Solve for x.

x−9=−524

Enter your answer as a mixed number in simplest form by filling in the boxes.

x = $$

Answer:

  1 ≤ x < 7/4

Step-by-step explanation:

The function f(x) is defined as increasing on the domain (-8, 4), so the ordering of the arguments is not changed by the function. We can solve the inequality as though f(x) = x, which is increasing everywhere.

  f(4x -3) ≥ f(2 -x²)

  4x -3 ≥ 2 -x² . . . . . . using our assumed definition of f(x)

  x² +4x -5 ≥ 0 . . . . . subtract 2-x²

  (x -1)(x +4) ≥ 0 . . . . factored form; zeros at -4, +1

The values of x that make this true are ones that make the factors have the same signs: x ≤ -4 or x ≥ 1.

The domain of f(x) is -8 < x < 4, so we require the arguments of f be restricted to those values

Left side

  -8 < 4x -3 < 4

  -5 < 4x < 7

  -5/4 < x < 7/4

Right side

  -8 < 2 -x² < 4 . . . . . right side is always true

  x² < 10 . . . . . . . . . . . add x² +8

  |x| < √10 . . . . . . . . . . less restrictive than the the left-side restriction

With the given domain restrictions on f(x), the inequality will be true on the interval ...

  1 ≤ x < 7/4

__

Additional comment

The attached graph shows the left-side function argument (dashed blue) and the right-side function argument (dashed green) with the given domain restrictions. The red curve is the difference in function values for the function defined as above. It is only non-negative between 1 and 1.75 as we found above.

This general behavior is applicable for any f(x) that can be described as in the problem statement. For example, f(x) = √(x+8) also gives an increasing curve for the difference f(4x-3)-f(2-x²) on the interval (-5/4, 7/4) with an x-intercept of +1.

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Answer:

Step-by-step explanation:

he paid a 3 dollar fee so we can remove that 23.79-3 = 20,79

now we devide 20,79 by 11 or 189 minutes.

Value is -1 , Hope this helps.

Answer:

x = 9,-21

Step-by-step explanation:

Given:

[tex]\displaystyle \large{|x+6|-7=8}[/tex]

Transport -7 to add 8:

[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]

Cancel absolute sign and add plus-minus to 15:

[tex]\displaystyle \large{x+6=\pm 15}[/tex]

Transport 6 to subtract ±15:

[tex]\displaystyle \large{x=\pm 15-6}[/tex]

Consider:

[tex]\displaystyle \large{x= 15-6}[/tex] or [tex]\displaystyle \large{x = -15-6}[/tex]

[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

Solution:

[tex]\displaystyle \large{x = 9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

__________________________________________________________

Second Method

Given:

[tex]\displaystyle \large{|x+6|-7=8}[/tex]

Transport -7 to add 8:

[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]

Absolute Function Property:

[tex]\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}[/tex]

Consider both intervals:

When x ≥ a then:

[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}[/tex]

Transport 6 to subtract 15:

[tex]\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}[/tex]

When x < a then:

[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}[/tex]

Transport -6 to add 15:

[tex]\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}[/tex]

Transport negative sign to 21:

[tex]\displaystyle \large{x=-21}[/tex]

Solution:

[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

__________________________________________________________

Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!

Answer:

Line 2

Step-by-step explanation:

When factoring the second bracket, 1 x -8 is -8.

Answer:

4

Step-by-step explanation:

Check the picture below.

so the surface area of the pyramid will be the sum of the areas of the base and the four triangular faces.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{4 triangular faces}}{4\left[ \cfrac{1}{2}(7.5)(16) \right]}~~ + ~~\stackrel{\textit{rectangular base}}{(7.5)(7.5)}}\implies 240~~ + ~~56.25\implies 296.25~ft^2[/tex]

The figure given in the image is a cuboid which have 3 sides, with Length, breadth and height, it's basically a 3-D shape, so here for volume of the cuboid, we can just multiply all the sides and we will be just done then after writing the SI unit of volume against it

[tex]{:\implies \quad \sf So,\:\: Volume=4\dfrac{2}{5}\times 10\times 3}[/tex]

[tex]{:\implies \quad \sf Volume=\bigg(\dfrac{20+2}{5}\bigg)\times 10\times 3}[/tex]

[tex]{:\implies \quad \sf Volume=\dfrac{22}{5}\times 10\times 3}[/tex]

[tex]{:\implies \quad \sf Volume=22\times 2\times 3}[/tex]

[tex]{:\implies \quad \sf Volume=44\times 3=\boxed{\bf{132\:\: m^{3}}}}[/tex]

Answer:

She was finished with dinner at 6:50

Step-by-step explanation:

3:45 + 2 = 5:45

5:45 + 30 = 6:05

6:05 + 45 = 6:50

Answer:

54

Step-by-step explanation:

9x6=54

Answer:

9000 grams

Step-by-step explanation:

multiply the mass value by 1000

Answer:

$149 - skateboard price

$52 - carly's money

$20 × 5 cars = $100

$100 + $52 = $152

$152 - $149 = $3 left

Answer:

54 kg

Step-by-step explanation:

We need to multiply!!

6 x 9 = 54

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

is this from flvs?

Step-by-step explanation:

Answer:

"4 or less, let it rest. 5 or more, raise the score."

Step-by-step explanation:

1) 5.57, 5.62, 5.59

2) 2.349, 2.352, 2.346, 2.354

3)

0.7

0.3

1.5

3.4

4)

3.74

0.93

0.33

1.56

I hope this helps! Have a lovely day!! :)

(I would appreciate brainliest!!)

Answer:

h=9

g=61

Step-by-step explanation:

16-h=7

g+4=65

&

Opposite angles and sides are equal in a paralleogram

Amd

Answer:

[tex]\displaystyle \textcolor{black}{4.}\:[-3, -5][/tex]

[tex]\displaystyle \textcolor{black}{3.}\:[8, -1][/tex]

[tex]\displaystyle \textcolor{black}{2.}\:[4, -7][/tex]

[tex]\displaystyle \textcolor{black}{1.}\:[3, -2][/tex]

Step-by-step explanation:

When using the Elimination method, you eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-5x - 3y = 30}} \right.[/tex]

{2x - 3y = 9

{⅖[−5x - 3y = 30]

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-2x - 1\frac{1}{5}y = 12}} \right. \\ \\ \frac{-4\frac{1}{5}y}{-4\frac{1}{5}} = \frac{21}{-4\frac{1}{5}} \\ \\ \boxed{y = -5, x = -3}[/tex]

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

[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {x + 3y = 5}} \right.[/tex]

{x - 2y = 10

{⅔[x + 3y = 5]

[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {\frac{2}{3}x + 2y = 3\frac{1}{3}}} \right. \\ \\ \frac{1\frac{2}{3}x}{1\frac{2}{3}} = \frac{13\frac{1}{3}}{1\frac{2}{3}} \\ \\ \boxed{x = 8, y = -1}[/tex]

_______________________________________________

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {y = -8x + 25}} \right.[/tex]

{y = −3x + 5

{−⅜[y = −8x + 25]

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {-\frac{3}{8}y = 3x - 9\frac{3}{8}}} \right. \\ \\ \frac{\frac{5}{8}y}{\frac{5}{8}} = \frac{-4\frac{3}{8}}{\frac{5}{8}} \\ \\ \boxed{y = -7, x = 4}[/tex]

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

[tex]\displaystyle \left \{ {{y = -x + 1} \atop {y = 4x - 14}} \right.[/tex]

{y = −x + 1

{¼[y = 4x - 14]

[tex]\displaystyle \left \{ {{y = -x + 1} \atop {\frac{1}{4}y = x - 3\frac{1}{2}}} \right. \\ \\ \frac{1\frac{1}{4}y}{1\frac{1}{4}} = \frac{-2\frac{1}{2}}{1\frac{1}{4}} \\ \\ \boxed{y = -2, x = 3}[/tex]

_______________________________________________

I am joyous to assist you at any time.

Answer:

x=17.771mm

Step-by-step explanation:

given a right triangle

to find vslue of x

solution (perpendicular) ² + (base) ² =(hypotenus) ²

using pythagorus theorem

(16.5)²+(6.6)²=(x)²

272.25+43.56=(x)²

315.81=(x)²

√315.81=x

x=17.771mm

Answer:

By Pythagoras theorem

H^2=P^2+B^2

x^2=(6.6)^2+(16.5)^2

x^2=43.56+272.25

x^2=315.81

x=√315.81

x=17.771mm

Answer:

I don't know if these are right

2.756

3. 1,426.42

well, hmmm to check for polar symmetry, hmmm say we simply replace the value for either "r" or "θ" or both in the original equation, if the equation rendered is the same as the original, there you have it, symmetry, so let's do that.

[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=-7+2cos(3\theta )\implies (-r)=-7+2cos[3(-\theta )]\implies -r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\implies r=7-2cos(3\theta )\impliedby \textit{woopsie, no dice} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=-7+2cos(3\theta )\implies r=-7+2cos[3(-\theta )]\implies r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\impliedby \textit{low and behold\qquad \Large \checkmark}[/tex]

now, we could run a test for "the pole" or namely the origin by simply changin r = -r, however we already know where the symmetry is, so no need.

Check the picture below.

Answer:

5b

Step-by-step explanation:

Hope this helps <3

The measure of the angle that would maximize the area of this isosceles trapezoid is equal to 0.4395 rad.

Given the following data:

Mathematically, the area of a trapezium is given by this formula:

A = ½ × (a + b) × h

A = ½ × (12 + 2l) × h

A = h(6 + l)

Next, we would derive a mathematical expression for A in terms of h as follows;

A = (6 + 4sin(θ)) × 4cosθ

In order to determine the value of θ for which the area of this isosceles trapezoid is maximized, we would differentiate the area (A) with respect to angle (θ):

Note: sin²θ + cos²θ = 1   ⇒ cos²θ = 1 - sin²θ.

[tex]\frac{dA}{d\theta} =16 cos^{2} \theta - 4sin \theta(6+4sin \theta)\\\\\frac{dA}{d\theta} = 16 cos^{2} \theta - 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} =16(1-sin^{2} \theta)- 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} = - 32 sin^{2} \theta - 24sin\theta+16\\\\32 sin^{2} \theta + 24sin\theta-16=0[/tex]

Next, we would use the quadratic formula to solve for the value of sinθ.

Mathematically, the quadratic formula is given by this equation:

[tex]sin\theta = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Where:

Substituting the parameters into the formula, we have;

[tex]sin\theta = \frac{-24\; \pm\; \sqrt{24^2 - 4(32)(-16)}}{2(32)}\\\\sin\theta = \frac{-24\; \pm\; \sqrt{2624}}{64}\\\\sin\theta = \frac{-24\; \pm\; 51.23}{64}\\\\sin\theta = \frac{-24\;+\; 51.23}{64}\\\\sin\theta = \frac{27.23}{64}\\\\sin\theta = 0.4255\\\\\theta = sin^{-1}(0.4255)[/tex]

θ = 0.4395 rad.

Note: We would only consider the positive value of the quadratic root.

For the obtuse interior angles of the trapezoid, we have [tex](\frac{\pi}{2} +0.4395)[/tex]

Similarly, the measure of the acute interior angles of the trapezoid is [tex](\frac{\pi}{2} -0.4395)[/tex]

Read more on isosceles trapezoid here: https://brainly.com/question/4758162

Step-by-step explanation:

18 ÷ 60 = 0.3

so 0.3 km per min.

0.3 × 20 = 6

so 6 km per hour

Answer:Number of subsets will be given by 2^n, where n is the number of elements in the set.

Step-by-step explanation:

Number of elements is 5. Therefore, the number of subsets that can be formed from the given set is 2^5 = 32.

Answer:

an = a1 + d (n - 1)

aⁿ = a₁ˣ⁻1

Answer:

[tex] \orange{ \boxed{ \sf{ ( \: {x}^{2} + 11x + 18 \: ) \: sq. \: units}}}[/tex]

Solution :

Lenght = x + 9

Width = x + 2

[tex] \sf \green{area \: = \: (x + 9)(x + 2)} \\ \sf \green{ = \: { {x}^{2} + 11x + 18}} [/tex]

Answer:

[tex]x^2+11x+18\: \sf(square\:units)[/tex]

Step-by-step explanation:

To use the area model of solving multiplication and division problems, calculate the area of each of the colored rectangles and add them together.

Area of a rectangle = Length × Width

Area of blue rectangle:  [tex]x \times x = x^2[/tex]

Area of pink rectangle:  [tex]x \times 9 = 9x[/tex]

Area of green rectangle:  [tex]2 \times x=2x[/tex]

Area of orange rectangle:  [tex]2 \times 9=18[/tex]

Area of entire rectangle = blue + pink + green + orange

                                        = [tex]x^2+9x+2x+18[/tex]

                                        = [tex]x^2+11x+18\: \sf(square\:units)[/tex]

Answer:

(2a-b)(2a+b-1)

Step-by-step explanation:

Answer:

divide the anser in the pasage

Step-by-step explanation:

divide the two numbers

Answer: ur dad

Step-by-step explanation:

lol

There are 7 positive integers in between 28/3 and 83/5.

What is an integer?

An integer is a whole number (not a fractional number) that can be positive, negative or zero.

Given that;

Two fractions are;

28/3 and 83/5.

Now, Write fraction into decimal form as;

28/3 = 9.33

83/5 = 16.6

So, All Integers in between 9.33 and 16.6 are;

⇒ 10, 11, 12, 13, 14, 15, 16

Thus, There are 7 positive integers in between 28/3 and 83/5.

Learn more about the integers visit:

https://brainly.com/question/24653557

#SPJ2

the lcm would be 79380

Step-by-step explanation:

5×7×7

2×2

×3×3×3×3

muliply all the 3 numbers and then you get 79380