of cot (−270°), we need to understand where −270° places us on the unit circle. A full circle is 360°, so starting at the positive x-axis and moving clockwise (since the angle is negative), we move 270° to end up at the positive y-axis. The cotangent function is the ratio of the adjacent side to the opposite side in a right triangle, or the cosine divided by the sine.
At −270° (or 270° in the positive, counter-clockwise direction), the coordinate on the unit circle is (0, 1). The sine of −270° is the y-coordinate (which is 1), and the cosine of −270° is the x-coordinate (which is 0). Therefore, cot (−270°) = cos (−270°) / sin (−270°) = 0/1. Since division by zero is undefined, cot (−270°) is undefined.
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Answer:
La ecuación del círculo en la forma es (x - 145/12)² + (y - 109/16)² = (545/48)²
Step-by-step explanation:
La información dada son;
La primera línea tangente al círculo en el punto (10, -1) = 3·x - 4·y = 34
La segunda línea tangente al círculo en el punto (3, 0) = 4·x + 3·y = 12
Las rectas tangentes dadas en forma de pendiente e intersección, y = m·x + c son;
3·x - 4·y = 34
4·y = 34 - 3·x
y = 34/4 - 3/4·x = 8.5 - 3/4·x
Primera tangente
y = 8.5 - 3/4·x
3·y = 12 - 4·x
y = 12/3 - 4/3·x = 4 - 4/3·x
Segunda tangente
y = 4 - 4/3·x
La recta de la ecuación de los radios es perpendicular a la tangente y se encuentra con la tangente en el punto de intersección con el círculo como sigue;
La primera ecuación radial tiene pendiente, m = 1/(-3/4) = 4/3
La ecuación en forma de punto y pendiente es y - (-1) = 4/3×(x - 10)
y = 4/3×(x - 10) - 1 = 4/3·x - 40/3 - 1 = 4/3·x - 43/3
Por tanto, la ecuación del primer radio es;
y = 4/3·x - 43/3
La segunda ecuación radial tiene pendiente, m = 1/(-4/3) = 3/4
La ecuación en forma de punto y pendiente es y - 0 = 3/4×(x - 3)
y = 3/4×(x - 3) = 3/4·x - 9/4
Por tanto, la ecuación del segundo radio es;
y = 3/4·x - 9/4
Los dos radios se encuentran en el centro dado como sigue;
4/3·x - 43/3 = 3/4·x - 9/4
4/3·x - 3/4·x = 43/3 - 9/4
7/12·x = 145/12
x = 145/12
y = 3/4·x - 9/4 = 3/4·145/12 - 9/4 = 109/16
Las coordenadas del centro = (h, k) = (145/12, 109/16)
La longitud del radio, r = √((109/16 - 0)² + (145/12 - 3)²) = 545/48
La ecuación del círculo en la forma (x - h)² + (y - k)² = r² es, por lo tanto;
(x - 145/12)² + (y - 109/16)² = (545/48)².