The solution to an absolute value inequality is shown on the graph below.

Answer:

  y = (x/(1-x))√(1-x²)

Step-by-step explanation:

The equation can be translated to rectangular coordinates by using the relationships between polar and rectangular coordinates:

  x = r·cos(θ)

  y = r·sin(θ)

  x² +y² = r²

__

  r = sec(θ) -2cos(θ)

  r·cos(θ) = 1 -2cos(θ)² . . . . . . . . multiply by cos(θ)

  r²·r·cos(θ) = r² -2r²·cos(θ)² . . . multiply by r²

  (x² +y²)x = x² +y² -2x² . . . . . . . substitute rectangular relations

  x²(x +1) = y²(1 -x) . . . . . . . . . . . subtract xy²-x², factor

  y² = x²(1 +x)/(1 -x) = x²(1 -x²)/(1 -x)² . . . . multiply by (1-x)/(1-x)

  [tex]\boxed{y=\dfrac{x\sqrt{1-x^2}}{1-x}}[/tex]

__

The attached graph shows the equivalence of the polar and rectangular forms.

Answer:

y=4/3x-2

Step-by-step explanation:

We know the base equation is mx+b and the y-intercept is at -2 so we can determine that as the b value. The m value is 4/3 because if you look at where the line meets the next point is over 3 and up 4 indicating that the m value is 4/3. Hope this helps!

The equation of the line is y = 4/3x -2.

The y-intercept is -2 because the line crosses the y-axis at (0,-2).

The slope is 4/3x because the rise over run of the line is 4/3.

Answer:2/1

Step-by-step explanation:

Y1-y2/ x1-x2= 2/1

Answer:

Answer:::::1 only ...I think

Given:

Jamie and Marshall's team tied Shawna and Wyatt's team for the top team score.

Marshall scores 12 less than Jamie. Shawna scored twice as much as Marshall. Wyatt scored 4 less than Shawna.

To find:

The individual score of each person.

Solution:

Let x be the score of Jamie.

Marshall scores 12 less than Jamie.

Marshall score = x-12

Shawna scored twice as much as Marshall.

Shawna score = 2(x-12)

Wyatt scored 4 less than Shawna.

Wyatt score = 2(x-12)-4

Now,

Score of Jamie and Marshall's team [tex]=x+(x-12)[/tex]

Score of Shawna and Wyatt's team [tex]=2(x-12)+2(x-12)-4[/tex]

Jamie and Marshall's team tied Shawna and Wyatt's team

[tex]x+(x-12)=2(x-12)+2(x-12)-4[/tex]

[tex]x+x-12=2x-24+2x-24-4[/tex]

[tex]2x-12=4x-52[/tex]

Isolate x.

[tex]2x-4x=-52+12[/tex]

[tex]-2x=-40[/tex]

Divide both sides by -2.

[tex]x=\dfrac{-40}{-2}[/tex]

[tex]x=20[/tex]

So, Jamie score = 20

Marshall score = 20-12

                        = 8

Shawna score = 2(20-12)

                        = 2(8)

                        = 16

Wyatt score = 2(20-12)-4

                     = 2(8)-4

                     = 16-4

                     = 12

Therefore, the scores of Jamie, Marshall, Shawna and Wyatt are 20, 8, 16 and 12 respectively.

Answer:

3([tex]x^{2}[/tex]+2)

Step-by-step explanation:

3 is the GCF between 3 and 6

Place 3 outside parenthesis then

divide each term by the GCF

Answer:

x=49/3

Step-by-step explanation:

move all terms that don't contain x to the right side and solve the problem.

Answer:

Step-by-step explanation:

7.  3x + 6 = 55

          - 6   - 6

  3x = 49

 /3      /3

x = 49/3  OR  x = 16.33

8.  50 = 6x + 2

    - 2          - 2

    48 = 6x

    /6    /6

     8 = x

Check/verify your answer:

50 = 6x + 2

50 = 6(8) + 2

50 = 48 + 2

50 = 50

This statement is correct.

Hope this helps!

a. What percentage of the students do not have a scholarship?

     80% don't have a scholarship

b. How many students have a scholarship?

     800 students

c. How many students don't have a scholarship?

3200 students dont have a schscholarship

Answer:

a ray must be named by its endpoint first then an another point it that the ray goes through

Step-by-step explanation:

a ray has 1 endpoint and it goes through an infinite number of points but you name a ray by naming it's endpoint than a other point which the ray goes through hopes this helps have a nice day and good luck

Answer:

B, C, E

Step-by-step explanation:

Edg 2021

A dilation preserves angle measures.  A dilation preserves the direction that the shape faces. The side lengths of a dilated image are proportional to the side lengths of the pre-image.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure by a factor k, hence the side lengths of a dilated image are proportional to the side lengths of the pre-image.

