A city determines that a planned community must have at least 4 acres of developed and open space, and the difference between the number of developed acres, y, and the number of open acres, x, can be no more than 1. Which graph represents the system of inequalities for this scenario? x + y ≤ 4 y – x ≥ 1

[tex]\displaystyle\\\text{Decompose numbers into prime factors.}\\\\32=2^5\\\\48=2^4\times3\\\\64=2^6\\\\\text{greatest common divisor (gcd)~}~=2^4=\boxed{\bf16 m}\\\\\boxed{\text{\bf The maximum possible length of each wire cut is 16 m.}}[/tex]

The maximum possible length for each cut of wire that Mrs. Agustin can make from the 32m, 48m, and 64m wire coils is 16m.

In this problem, Mrs. Agustin is aiming to cut three different lengths of wires into equal parts. Therefore, the maximum possible length of each cut of wire can be calculated by finding the greatest common divisor (GCD) of the lengths of the three wires. The lengths of the wire coils are 32 m, 48 m, and 64 m. The GCD of these numbers is 16 m.

Thus, the maximum possible length of each cut wire would be 16 m.

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Answer:

Step-by-step explanation:

[tex](g-f)(x)=g(x)-f(x)\\\\f(x)=4-x,\ g(x)=6x\\\\(g-f)(x)=6x-(4-x)=6x-4-(-x)=6x-4+x=7x-4\\\\(g-f)(3)-\text{put}\ x=3\ \text{to the expression}\\\\(g-f)(3)=7(3)-4=21-4=17[/tex]

[tex]\bf \begin{array}{ccll} gallons&minutes\\ \cline{1-2} 4.39&1\\ 280&x \end{array}\implies \cfrac{4.39}{280}=\cfrac{1}{x}\implies 4.39x=280\implies x=\cfrac{280}{4.39} \\\\\\ x\approx \stackrel{\textit{minutes}}{63.78}~\hspace{7em}63.78 ~~\begin{matrix} min \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \cdot \cfrac{hr}{60 ~~\begin{matrix} min \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ } \implies \boxed{1.063~hr}[/tex]

a = hours worked by the first mechanic

b = hours worked by the second mechanic.

since the first mechanic charges $55 per hour, then for "a" hours that'd be a total of 55*a or 55a, likewise, for the second mechanic that'd be a total charge of 80*b or 80b.

we know all hours combined are 15, so then a + b = 15.

we also know that all charges combined are $950, so 55a + 80b = 950.

[tex]\bf \begin{cases} a+b=15\\ \boxed{b}=15-a\\ \cline{1-1} 55a+80b=950 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{55a+80\left( \boxed{15-a} \right)=950} \\\\\\ 55a+1200-80a=950\implies -25a+1200=950\implies -25a=-250 \\\\\\ a=\cfrac{-250}{-25}\implies \blacktriangleright a = 10\blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=15-a\implies }b=15-10\implies \blacktriangleright b=5 \blacktriangleleft[/tex]

Answer:

3 + 2i

Step-by-step explanation:

3 + √(-4) = 3 + i√4 = 3 + 2i

Recall that √(-1) = i

Answer:

  250

Step-by-step explanation:

If we let p represent the 1975 population, we have ...

  p + 140%×p = 600

  p(1 +1.40) = 600

  p = 600/2.4 = 250

There were 250 grizzly bears living in the wild in 1975.

Answer:

False

Step-by-step explanation:

A counterexample goes against what you said in the conjecture. An example of a counterexample in this case would be that your dog ate a burger, which is not dog food, last night.

Answer:

A:(1,-3/4)

Step-by-step explanation:

Use substitution to solve the system

y= 1/4x-1

y= -1/2x-1/4

1/4x-1 = -1/2x-1/4, Solve for x

3/4x= 3/4, x = 1, Next solve for y by plugging the x-value into either equation.

y=1/4(1)-1

y=-3/4

Answer:

1,-3/4

Step-by-step explanation:

Answer:

Part A: x^2 + 6x + 8 = 0 use the factoring the equation method

Part A: x^2 + 6x + 8 = 0 use the quadratic formula

Step-by-step explanation:

Part A;

The equation is  x^2 + 6x + 8 = 0 , looking at this quadratic expression, you notice it is written in a quadratic equation standard form  of ax^2+bx+c=0. Additionally, you notice that can find what multiplied to get the quadratic equation,factor.You can identify two numbers that multiply to get ac and add to give b.In this question;

a=1,b=6,c=8

ac=8

The numbers are 4 and 2. Factoring the equation method will give;

x²+6x+8=0

x²+4x+2x+8=0

x(x+4)+2(x+4)=0

(x+2)+(x+4)=x²+6x+8

x+2=0, x=-2  and x+4=0, x=-4

Part B

The quadratic equation is ;

x²+6x-11=0

You notice that there are no factors that multiply direct to get the quadratic equation like in part 1. When you observe, a=1, b=6 and c=-11

ac=1×-11=-11 and b=6 .You notice there are no factors that multiply to give -11 and add to get 6, hence the factorizing the equation method can not be used.However, you can apply the quadratic formula that requires coefficients. You have a=1, b=c and c=-11 as the coefficients to use in the quadratic formula.

