A square piece of gold has an area of 36 square millimeters. How long is each is each side?

Answer:

y = 2x + 1

Step-by-step explanation:

This line goes through the points (-2, 0) (the x-intercept) and (0, 1) (the y-intercept).

As we move from -2 to 0, x increases by 2, and at the same time y increases from 0 to 1, that is, by 1.  Thus, the slope of this line is m  = rise / run = 2/1 = 2.

Starting with the slope-intercept formula for a straight line:

y = mx + b becomes y = 2x + 1.    (We had already found b.)

The equation of line is x - 2y + 2 = 0.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Here, x-intercept = -2

         y- intercept = 1

Now, equation of line

             x/a + y/b = 1

              x/-2 + y/1 = 1

              (x - 2y)/-2 = 1

               x - 2y = -2

               x - 2y + 2 = 0

Thus, the equation of line is x - 2y + 2 = 0.

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Answer:

see explanation

Step-by-step explanation:

Using the rules of exponents

• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

(a)

[tex]27^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{27}[/tex] = 3

(b)

[tex]25^{-\frac{1}{2} }[/tex]

= [tex]\frac{1}{25^{\frac{1}{2} } }[/tex] = [tex]\frac{1}{\sqrt{25} }[/tex] = [tex]\frac{1}{5}[/tex]

For this case we must find the value of the variable "x" of the following equation:

[tex]12 = x + 3[/tex]

So, we follow the steps:

Subtracting 3 from both sides of the equation we have:

[tex]12-3=x+3-3[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]9 = x\\x = 9[/tex]

Thus, the value of x is 9.

Answer:

[tex]x = 9[/tex]

Answer:

x=√2, x=-√2, x= 3 and x=-3

Step-by-step explanation:

We need to solve the equation x^4 - 11x^2+18=0

We can replace x^4 = u^2 and x^2 = u

So, the equation will become

u^2 -11u+18 = 0

Factorizing the above equation:

u^2 -9u-2u+18 =0

u(u-9)-2(u-9)=0

(u-2)(u-9)=0

u=2, u=9

As, u = x^2, Putting back the value:

x^2 =2 , x^2 =9

taking square roots:

√x^2 =√2 ,√x^2=√9

x=±√2 , x = ±3

so, x=√2, x=-√2, x= 3 and x=-3

Final answer:

The real zeros of the polynomial equation x^4 - 11x^2 + 18 = 0 are found by factoring the equation as a quadratic in x^2, which yields the real zeros x = 3, x = -3, x = √2, and x = -√2.

Explanation:

To find the real zeros of the polynomial equation x4 - 11x2 + 18 = 0, we can attempt to factor it. Notice that the equation resembles a quadratic in form, with x2 taking the place of x. If we let y = x2, our equation becomes y2 - 11y + 18 = 0, which is a quadratic equation.

Factoring the quadratic equation gives us (y - 9)(y - 2) = 0. Thus, the solutions for y are y = 9 and y = 2. Since y = x2, we now solve for x by finding the square roots of these solutions.

For y = 9, the values of x are x = 3 and x = -3. For y = 2, the values of x are x = √2 and x = -√2. Therefore, the real zeros of the original polynomial equation are x = 3, x = -3, x = √2, and x = -√2.

Answer:

2x^(10)y^(12)

Hope This Helps!   Have A Nice Day!!

Answer:

The correct answer is 2X¹⁰Y¹²

Step-by-step explanation:

Points to remember

identities

Xᵃ * Xᵇ = X⁽ᵃ⁺ᵇ⁾

Xᵃ/Xᵇ = X⁽ᵃ⁻ᵇ⁾

To find the equivalent to given expression

It is given that,

60X²⁰Y²⁴/30X¹⁰Y¹²

Using identities we can write,

60X²⁰Y²⁴/30X¹⁰Y¹² = (60/30) * (X²⁰/X¹⁰) * (Y²⁴/y¹²)

  = 2 * X⁽²⁰ ⁻ ¹⁰⁾ * Y⁽²⁴ ⁻ ¹²⁾

  = 2 * X¹⁰ * Y¹²

  = 2X¹⁰Y¹²

The correct answer is 2X¹⁰Y¹²

Answer:

Step-by-step explanation:

Look at the picture.