Dilation does not preserve the side lengths but it preserves the angle measures. Dilation also preserves the orientation (i.e. the direction that the shape faces).

Dilation is not an isometric transformation.

Find out more at: https://brainly.com/question/13176891

This is really simple, all you have to do is establish a new relation which describes this particular case;

For example if i wanted to find the area of the full circle (360°), i would use the equation which states that;

[tex]a = \pi \: r {}^{2} [/tex]

[tex]a = \pi \: 8 {}^{2} [/tex]

[tex]a = 3.14 \times 64[/tex]

[tex]a = 201.06 \: inches {}^{2} [/tex]

But do i really wan the full 360 degrees?

In reality i only need a 70 degree circle (in a sense).

If 360 makes a full circle

How many circles is 70?

Use the triple rule to find that;

[tex]x = \frac{70}{360} = 0.1945 \: cirles[/tex]

So that area would be;

[tex] \alpha = 0.1945 \times 201.06 = 39.0617 \: [/tex]

That is your area. a=39 inches² rounded to the nearest tenth.

Answer:

  0 < c < 1

Step-by-step explanation:

Descarte's rule of signs tells you the quadratic will have two or zero positive real roots when the sign of c is positive. (c > 0)

The discriminant tells you the quadratic will have real roots when ...

  b² -4ac > 0 . . . . . . where a, b, c are the coefficients of ax² +bx +c = 0

  (-2)² -4(1)c > 0

  1 -c > 0

  c < 1

The equation will have two positive real roots when 0 < c < 1.

Answer: A. Zero

Step-by-step explanation: If the quadratic equation is incomplete, b will always equal 0.

The Square Root Property is used in solving incomplete quadratic equations where b is equal to zero. Then the correct option is A.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

If the value of the a is zero, then the equation will be linear, So the value of the variable a can not be zero.

But the value of the b and c can be zero for a quadratic equation, but the number of the terms will be missing, so the quadratic equation is incomplete.

The Square Root Property is used in solving incomplete quadratic equations where b is equal to zero. Then the correct option is A.

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

#SPJ2

Answer:

5 Months

Step-by-step explanation:

For Avas its 50 dollars times 5 months which equals 250 plus the 100 dollar fee makes 350

For Mark its 60 times 5 equals 300 plus the 50 dollar fee makes also 350

Answer:the correct answer would be 5 months

Step-by-step explanation:

Answer:

SA=231.5 in^2

Step-by-step explanation:

2(1/2[5x4.3])+3(5x14)

2(1/2x21.5)+3x70

2(10.75)+3x70

21.5+3x70

21.5+210

231.5

Step-by-step explanation:

Let S be the number of single tickets sold.

Let C be the number of couple tickets sold.

[tex]20s + 35c = 2845[/tex]

[tex]s + c = 128[/tex]

Multiplying the lower system by -20 we get;

[tex]20s + 35c = 2845[/tex]

[tex] - 20s - 20c = - 2560[/tex]

Adding the two systems i get;

[tex]35c - 20c = 2845 - 2560[/tex]

[tex]15c = 285[/tex]

[tex]c = \frac{285}{15} = 19[/tex]

Substituting C=19 in s+c=128,

we get that;

[tex]s + 19 = 128[/tex]

[tex]s = 128 - 19[/tex]

[tex]s = 117[/tex]

Answer:

a) Rs. 2425.55, Rs. 2626.36 (2 d.p.)

b) Rs. 1320

Step-by-step explanation:

Please see the attached pictures for the full solution.

Answer:

hey please follow back me I follow you and I am good in Science and Maths

Answer:

15 square units

Step-by-step explanation:

Equation

Area of a triangle = 1/2 × base × height

Given values:

Substitute given values into the equation:

⇒ Area  = 1/2 × 3 × 10

              = 15 square units

Answer:

15

Step-by-step explanation:

area=1/2hb

=1/2×10×3

=15

pls brainliest

Step-by-step explanation:

Width = 4x + 3

Length = 2(4x + 3) = 8x + 6

Area = Width x Length

Area = (4x + 3)(8x + 6)

Area = 32x² + 24x + 24x + 18

Area = 32x² + 48x + 18

Answer:

A

Step-by-step explanation:

A is the answer because it gives direct address to parents and kids. All the others don't give a direct subject, unlike A that says parents and kids.

