Scenario:

A rectangular plot of ground is 5 meters longer than it is wide. Its area is 20,000 square meters.

Question:

What equation will help you find the dimensions?

Note: Let W represent the width.

Options:

w(w+5)=20,000
w^2=20,000+5
(w(w+5))/2=20,000
w+2(w+5)=20,000

Answer:

The center of the circle is (-3,-2)

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center

r is the radius

In this problem we have

[tex]x^{2} +y^{2}+6x+4y-3=0[/tex]

Completing the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](x^{2}+6x) +(y^{2}+4y)=3[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex](x^{2}+6x+9) +(y^{2}+4y+4)=3+9+4[/tex]

[tex](x^{2}+6x+9) +(y^{2}+4y+4)=16[/tex]

Rewrite as perfect squares

[tex](x+3)^{2} +(y+2)^{2}=16[/tex]

therefore

The center of the circle is (-3,-2)

Answer: ITS D !! ON EDGE

Step-by-step explanation:

Answer:

(4334/100)*93 = $ 4,030.62

Step-by-step explanation:

N/A

Answer:

7pi/2

Step-by-step explanation:

If was a full, the circumference or the arc length would be 2pi*r where r in this case is 7 so it would be 14pi.

Now this only a quarter of that, so this arc length is actually 14pi/4.

This can be reduced 14pi/4 =7pi/2

Answer:

3.5pi

Step-by-step explanation:

KA

Answer:

4,-2 and 1

Step-by-step explanation:

These are all quantities greater than -5

-5 < 4

-5 < -2

-5 < 1

So C, D and E

Answer:

2 11/12

Step-by-step explanation:

(50/3)/(40/7)

=50/3*7/40

=5/3*7/4

=35/12

=2 11/12

let's convert firstly, the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{16\frac{2}{3}}\implies \cfrac{16\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{50}{3}}~\hfill \stackrel{mixed}{5\frac{5}{7}}\implies \cfrac{5\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{40}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{50}{3}\div\cfrac{40}{7}\implies \cfrac{\stackrel{5}{\begin{matrix} 50 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{3}\cdot \cfrac{7}{\underset{4}{\begin{matrix} 40 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\implies \cfrac{35}{12}\implies 2\frac{11}{12}[/tex]

Answer:

-6

Step-by-step explanation:

A(n)=-6+(1-1)(1)

simplified, this equals:

A(n) = -6+(0)(1)

A(n)=-6+0

A(n) = -6, for any given n term.

Answer:

The two numbers are 28 and 7.

Step-by-step explanation:

Let the first number be x

Let the second number be y

The difference of x and y is x-y=21

The quotient of two numbers is x/y = 4

x-y =21    (This is equation 1)

x/y=4    (This is equation 2)  

By solving equation 2 we will get the value of x.

x/y=4

x=4y (Lets call it equation 3)

Now, put the value of x(equation 3) in (equation 1)

x-y=21

4y-y=21

3y=21

y=21/3

y=7

Now put the value of y in equation 3 to get the value of x

x=4y

x=4(7)

x=28

Solution Set {(x,y)(28,7)}

Answer:

28 and 7

Step-by-step explanation:

Answer:

c [tex]113\:m[/tex]

Step-by-step explanation:

[tex]113,391 = 4\frac{9}{10}[2\frac{1}{10}]^{2} + 135 \\ \\ 113 ≈ h[/tex]

I am joyous to assist you anytime.

Answer:

A. [tex]h=\frac{SA-2B}{P}[/tex]

Step-by-step explanation:

We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula.

[tex]SA=Ph+2B[/tex]

First of all, we will switch sides for our given equation as:

[tex]Ph+2B=SA[/tex]

Now, we will subtract 2B from both sides of our equation.

[tex]Ph+2B-2B=SA-2B[/tex]

[tex]Ph=SA-2B[/tex]

Now, we will divide both sides of our equation by P.

[tex]\frac{Ph}{P}=\frac{SA-2B}{P}[/tex]

[tex]h=\frac{SA-2B}{P}[/tex]

Therefore, option A is the correct choice.