We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.

We have:

[tex]a\sqrt3=5\sqrt3[/tex]          divide both sides by √3

[tex]a=5[/tex]

It's a right triangle.

Answer:

8 - 6x

Step-by-step explanation:

just trust me the other guy's wrong

let's notice that the center of the circle is at the orgin, and that the distance from the center to an endpoint B is its radius.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ O(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]

[tex]\bf \stackrel{radius}{r}=\sqrt{(4-0)^2+(5-0)^2}\implies r=\sqrt{4^2+5^2} \\\\\\ r=\sqrt{16+25}\implies r=\sqrt{41} \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{0}{ k})\qquad \qquad radius=\stackrel{\sqrt{41}}{ r} \\\\\\ (x-0)^2+(y-0)^2=(\sqrt{41})^2\implies x^2+y^2=41[/tex]

Answer:

The correct answer is option B

Step-by-step explanation:

B.  x2 + y2 − 41 = 0

Answer:

-2p² − 11p − 35

Step-by-step explanation:

Simplifying:

-2(p + 4)² − 3 + 5p

-2(p² + 8p + 16) − 3 + 5p

-2p² − 16p − 32 − 3 + 5p

-2p² − 11p − 35

This is also the standard form.

Answer:

-2p^2 - 11 p - 35

Step-by-step explanation:

Please, use " ^ " to indicate exponentiation.  Thus:

–2(p + 4)^2 – 3 + 5p

Now perform the exponentiation first, obtaining:

-2(p^2 + 8p + 16) - 3 + 5p, or

-2p^2 - 16 p - 32  - 3 + 5p

Now rearrange these terms in descending order by powers of p:

-2p^2 - 11 p - 32  - 3, or

-2p^2 - 11 p - 35

Answer:

[tex]\large\boxed{A=25\pi}[/tex]

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

We have the center A(-3, 3) and the point on the circle B(1, 6).

The radius is equal to the distance between the center and the any point on the circle.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute:

[tex]r=\sqrt{(1-(-3))^2+(6-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex]

[tex]A=\pi(5^2)=25\pi[/tex]

The area of the circle centered at A(-3, 3) and passing through B(1, 6) is 25π square units.

The subject of this problem is geometry, specifically about the area of a circle.To find the area of a circle, we need to know the radius. Since B is on the circle, AB is the radius. The area (A) of a circle is found using the formula A = πr², where r represents the radius of the circle. Here, the radius of the circle can be determined by finding the distance between the center A(-3, 3) and a point on the circle B(1, 6).

The formula for distance between two points in a plane is √[(x₂ - x₁)² + (y₂ - y₁)²]. Substituting values, we get r = √[(1 - -3)² + (6 - 3)²] = √[(4)² + (3)²] = √[16 + 9] = √25 = 5. Therefore, the radius is 5.

Substitute r = 5 in the area formula: A = π * (5)² = 25π square units.

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Answer: Sqrt(36/16)

sqrt(36/16)=6/4=3/2 rational

Answer:

C

Step-by-step explanation:

Given ΔLMN and ΔPQR are similar, then

∠L, ∠P and ∠M, ∠Q and ∠N, ∠R are congruent

Hence ∠L = ∠P = 80° → C

Answer:

The Answer is C, 80 degrees

Step-by-step explanation:

Answer:

(4,4), (2,8)  (4,8)  and all points in the shaded region as attached below

Step-by-step explanation:

This question is on solutions for inequalities equations

Give the equation as;

x+2y ≥ 10.......................................rewrite the equation for graphing purposes

x+ 2y = 10.............................................compose a table for values of x with corresponding values of y

x  -2    0   2  

y   6    5    4

Plot and shade the wanted region as show in the attached graph

For example point (4,4)  or point (2,6) will satisfy the  inequality  x+2y ≥ 10 as;

(4,4)........ x+2y ≥ 10------4+2(4)  ≥ 10

20 ≥ 10 ,,,,,,,,,,,,,,,,,,which is okay

Answer:

D

Step-by-step explanation:

This is called "implication". So if A (is true), then B MUST be true. If B is false, the implication is false. In all other cases, the implication is true. Suppose A is false, then it doesn't matter what B is, the implication is true, since we don't care what B is.

It's a bit confusing I suppose. Below is a truth table using P and Q in stead of A and B.

Final answer:

The correct answer is D: If A is true, then B must be true. This represents a logical conditional where the statement is true unless the antecedent A is true and the consequent B is false.

Explanation:

The statement "If A, then B" is a logical conditional, which can be represented as A
ightarrow B in logical notation. This statement best matches option D: If A is true, then B must be true. In logic, the only time a conditional statement is false is when the first part (the antecedent A) is true and the second part (the consequent B) is false. Otherwise, the statement is considered true, regardless of the individual truth values of A or B. This includes when A is false; the truth value of B does not affect the truth value of the conditional in this case. Therefore, if A is true, the conditional obliges B to also be true for the statement to remain true.

Answer:

x = 4

Step-by-step explanation:

Simplify the equation 5x + 4y = 8 to get y = 2 - [tex]\frac{5}{4}[/tex] x

then substitute the y into 2x - 3y = 17 to get the answer. sorry im not good at explaining but it should be right.

To find the x-value of the solution to the system of equations, we can use the method of substitution. Solve one equation for x, substitute it into the other equation, and solve for y. Finally, substitute the value of y back into the expression for x to find the x-value.

To find the value of x in the system of equations, we can use the method of substitution. Firstly, solve one of the equations for x or y. Let's solve the second equation for x:

2x - 3y = 17 → 2x = 17 + 3y → x = (17 + 3y)/2

Now substitute this value for x into the first equation and solve for y:

5((17 + 3y)/2) + 4y = 8 → 17 + 3y + 4y = 8 → 17 + 7y = 8 → 7y = -9 → y = -9/7

Finally, substitute the value of y back into the expression we found for x:

x = (17 + 3(-9/7))/2 → x = (17 - 27/7)/2 → x = (119/7 - 27/7)/2 → x = 92/7/2 → x = 92/14 → x = 46/7

Therefore, the x-value of the solution to the system of equations is 46/7.

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To solve the inequality, you need to isolate/get x by itself:

171 > -6x    Divide -6 on both sides [dividing/multiplying a negative number on

-28.5 < x      [dividing/multiplying a negative number in an inequality causes the sign (<, >, ≤, ≥) to flip]

-28.5 < x    [x is a number greater than -28.5]

So your graph should have an open circle at -28.5 (the first small line next to -28), and the arrow pointing to the right since x is greater than -28.5 (increasing)      The 1st option is your answer

[use the o---> and put it at -28.5]

Answer:

the measure of the obtuse base angle of the trepezoid is 111.

Step-by-step explanation:

An isosceles triangle has one vertex angle and two congruent base angles. Also, we know that the sum of all angles in a triangle must equal 180 degrees. So we can say that:

Vertex Angle + Base Angle + Base Angle = 180.

Vertex Angle + 2 x (Base Angle) = 180.

2 x (Base Angle) = 180 - Vertex Angle

2 x (Base Angle) = 180 - 42

2 x (Base Angle) = 138

Base Angle = 69

Also, we know that angles on one side of a straight line always add to 180 degrees.

So we can say that:

Base Angle + ? = 180

? = 180 - Base Angle

? = 180 - 69

? = 111

So, the measure of the obtuse base angle of the trepezoid is 111.

15/2.0=7.5. The average velocity of the person is 7.5.

Answer:I believe the answer is 12 because it takes 4, 1/4 unit cube to make 1 cubic unit so to make 3 cubic units you need 12, 1/4 unit cubes if that makes any sense. :) Please make Brainliest if this helped.

Answer:

28 grams

Step-by-step explanation:

1 cup is 8 grams of fiber, since a half a cup is 4 you times it by 2

then 8x3 because you're multiplying the fiber of one cup by 3. which equals 24, but you still have a half of cup of oats left. and since 4 grams equal a half a cup you just simply add 4 onto 24 which equals 28

Answer:

28 grams

Step-by-step explanation:

because i a mulpitplyed the numbers to get my answer

Answer:

105

Step-by-step explanation:

15 x 4 = 60

9 x 5 = 45

45 + 60 = 105

Answer:

105

Step-by-step explanation:

4x15=60

5x9=45

45=60=105

Answer:

r = 17/10

Step-by-step explanation:

Let the common ratio be r.  Then 5r = 8.5, and r = 17/10.

Answer:

1.7

Step-by-step explanation:

Answer:

The correct answer option is A. [tex]\frac{1}{16}[/tex].

Step-by-step explanation:

We are given the following geometric sequence and we are to find its 8th term:

[tex]1024, 256,64,...[/tex]

Here [tex]a_1=1024[/tex] and common ratio [tex](r) = \frac{64}{256} =0.25[/tex].

The formula we will use to find the 8th term is:

nth term = [tex]a_1 \times r^{(n-1)}[/tex]

Substituting the values in the formula to get:

8th term = [tex]1024 \times 0.25^{(8-1)}[/tex]

8th term = [tex] \frac { 1 } { 1 6 } [/tex]

Answer:

[tex]\large\boxed{(3x-7)(3x-5)=9x^2-36x+35}[/tex]

Step-by-step explanation:

[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(3x-7)(3x-5)\\\\=(3x)(3x)+(3x)(-5)+(-7)(3x)+(-7)(-5)\\\\=9x^2-15x-21x+35\qquad\text{combine like terms}\\\\=9x^2+(-15x-21x)+35\\\\=9x^2-36x+35[/tex]

Answer:

B

Step-by-step explanation:

formula   s =4*pi*r^2

s=4(3.14)(3^2)

s = 12.56(9)s= 113.04

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 3 = - 9(x + 4) ← is in point- slope form

with slope m = - 9

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-9}[/tex] = [tex]\frac{1}{9}[/tex]

The point (a, b) = (4, - 3), hence

y + 3 = [tex]\frac{1}{9}[/tex] (x - 4) ← equation of perpendicular line

Answer:

a

Step-by-step explanation:

Option: A is the correct answer.

The appropriate domain for the function is:

            A. All non-negative integers

We know that a domain of a function is the set of all the value of the independent variable  at which the function is defined.

Here  x represents the number of cars sold and F(x) represents their net profits (in dollars)

As we know that the profit will be zero when none of the car will be sold and also the car will be sold as a whole.Also, the profit is calculated when some cars are sold.

Hence, the x-value will be the set of all the positive integers.

           Hence, the correct answer is:

              Option: A

Answer:

y = 1

x = 4

{x,y} = {4,1}

Step-by-step explanation:

[2]

x - 3y = 1

 + 3y       +3y

x = 3y + 1

[1]

x + 3y = 7

(3y + 1) + 3y = 7

      - 1            - 1

(3y) + 3y = 6

6y = 6

6      6

y = 1

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

x = 3y + 1

y = 1

x = 3(1) + 1

x = 4

y = 1

x = 4

{x,y} = {4,1}

Answer:

0.42% Chance Of The Counters Being Red

Step-by-step explanation:

1.00

-0.58

=0.42% Probability

The probability that a randomly picked counter from a bag containing only red and blue counters is red, given that the probability the counter is blue is 0.58, is 0.42.

The subject here is

probability

, which in

mathematics

is a measure of the likelihood that a particular event will occur. The problem states that the

probability

that a counter is blue is 0.58. Since we only have red and blue counters in the bag, and the probabilities of all possible outcomes must add up to 1, the

probability

that a counter picked at random is red is 1 - the

probability

that the counter is blue. So, to find the

probability

that the counter is red, subtract 0.58 from 1. The resulting

probability

that a randomly picked counter is red is therefore 0.42.

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It is B

-2 =3(-1) + 1