Answer:

Yes, the lines are perpendicular because the product of their slopes equals -1 ⇒ B

Step-by-step explanation:

The product of the slopes of the perpendicular lines is -1

So to prove that the lines are perpendicular let us find their slopes

The rule of the slope is:

[tex]m=\frac{y2-y1}{x2-x1}[/tex] , where (x1, y1) and (x2, y2) are two points on the line

∵ Line M passes through points (2, -5) and (4, -3)

∴ x1 = 2 and x2 = 4

∴ y1 = -5 and y2 = -3

→ By using the rule of the slope above

∴ [tex]m=\frac{-3-(-5)}{4-2}=\frac{-3+5}{2}=\frac{2}{2}[/tex]

∴ The slope of line M is 1

∵ Line N passes through points (-4, -8) and (-6, -6)

∴ x1 = -4 and x2 = -6

∴ y1 = -8 and y2 = -6

→ By using the rule of the slope above

∴ [tex]m=\frac{-6-(-8)}{-6-(-4)}=\frac{-6+8}{-6+4}=\frac{2}{-2}[/tex]

∴ The slope of line N is -1

∵ 1 × -1 = -1

∴ The product of the slopes of lines M and N is -1

∴ Lines M and N are perpendicular

∴ Yes, the lines are perpendicular because the product of their

   slopes equals -1.

Answer:

She has  n= 4 side dishes.

Total side dishes ordered = 5n = 20

Step-by-step explanation:

The total cost is given by

TC= 10 . 50 + 1 . 50 ( n − 1 )

She orders same 5 lunches for $ 75

$ 75= 5{ 10 . 50 + 1 . 50 ( n − 1 ) }

Or

Cost of 1 lunch would be $ 15

$ 75/5 = { 10 . 50 + 1 . 50 ( n − 1 ) }

or

$ 15 = 10 . 50 + 1 . 50 ( n − 1 )

$ 15-$  10 . 50 = 1 . 50 ( n − 1 )  

$ 4.5/ 1.5= n-1

$ 3= n-1

3+1= n

n= 4

She has  n= 4 side dishes.

Total side dishes ordered = 5n = 20

She spent

$ 1.50 ( 4-1) = $ 4.5 each day or $22.5 on side dishes for 5 days.

☆▪︎y=-x-4▪︎☆

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Answer:  x = 23

Step-by-step explanation:

The sum of interior angles in a triangles is equal to 180°, therefore:

(2x - 1) + 110 + 25 = 180

1. Get rid of parentheses.

 2x - 1 + 110 + 25 = 180  

2. Add the number up in the left side.

            2x  + 134 = 180

3. Subtract 134 from both sides.

                      2x = 46

4. Divide by 2 from both sides.

                      x = 23

Answer:

-3,-2

Step-by--step explanation:

Answer:

his brother

Step-by-step explanation:

because 2 foot 7 inches in inches is 31 inches so therefore his brother has the longer fish.

1 foot = 12 inches.

2 feet x 12 = 24 inches + 7 = 31 inches.

Daves fish was 31 inches.

his brothers fish was bigger.

The correctly evaluated logarithmic expressions are expressions that are true on both sides of the equation, and the expression is ln 1=0

As a general rule, ln 1 = 0

Express 9 as 3^2

[tex]\log_2(3^2) =3[/tex]

Apply the law of logarithm

[tex]2\log_2(3) = 3[/tex]

Evaluate

[tex]3.17 = 3[/tex]

The above is not true

Express 1/100 as 10^-1

[tex]\log(10^{-2}) = 12[/tex]

Apply law of logarithm

[tex]-2\log(10) = 12[/tex]

Evaluate

[tex]-2 = 10[/tex]

The above is not true

Options (d) and (e) are also false

Hence, the correctly evaluated logarithmic expressions is ln 1=0

Read more about logarithmic expressions at:

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 60}}{\left( \cfrac{25}{100} \right)60}\implies 15[/tex]

about Mark and his Pizzas

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{35\% of 12}}{\left( \cfrac{35}{100} \right)12}\implies 4.2~\hfill \underset{cheaper~price}{\stackrel{12~~ - ~~4.2}{7.80}}[/tex]

Answer: 55 degrees

Step-by-step explanation:

Angle sum of a triangle = 180 degrees

40+85= 125

180-125= 55

Answer:

its 68mm

Step-by-step explanation: