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Korvikt [17]
3 years ago
15

Solve: (3-x)(4x+3)<(2x-1)(3-x)

Mathematics
1 answer:
sergiy2304 [10]3 years ago
3 0

Please refer to the above attachment

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Josh bought 2 pairs of jeans for $25.60 each and some shirts for $15.30 each. If he spent a total of $112.40,
mojhsa [17]

Answer:

5 shirts

Step-by-step explanation:

2 pairs of jeans $25.60

$112.40-$25.60=$86.80

if each pair of T-shirts cost $15.30

$15.30 times 5=$76.50

$86.80 - $76.50=$10.30

so John bought 5 shirts however he got some many left $10.30

5 0
2 years ago
Connor is painting a superhero with this belt buckle shown. What is the area of the belt buckle in square Inches? 9 inches 2.5 i
antoniya [11.8K]

Answer:

87.5 square inches

Step-by-step explanation:

The belt knuckle as shown in the diagram above consist of a 4 rectangles (2 are the of the same dimension, the other two are of the same direction differently) and a rectangle.

Area of the belt knuckle = area of the 4 triangles + area of the rectangle

✔️Area of the 2 rectangles with the following dimensions:

base (b) = 9 inches

height (h) = 2.5 inches

Area of the two triangles = 2(½*b*h)

= 2(½*9*2.5)

= 22.5 inches²

✔️Area of the 2 rectangles with the following dimensions:

base (b) = 4 inches

height (h) = 5 inches

Area of the two triangles = 2(½*b*h)

= 2(½*4*5)

= 20 inches²

✔️Area of the rectangle = l*w

l = 9 inches

w = 5 inches

Area = 9*5 = 45 inches²

✔️Area of the belt knuckle = 22.5 + 20 + 45 = 87.5 square inches

3 0
2 years ago
Save me the headache
maxonik [38]

(9\sin2x+9\cos2x)^2=81

Taking the square root of both sides gives two possible cases,

9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1

or

9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1

Recall that

\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta

If \alpha=2x and \beta=\dfrac\pi4, we have

\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}

so in the equations above, we can write

\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1

Then in the first case,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi

(where n is any integer)

\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi

\implies x=n\pi\text{ or }\dfrac\pi4+n\pi

and in the second,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi

\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi

\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi

Then the solutions that fall in the interval [0,2\pi) are

x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4

5 0
3 years ago
Read 2 more answers
A total of 766 tickets were sold for the school play. They were either adult tickets or student tickets. There were 66 more stud
Svetllana [295]
350 because 350+416=766
8 0
3 years ago
the graph of a linear function is given below. What is the zero of the function? a) -5. b) 2/5. c) 2. d) 5/2
Murrr4er [49]

The zero of a function is the x-value at which the function value is zero. That is, the value of the function that intersects the x-axis. From the picture, the zero is -5

4 0
1 year ago
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