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Archy [21]
3 years ago
7

Solve the inequality: –3(x + 2) > 4x + 5(x – 7)

Mathematics
1 answer:
Gwar [14]3 years ago
4 0

Answer:

29/12 > x

Step-by-step explanation:

–3(x + 2) > 4x + 5(x – 7)

Distribute

-3x -6 > 4x +5x-35

Combine like terms

-3x-6 > 9x -35

Add 3x to each side

-3x+3x-6 > 9x+3x -35

-6 > 12x-35

Add 35 to each side

-6+35 > 12x -35+35

29 > 12x

Divide each side by 12

29/12 > 12x/12

29/12 > x

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Which inequality statement describes the two numbers on a number line? "−5 and a number 4 units to the right of −5" A) 4 < −5
Marina CMI [18]

Answer: D

Step-by-step explanation:be cause you have to add 4 to negetive 5 and and that negetive 1 which is greater than -5

8 0
3 years ago
What quadrilateral always has 4 congruent angles and opposite that are congruent and paralle
nignag [31]
Another quadrilateral that you might see is called a rhombus. All four sides of a rhombus are congruent. Its properties include that each pair of opposite sides is parallel, also making it a parallelogram. In summary, all squares are rectangles, but not all rectangles are squares.
8 0
3 years ago
Read 2 more answers
1-sin^2x/sinx-cscx <br><br>How do I solve this problem? I keep getting the wrong answer.
Annette [7]

Answer:

-sinx

Step-by-step explanation:

a trig identity that is crucial to solving this problem is: sin^2 + cos^2 = 1

with knowing that, you can manipulate that and turn it into 1 - sin^2x = cos^x

so 1-sin^2x/sinx - cscx becomes cos^2x/sinx - cscx

it is also important to know that cscx is the same thing as 1/sinx

knowing this information, cscx can be replaced with 1/sinx

(cos^2x)/(sinx - 1/sinx)

now sinx and 1/sinx do not have the same denominator, so we need to multiply top and bottom of sinx by sinx; it becomes....

cos^2x

---------------------

(sin^2x - 1)/sinx

notice how in the denominator it has sin^2x-1 which is equal to -cos^2x

so now it becomes:

cos^2x

--------------

-cos^2x/sinx

because we have a fraction over a fraction, we need to flip it

cos^2x          sinx

---------- * ----------------

1                  -  cos^2x

because the cos^2x can cancel out, it becomes 1

now the answer is -sinx

3 0
3 years ago
In circle D, angle ADC measures (7x + 2)°. Arc AC
Akimi4 [234]

Answer:

The measure of angle ABC is 36° ⇒ 1st answer

Step-by-step explanation:

Let us revise some important facts in the circle

The measure of the center angle is equal to the measure of its subtended arc

The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc

The vertex of a central angle is the center of the circle and its sides are radii in the circle

The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle

In circle D

∵ D is the center of the circle

∵ A and C lie on the circle

- DA and DC are radii

∴ ∠ADC is a central angle subtended by arc AC

∴ m∠ADC = m of arc AC

∵ m∠ADC = (7x + 2)°

∵ m of arc AC = (8x - 8)°

- Equate them to find x

∴ 8x - 8 = 7x + 2

- subtract 7x from both sides

∴ x - 8 = 2

- Add 8 to both sides

∴ x = 10

Substitute the value of x in the measure of ∠ADC

∵ m∠ADC = 7(10) + 2 = 70 + 2

∴ m∠ADC = 72°

∵ AB and BC are two chords in circle D

∴ ∠ABC is an inscribed angle subtended by arc AC

∵ ∠ADC is a central angle subtended by arc AC

- By using the 2nd fact above

∴ m∠ABC =  m∠ADC

∴ m∠ABC =  × 72

∴ m∠ABC = 36°

7 0
2 years ago
The image point of A after a translation right 4 units and up 3 units is the point
e-lub [12.9K]

Answer:

(--6,-1)

Step-by-step explanation:

Right 4 units, to go back, left 4 units

Up 3 units, to go back, down 3 unites

Left : -2 - 4  = -6

Down : 2 - 3 = -1

4 0
3 years ago
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