Answer:

A

Step-by-step explanation:We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula

First of all, we will switch sides for our given equation as:

Now, we will subtract 2B from both sides of our equation.

Now, we will divide both sides of our equation by P.

therefore its option A

Let the amount saving by Sienna and Jacob be x

Sienna has $8 and is saving $3 per week

So the equation will be 3x + 8

Jacob has $6 and is saving $4 per week

So the equation will be 4x + 6

Sienna will have same amount as Jacob, so

3x + 8 = 4x + 6

So the model two will represents the equation that Sienna will have same amount as Jacob.

Answer:

Model B

Step-by-step explanation:

Model B correctly displays sienna's and jacob's equations.

For sienna, the $8 can be represented as 8 unit blocks, which is displayed in model 2. The $3 per week can be represented as 3 x tiles, as shown in the picture, because it represents how many weeks.

For jacob, the model shows 6 unit blocks which represents his 6 dollars. The $4 per week is represented with the 4 x tiles, and we use x tiles because we are calculating how many weeks.

D. is the correct answer

Hopes this helps

Answer:-568/5

Step-by-step explanation:

Answer:

-568/5 is the answer

Answer:

Midpoint

Step-by-step explanation:

Equidistant from the pre = image AA would be the middle

Answer:

Mid Point, thats all there is, its the answer, just that

Step-by-step explanation:

Answer:

It's C on e2020

Step-by-step explanation:

Answer:

A: Line Segment WX

Step-by-step explanation:

100% on edge 2020

Answer:

WX is correct

Step-by-step explanation:

Got a 100 in edge quiz.

This is a piecewise function because it is defined by more than two functions. Basically, we want to take the limit here. Recall that if a function [tex]f(x)[/tex]  approaches some value [tex]L[/tex]  as [tex]x[/tex]  approaches [tex]a[/tex]  from both the right and the left, then the limit of [tex]f(x)[/tex] exists and equals  [tex]L[/tex]. Here we won't calculate the limit, but apply some concepts of it. So:

a. [tex]as \ x \rightarrow +\infty, \ k(x) \rightarrow +\infty[/tex]

Move on the x-axis from the left to the right and you realize that as x increases y also increases without bound.

b. [tex]as \ x \rightarrow -\infty, \ k(x) \rightarrow 0[/tex]

Move on the x-axis from the right to the left and you realize that as x decreases to negative values y approaches zero.

c. [tex]as \ x \rightarrow 2, \ k(x) \rightarrow 0[/tex]

Since the function is continuous here, we can say that [tex]k(2)=0[/tex]

d. [tex]as \ x \rightarrow -2, \ k(x) \rightarrow 0[/tex]

The function is discontinuous here, but [tex]k(-2)[/tex] exists and equals 0 as the black hole indicates at [tex]x=-2[/tex].

e. [tex]as \ x \rightarrow -4, \ k(x) \rightarrow 2[/tex]

The function is also discontinuous here, but the black hole indicates that this exists at [tex]x=-4[/tex], so [tex]k(-4)=2[/tex]

f. [tex]as \ x \rightarrow 0, \ k(x) \rightarrow 4[/tex]

Since the function is continuous here, we can say that [tex]k(0)=4[/tex]

Answer:

(4b + 5)

Step-by-step explanation:

To get 4b^2 you already have b^2 if you put b  inside the second set of brackets. But that would mean you don't have 4 anywhere to get 4b^2.

So the first step has to be

(b + 3)(4b

Now look at the 15 for a moment. It is plus 15. The only way you can get a plus 15 is if both signs are plus (after the b terms) or both terms are minus.

The middle term (17b) is plus so both terms after b are plus.

(b + 3)(4b +

Now we need something that multiplies to 15. 3*5 = 15. So the term you want is 5.

(b + 3)(4b + 5)

Does the middle term work?

5*b + 3*4b = 5b + 12b = 17b

Everything looks fine.

The second factor is 17b.

The number of batches is 4.

When a problem arises if 4 is required for 2 of these things then how many things does 20 require?

We use the unitary method to solve the problem where we find how much is required for one thing and then multiply it by the required.

1/6 tub of peanut butter is used for one batch of cookies.

2/3 of it was used for the whole day.

