Solve |2x - 6| < 10

{x|-2 < x < 8}
{x|2 < x < 8}
{x|-8 < x < 8}

Answer:

The factors of the given equation are:

(11x−8)(11x+2)

Step-by-step explanation:

Since both terms are perfect squares,

Factorize using the difference of squares formula,

[tex]a^{2} -b^{2}[/tex][tex]=(a+b)(a-b)[/tex]

where a=11x−3 and b=5.

=> (11x-3+5)(11x-3-5)

=> (11x+2)(11x−8)

=>[tex](11x-3)^{2}-25[/tex]

Use the binomial theorem [tex](a-b)^{2}=a^{2} +b^{2} -2ab[/tex] to expand[tex](11x-3)^{2}-25[/tex]

=> [tex](11x^{2})+(3)^{2}- 2(11x)(3)-25[/tex]

=>[tex]121x^{2} + 9 - 66x -25[/tex]

=> [tex]121x^{2} -16+ 66x[/tex]

By the splitting method,

=> (11x−8)(11x+2)

The factors of the equation are (11x−8)(11x+2).

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Answer:  [tex]\textsf{y = 3/4x - 7.75}[/tex]

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Given:  [tex]\textsf{Passes through (5, -4) with a slope of 3/4}[/tex]

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

Solution:  In order to determine the equation we need to first plug the values into the point-slope form, simplify, distribute, and solve for y to get our final result.

Plug in the values

Simplify the expression and distribute

Subtract 4 from both sides

The equation in slope-intercept form that follows the information that was provided is y = 3/4x - 7.75

Answer:

a. y-intercept:(0,  -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)

b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)

Step-by-step explanation:

a:

 So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes [tex]y=(0)^2-0-6[/tex] which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]. In this case a=1, b=-1, c=-6. So plugging those values in you get [tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}[/tex], which simplifies to [tex]x=\frac{1\pm5}{2}[/tex]. This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of [tex]y=(x-h)^2+k[/tex] where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be

Move c to the other side

[tex]y+6=x^2-x[/tex]

Complete the square by adding (b/2)^2

[tex]y+6+0.25 = x^2-x+0.25[/tex]

Rewrite as square binomial

[tex]y+6.25 = (x-0.5)^2[/tex]

Isolate y

[tex]y=(x-0.50)^2-6.25[/tex]

(h, k) = 0.50, -6.25 which is the vertex

b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation [tex]y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}[/tex]. which simplifies to [tex]x=\frac{-1\pm5}{-2}[/tex] which gives the values -2 and 3. To find the vertex it's the same process as before

Factor out -1

[tex]y=-(x^2-x-6)[/tex]

Add 6 to both sides (on the left side add -6 since -1 was factored out).

[tex]y-6=-(x^2-x)[/tex]

Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)

[tex]y-6-0.25 = -(x^2-x+0.25)[/tex]

Rewrite as square binomial

[tex]y-6.25=-(x-0.5)^2[/tex]

Add 6.25 to both sides

[tex]y=(x-0.50)^2+6.25[/tex]

(h, k) = (0.50, 6.25)

When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.

Answer:

a) y-intercept (0,  -6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, -6.25)

b) y-intercept (0, 6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, 6.25)

Step-by-step explanation:

Answer:

440cm²

Step-by-step explanation:

*Area= (a+b)/2×h

(19+25)/2*20

= _ * 440cm². *_

Answer:

440cm²

Step-by-step explanation:

I believe its right

Answer:

D

Step-by-step explanation:

2 units right 1 unit down

Good luck

Answer:

(x-2, y+1)

Step-by-step explanation:

G(0, 4) -> G'(-2, 5)

H(2, 4) -> H'(0, 5,)

E(0, 2) -> E'(-2, 3)

F(-1, 2) -> F'(-3, 3)

Answer:

800

Step-by-step explanation:it's cuz g represents

[tex]\boldsymbol{5x+15=30}[/tex]

Subtract 15 from both sides.

Subtract 15 from 30 to get 15.

Divide both sides by 5.

Divide 15 by 5 to get 3.

Let x=3.

Checked ✅

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

B. took test

Step-by-step explanation:

Answer:

B. Jonathan is correct. Kevin made an error at step 3.

Step-by-step explanation:

Answer:

The area is approximately 28.73ft²

Step-by-step explanation:

Given: Circumference = 19 ft

The necessary formula area,

Area: A = πr²

Circumference: C = 2πr

Combine:

A = [tex]\frac{C^{2} }{4\pi }[/tex]

A = [tex]\frac{19^{2} }{4\pi } \\\\ \frac{361 }{4\pi }[/tex]

A = 28.72747

Answer:

196

Step-by-step explanation:

70% multiply by 4/5(80%) which is 56%

56% times 350

Answer:

B

Step-by-step explanation:

look at the graph, it is really easy with such basic numbers involved :

the red dotted line is

y = 2

since the line is dotted (= the points on the line are not included in the solution), the colored area is below the line is

y < 2

the blue line is clearly just a 45° basic line through the origin (0,0), and that means for every point in that line x is equal to y.

y = x

and the line is solid, so the points are included in the solution. the shaded area is above the line, so, we need to use the ">" relation :

y >= x

the required solution is the combination of both, and therefore, B is correct.

Answer:

0.32

Step-by-step explanation:

2^3 = 2*2*2 = 8

5^2 = 5*5 = 25

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8/25 = 0.32

Answer:

-1/2

Step-by-step explanation:

sin(30 degrees) = sin (pi/6) = 1/2

cos(30 degrees) = cos (pi/6) = [sqrt(3)]/2]

sin (60 degrees) = sin(pi/3) = [sqrt(3)]/2]

1/2 - [sqrt(3)/2] / [sqrt(3)/2] = -1/2

The rational exponent form of the given expression is b³. The correct option is the second option b³

From the question, we are to determine the rational exponent form of the given expression

The given expression is

[tex]\sqrt{b^{6} }[/tex]

From one of the laws of indices, we have that

[tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]

Thus,

[tex]\sqrt{b^{6} } = b^{\frac{6}{2} }[/tex]

= [tex]b^{3}[/tex]

∴√b⁶ = b³

Hence, the rational exponent form of the given expression is b³. The correct option is the second option b³

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Answer:

D

Hope this helps!

In the triangle ABC, the length of the line segment SA=3 ft ( 3rd option).

In triangle ABC,

According to the triangle proportionality theory, we know that if a triangle has a line segment parallel to one of its sides, the line segment splits the other sides correspondingly.

Hence,

SA/SB=CT/BT

⇒SA/10=2.7/9

⇒SA=(2.7*10)/9

⇒SA=3

So, the length of SA is 3 ft.

Therefore the 3rd option is correct.

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Answer:

1.   won 50 games and lost 32 games

2.  233 Democrats and 202 Republicans

3.  360 miles

4.  6 hours

5.  18 miles

Step-by-step explanation:

Question 1

From the given information:

Substitute Equation 2 into Equation 1 and solve for y:

⇒ y - 18 + y = 82

⇒ 2y - 18 = 82

⇒ 2y = 100

⇒ y = 50

Substitute found value of y into Equation 2 and solve for x:

⇒ x = 50 - 18

⇒ x = 32

Therefore, the team won 50 games and lost 32 games.

Question 2

From the given information:

Substitute Equation 2 into Equation 1 and solve for d:

⇒ r + 31 + r = 435

⇒ 2r + 31 = 435

⇒ 2r = 404

⇒ r = 202

⇒ d = 233

Substitute found value of d into Equation 2 and solve for r:

⇒ 233 = r + 31

⇒ r = 202

Therefore, there were 233 Democrats and 202 Republicans.

Question 3

Given:

Distance (d) = vt

⇒ d = 180 × 2

⇒ d = 360 miles

Question 4

Given:

Time (t) = d ÷ v

⇒ t = 420 ÷ 70

⇒ t = 6 hours

Question 5

If the velocity of the bus is 12 mph less than the car then:

⇒ c = b + 12

Given journey times:

Distance (d) = vt

Create two equations for distance:

Bus

⇒ d = b × 0.75 = 0.75b

⇒ d = 0.75b

Car

⇒ d = (b + 12) × 0.5

⇒ d = 0.5b + 6

Distance for both vehicles is the same. Equate the two equations for d and solve for b (velocity of bus):

⇒ d = d

⇒ 0.75b = 0.5b + 6

⇒ 0.25b = 6

⇒ b = 24 mph

Substitute the value of b into one of the distance formulas and solve for d:

⇒ d = 0.5(24) + 6

⇒ d = 18 miles

Answer:

Un= 1 + (n-1)4

Step-by-step explanation:

a=1

d=5-1=9-5=4

using the formula Un=a+(n-1)d

Answer:

225 cm²

Step-by-step explanation:

dilatation factor = 3 , then

area factor = 3² = 9

the area of the dilated polygon is then 9 times the area of the original so

area of dilated polygon = 9 × 25 = 225 cm²

Answer:

b

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

the second option is the only expression that came up with the value of 64

(2^6)

Answer:2,⁶     (–8)²    and  (–2)⁶   hope I helped.        : )

Step-by-step explanation:                                                                                                                                              

hi :)

The solution of the inequality x³ + 4x² > x + 4 will be -4 < x < -1 or x > 1. Then the correct option is C.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

x³ + 4x² > x + 4

Then the inequality can be written as

x³ + 4x² – x – 4 > 0

Then the factor will be

x²(x + 4) – 1(x + 4) > 0

       (x² – 1)(x + 4) > 0

(x – 1)(x + 1)(x + 4) > 0

Then the solution will be

x – 1 > 0

     x > 1

x + 1 < 0

    x < -1

x + 4 > 0

     x > -4

Then the correct option is C.

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Step-by-step explanation:

Answer:

(x-9)(x+8)

Step-by-step explanation:

Use the AC method

Answer:

The square root of 36/196 is 3/7.

The square root of 36/169 is 6/13.

Answer:

5x + 15

Step-by-step explanation:

To expand the binomial, you need to multiply each term inside the parentheses by 5.

(x + 3)5

= (x * 5) + (3 * 5)

= 5x + 15

Answer:

x = 55°

Step-by-step explanation:

Hello!

The sum of angles in a triangle is 180°.

To solve for x, we have to subtract the given angles from 180°.

The value of x is 55°.

Angle sum property of a triangle

∠A + ∠B + ∠C = 180°

We need to find the value of ∠A

According to the angle sum property of a triangle

⇢∠A + ∠B + ∠C = 180°

⇢∠A + 75° + 50° = 180°

⇢∠A + 125° = 180°

⇢∠A = 180° - 125°

⇢∠A = 55°