So to find the total number of batches we divide the total tub used by the amount of tub used for one batch of cookies hence = 2/3/(1/6) = 4

Hence the answer to the given problem is 4.

Learn more about the Unitary method here

https://brainly.com/question/19423643

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The given line that passes through the points (7,-4) and (-1,3).

The slope is

[tex]m = \frac{3 - - 4}{ - 1 - 7} = - \frac{7}{8} [/tex]

The point-slope form is obtained using:

[tex]y-y_1= m (x-x_1) [/tex]

When (7,-4) is used the point-slope form is

[tex]y + 4= - \frac{7}{8} (x - 7) [/tex]

We expand now to get;

[tex]y = - \frac{7}{8}x + \frac{49}{8} - 4[/tex]

This implies that,

[tex]y = - \frac{7}{8}x + \frac{17}{8}[/tex]

Answer:

-6

Step-by-step explanation:

m^2 - 36 = 0

Add 36 to each side

m^2 -36+36 = 0+36

m^2 = 36

Take the square root of each side

sqrt( m^2) = ± sqrt(36)

m = ±6

We know one root is 6

The other root is -6

Answer: [tex]5x^2-x+4[/tex]

Step-by-step explanation:

In addition of polynomials, you only have to add the like terms.

Remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Then, given the polynomial [tex]12x^2+3x+6[/tex] and the polynomial [tex]-7x^2-4x-2[/tex], you can find the sum of them by adding the like terms.

Observe the procedure below:

[tex](12x^2+3x+6)+(-7x^2-4x-2)=12x^2+3x+6-7x^2-4x-2=5x^2-x+4[/tex]

Therefore, the sum is:

[tex]5x^2-x+4[/tex]

Answer:

[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{13}{3}}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\===============================[/tex]

[tex]\text{We have the point:}\\\\(5,\ 1)\ \text{and}\ (-4,\ 7).\ \text{Substitute:}\\\\m=\dfrac{7-1}{-4-5}=\dfrac{6}{-9}=-\dfrac{6:3}{9:3}=-\dfrac{2}{3}\\\\\text{We have the equation in form:}\\\\y=-\dfrac{2}{3}x+b\\\\\text{Put the coordinates of the point (5, 1) to the equation:}\\\\1=-\dfrac{2}{3}(5)+b\\\\1=-\dfrac{10}{3}+b\qquad\text{add}\ \dfrac{10}{3}\ \text{to the both sides}\\\\\dfrac{3}{3}+\dfrac{10}{3}=b\to b=\dfrac{13}{3}\\\\\text{Finally:}\\\\y=-\dfrac{2}{3}x+\dfrac{13}{3}[/tex]

okay so we need to solve for x.

--

FIRST STEP:  12x^2+5x-4=12^2x+6 would turn into x2 + 5x - 4 = 2x + 6 so it'd have equal bases.

SECOND STEP: move any number with "x" in it to the left side. it ends up as  x2 + 3x - 4 = 6

THEN, we use the AC method to eliminate any unnecessary numbers.

you should end up with ( x - 2) (x + 5) = 0

SO, the answer is your third option. ( x = 2, x = -5)

Answer:

x=-5&x=2

Step-by-step explanation:

Since the bases on both sides of the equation are the same, they will cancel each other leaving the exponents

x²+5x-4 = 2x + 6

Collect like terms

x²+5x-2x-4-6=0

x²+3x-10=0

The highest power is 2 , so factorize

x²+5x-2x-10=0

x(x+5)-2(x+5)=0

(x+5)(x-2)=0

x = -5 or x = 2

Check

When x = -5

-5²+3*-5-10=0

25-15-10 =0

0=0

:.x=-5

When x=2

2²+3*2-10=0

4+6-10=0

0=0

Answer:

We have the following function: [tex]f(x) =\sqrt{x}[/tex]

We know that given a function f(x), the function g(x) = f(x+m) is exactly the same function f(x) but shifted m units to the left.

Therefore, to shift the function 12 units right we should:

[tex]f(x) =\sqrt{x}[/tex] ⇒ [tex]f(x-12) =\sqrt{x-12}[/tex]

We know that given a function f(x), the function g(x) = f(x)+m is exactly the same function f(x) but shifted m units up.

Therefore, to shift seven units down we should:

[tex]f(x) =\sqrt{x}[/tex] ⇒ [tex]f(x) =\sqrt{x}-7[/tex]

Answer:

factors (3p - 5) and (p + 1)

Step-by-step explanation:

The quadratic formula always "works" when you're looking to factor a quadratic expression or equation.  Here, the coefficients are a = 3, b = -2 and c = -5.  The discriminant is thus b²-4ac, which here is (-2)²-4(3)(-5), or 4+60, or 64.  Because this discriminant is positive, we know that the quadratic has two real, unequal roots.  These roots are:

        -(-2)±√64          2 ± 8

p = ------------------- = --------------- = 10/6 and -1, or 5/3 and -1.

           2(3)                      6

These roots correspond to the factors (3p - 5) and (p + 1).

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{4}{2(1)}~~,~~12-\cfrac{4^2}{4(1)} \right)\implies (-2~~,~~12-4)\implies (-2~,~8)[/tex]

well, the quadratic has a leading term with a positive coefficient, meaning is a parabola opening upwards, like a "bowl", comes from above down down down, reaches a U-turn, namely the vertex, and goes back up up up.

so the minimum value is at the vertex of course, and the minumum is well, just the y-coordinate of the vertex, 8.

Answer:

[tex](f*g) (x) =2x^3-13x^2-7 [/tex]

Step-by-step explanation:

We have the following functions

[tex]f (x) = 2x+1[/tex]

[tex]g (x) = x^2-7[/tex]

To find [tex](f*g)(x)[/tex] we must multiply the function f (x) with the function g (x)

Then we perform the following operation

[tex](f*g) (x) =(2x+1)(x^2-7)[/tex]

Apply the distributive property

[tex](f*g) (x) =2x^3-14x^2+x^2-7 [/tex]

[tex](f*g) (x) =2x^3-13x^2-7 [/tex]

Finally we have that:

[tex](f*g) (x) =2x^3-13x^2-7 [/tex]

Answer:

288 square units

Step-by-step explanation:

The formula for the area of a square when you know its diagonal is: [tex]\frac{1}{2} d^2[/tex]

So, since we know the half diagonal is 12, we need to multiply that by 2 to get the diagonal, which is 24.

Put 24 into the formula. [tex]\frac{1}{2} * 24^2[/tex]

Simplify the exponent. [tex]\frac{1}{2} * 576[/tex]

Finally, multiply. [tex]288[/tex]

x = total amount of students in 8th Grade.

we know only one-thrid of the class went, so (1/3)x or x/3 went.

we also know 5 coaches went too, and that the total amount of that is 41.

[tex]\bf \stackrel{\textit{one third of all students}}{\cfrac{1}{3}x}+\stackrel{\textit{coaches}}{5}=\stackrel{\textit{total}}{41}\implies \cfrac{x}{3}+5=41\implies \cfrac{x}{3}=41-5 \\\\\\ \cfrac{x}{3}=36\implies x=3(36)\implies x=108[/tex]

now, to verify, well, what do you get for (108/3) + 5?

Answer:

106.90 cm

Step-by-step explanation:

Given

Angle=30 degrees

Base=92.58 cm

So,

We will have to use the triangular ratios to find the hypotenuse.

The triangular ratio that will be used for this will be cosine because we know the value of angle and base since it involves both cosine will be used.

cos⁡θ=Base/Hypotense

cos⁡30=92.58/Hypotenuse

0.8660=92.58/Hypotenuse

Hypotenuse=92.58/0.8660

=106.90 cm ..

Answer:

Hypotenuse = 107.02

Step-by-step explanation:

Points to remember

If angles of a triangle are 30°, 60° and 90° then the sides are  in the ratio

1 : √3 : 2

It is given a right angled  triangle with angles 30°, 60°, 90°

and height = 95.58 cm

To find the hypotenuse

From the figure we can write,

Base : Height : Hypotenuse = 1 : √3 : 2 = Base : 92.58 : Hypotenuse

Therefore Hypotenuse = (92.58 * 2)/√3

  = 107.02 cm