Answer:

Part A  -  use the factor method

Part B - use the quadratic equation

Step-by-step explanation:

Thinking process:

Let's look at the two parts in the problem:

Part A: x^2 + 6x + 8 = 0

This is a quadratic equation. Now, the product of the first and last term produces 8x². This product is a common multiple of 4 x and 2 x. These numbers can be added to get the middle term: 6x. Hence the equation can be solved by factorization.

Part B: x^2 + 6x - 11 = 0

Part B is also a quadratic equation. This equation can be analysed as follows:

The product of the first and last product gives -22x². Two factors are possibe: -11x and 2x or -2x and 11 x. These factors wjhen added or subtracted do not give the middle term (6x). Hence factorization will not work.

The best way to solve the equation is to use the quadratic formula:

[tex]x= \frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]

Answer and Explanation:

Given : Consider the relationship [tex]3r+2t=18[/tex]

To find :

A.  Write the relationship as a function r=f(t)

B. Evaluate f(-3)

C. Solve f(t)= 2

Solution :

A) To write the relationship as function r=f(t) we separate the r,

[tex]3r+2t=18[/tex]

Subtract 2t both side,

[tex]3r=18-2t[/tex]

Divide by 3 both side,

[tex]r=\frac{18-2t}{3}[/tex]

The function is [tex]f(t)=\frac{18-2t}{3}[/tex]

B) To evaluate f(-3) put t=-3

[tex]f(-3)=\frac{18-2(-3)}{3}[/tex]

[tex]f(-3)=\frac{18+6}{3}[/tex]

[tex]f(-3)=\frac{24}{3}[/tex]

[tex]f(-3)=8[/tex]

C) Solve for f(t)=2

[tex]\frac{18-2t}{3}=2[/tex]

[tex]18-2t=6[/tex]

[tex]2t=12[/tex]

[tex]t=\frac{12}{2}[/tex]

[tex]t=6[/tex]

The value of f(-3), to write the relationship as a function (r = f(t)) and to solve the (f(t) = 2) expression, arithmetic operations can be use. Refer the below calculation for better understanding.

Given :

3r + 2t = 18

A) 3r = 18 - 2t

[tex]r = 6-\dfrac{2t}{3}[/tex]   ---- (1)

where,   [tex]\rm f(t)=6-\dfrac{2t}{3}[/tex]   ----- (2)

B)   [tex]r = 6-\dfrac{2t}{3}[/tex]

Given that f(-3) imply that t = -3. So from equation (2) we get

f(-3) = 8

C) Given that f(t) = 2. So from equation (2) we get,

[tex]2 = 6 -\dfrac{2t}{3}[/tex]

2t = 12

t = 6

The value of f(-3), to write the relationship as a function (r = f(t)) and to solve the (f(t) = 2) expression, arithmetic operations can be use.

For more information, refer to the link given below:

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Answer:

B. (x-4)^2 + (y - 3)^2 = 5^2

Step-by-step explanation:

The equation for a circle is given by

(x-h)^2 + (y-k) ^2 = r^2

where (h,k) is the center and r is the radius

We have a center of (4,3) and a radius of 5

(x-4)^2 + (y-3) ^2 = 5^2

For this case we have that by definition of multiplication of powers of the same base, the same base is placed and the exponents are added:

[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]

So, we can rewrite the given expression as:

[tex]8 ^ {3-5 + y} = \frac {1} {8 ^ 2}\\8 ^ {- 2 + y} = \frac {1} {8 ^ 2}[/tex]

So, if [tex]y = 0[/tex]:

[tex]8 ^ {- 2} = \frac {1} {8 ^ 2}\\\frac {1} {8 ^ 2} = \frac {1} {8 ^ 2}[/tex]

Equality is met!

Answer:

[tex]y = 0[/tex]

Answer:

Value of y=0

Step-by-step explanation:

We need to solve

[tex]8^3*8^{-5}*8^y=1/8^2[/tex]

We know that 1/a^2 = a^-2

[tex]8^3*8^{-5}*8^y=8^{-2}[/tex]

[tex]8^y=\frac{8^{-2}}{8^3*8^{-5}}\\8^y=\frac{8^{-2}}{8^{3-5}}\\8^y=\frac{8^{-2}}{8^{-2}}\\8^y=1[/tex]

Taking ln on both sides

[tex]ln(8^y)=ln(1)\\yln(8)=ln(1)\\y= ln(1)/ln(8)\\We\,\,know\,that\,\,ln(1) =0\\y=0[/tex]

So, value of y=0

Answer:

The correct answer is B⊂A.

Step-by-step explanation:

The sets are:

A={x|x is a polygon}

B={x|x is a triangle}

According to the given sets Option 2 is correct:

The correct option is B⊂A.. We will read it as B is a subset of A.

The reason is that the Set A contains polygon and Set B contains triangle. A triangle is also a simplest form of polygon having 3 sides and 3 angles but a polygon has many other types also. Like hexagon, pentagon, quadrilateral etc. All the triangles are included in the set of polygon.

Thus the correct answer is B⊂A....

Answer:

Step-by-step explanation:

i believe it is 4.

assuming feburary it snowed about 8.5 inches and in november it is at about the 3 in line you would subtract to get about 5.5 inches

Answer:

4) 5.4 inches

Step-by-step explanation:

5.4 inches of snow fell in February 1889 than November 1888.

According to the graph:

Feb '89: 8.5 inches

Nov '88: 3 inches

8.5 - 3 = 5.5 or 5.4.

Answer:

Let x be the number of guest and y be the quantity of meat,

According to the question,

[tex]y\geq \frac{x}{3}-2[/tex]

Since, the related equation of the above inequality,

[tex]y=\frac{x}{3}-2[/tex]

Having x-intercept = (6,0),

y-intercept = (0,-2)

Also,'≥' shows the solid line,

Now, 0 ≥ 0/3 - 2  ( true )

Hence, the shaded region of above inequality will contain the origin,

Therefore, by the above information we can plot the graph of the inequality ( shown below ).

Answer:

Its the 4th graph.

Step-by-step explanation:

Step-by-step explanation:

Definition:

A pyramid is a polyhedron formed by connecting a one polygonal base and a point, called the apex. Each base edge and apex form a triangle.

A) A pyramid has only one base.   TRUE   (definition)

(look at any photo with the pyramid)

B) The base of a pyramid is a polygon.   TRUE    (definition)

(look at any photo with the pyramid)

C) If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.   TRUE

(look at the picture)

D) The slant height is always the same length as the base of the pyramid.

FALSE

E) The lateral faces of a pyramid are rectangles.   FALSE   (definition)

(the lateral faces of a pyramid always are triangles)

F) The slant height is used to calculate the lateral area.   TRUE

(the lateral faces of a pyramid are triangles. The formula of an area of a triangle is A = (bh)/2. Where b - base of triangle, h - height of triangle)

Answer:

A: pyramid has only one base.

B: The base of a pyramid is a polygon.

C: If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.

F: The slant height is used to calculate the lateral area.

Answer: 398

Step-by-step explanation:

200^2 - 199^2 = 399

Answer:

397

Step-by-step explanation:

200^2 - 1 = 40000 - 1 =   39999

199^2 + 1 = 39601+ 1 =    39602

Difference =                         397

A couple of things you should keep in mind.

Answer:

60 inches squared

Step-by-step explanation:

The formula for the area of a triangle is as follows:

[tex]A=\frac{1}{2} bh[/tex]

Where A=area, b=base, and h=height.

Plug in 15 for your base and 8 for your height and solve.

[tex]A=\frac{1}{2} (15)(8)\\A=7.5(8)\\A=60[/tex]

Answer:

B) 60 squared inches

Step-by-step explanation:

To find the area of a triangle you have to use this equation:

A = 1/2 b*h

Now plug in the numbers,

A = 1/2 15*8

15*8 = 120

1/2 of 120 = 60

A = 60

The area of this triangle is 60 squared inches.

Answer:

The surface area of the structure is [tex]SA=2,500\pi\ m^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of a sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

In this problem we have

[tex]r=50/2=25\ m[/tex] -----The radius is half the diameter

substitute

[tex]SA=4\pi (25)^{2}[/tex]

[tex]SA=2,500\pi\ m^{2}[/tex]

B. You walk down 10 flights of stairs

The situation that can be represented by the opposite of 10 is B. You walk down 10 flights of stairs. The concept of 'opposite' here refers to the negative version of a number, which, in this case, would be -10. When you climb up 10 flights of stairs, that's a positive movement upward, analogous to a positive 10. However, walking down 10 flights is the opposite direction, corresponding to -10. Similarly, a temperature rise or a plant growing represents an increase, not the opposite of 10.

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases} \\\\\\ A=500\left(1+\frac{0.03}{1}\right)^{1\cdot 5}\implies A=500(1.03)^t[/tex]

Answer:

b

Step-by-step explanation:

Answer:

Answer is C

Step-by-step explanation:

The root is placed in the denominator section, and the exponent is placed in the numerator section. it is a fraction because you are not using the entire exponent, you will only be using part of it as the other part of the exponent is negated by the X

For this case we have that by properties of roots and powers it is fulfilled that:

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

So, if we have the following expression:

[tex]\sqrt [3] {8 ^ x}[/tex]

According to the given definition, we can rewrite it as:

[tex]8 ^ {\frac {x} {3}}[/tex]

ANswer:

[tex]8 ^ {\frac {x} {3}}[/tex]

Option C

Answer:

The answer is D.

Step-by-step explanation:

AQRT is a 30-60-90 triangle.

Answer:

The answer id D. AQRT is a 30-60-90 triangle.

Hope this Helps!

Answer:

y is 90

Step-by-step explanation:

The y/x is proportional per point (x,y) since this is a direct variation.

That is ,

[tex]\frac{30}{-3}=\frac{y}{-9}[/tex].

Cross multiply:

[tex]30(-9)=y(-3)[/tex]

Simplify:

[tex]-270=-3y[/tex]

Divide both sides by -3

[tex]\frac{-270}{-3}=y[/tex]

[tex]90=y[/tex]

Answer:

$176

Step-by-step explanation:

The function[tex]p(x) = 5x^4-3x^3 + 2x^2 + 24[/tex] represents how much money each girl spent based on the number of hours they were shopping.

Janelle goes shopping for 2 hours, then x=2 and

[tex]p(x)=5\cdot 2^4-3\cdot 2^3+2\cdot 2^2+24=5\cdot 16-3\cdot 8+2\cdot 4+24=80-24+8+24=88[/tex]

Thus, Janelle spent $88.

Carmen goes shopping for 2 hours, then x=2 and

[tex]p(x)=5\cdot 2^4-3\cdot 2^3+2\cdot 2^2+24=5\cdot 16-3\cdot 8+2\cdot 4+24=80-24+8+24=88[/tex]

Thus, Carmen spent $88 too.

Together they spent

$88+$88=$176

Answer:

176

Step-by-step explanation:

as you may already know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".

[tex]\bf \stackrel{f(x)}{y}=x^3-9\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\underline{y}^3-9}\implies x+9=y^3\implies \sqrt[3]{x+9}=\stackrel{f^{-1}(x)}{y}[/tex]

Answer:

The correct option is Option B.   $1293

Step-by-step explanation:

It is given that,the cost function for Judy’s new clothing store where she sells t-shirts is c=$11.50n + 925.  She sells 32 t-shirts this month

To find the total cost for this month

cost for n shirt , c=$11.50n + 925

 Cost for 32 shirts = 11.50 * 32 + 925

 =  368 + 925

 = 1293

Therefore the total cost = $1293

The correct answer is option B.  $1293

Answer:

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- To prove that all circles are similar, a translation and a scale factor

  from a dilation will be found to map one circle onto another

- So we can translate the circles to share the same center and dilated

 one of them by the scale factor of the dilation and the center of

 dilation is the common center of the circles

* Lets solve the problem

∵ Circle X has a radius 6 units

∵ Circle Y has a radius 2 units

- At first we translate the circles to share the same center

∴ Use translation to put the centers of the circles at the same point

- Find the scale factor of the dilation from the radii of the two circles

∵ The radius of circle X is 6 units

∵ The radius of circle Y is 2 units

∴ The scale factor = 6/2 = 3

∴ Dilate circle y by scale factor 3

* The steps would prove the circles are similar are;

  Translate the circles so they share a common center point, and

  dilate circle Y by a scale factor of 3.

Answer:

a=3

b=24

Step-by-step explanation:

If [tex]x^2+x-12[/tex] is a factor of [tex]x^3+ax^2-10x-b[/tex], then the factors of [tex]x^2+x-12[/tex] must also be factors of [tex]x^3+ax^2-10x-b[/tex].

So what are the factors of [tex]x^2+x-12[/tex]?  Well the cool thing here is the coefficient of [tex]x^2[tex] is 1 so all we have to look for are two numbers that multiply to be -12 and add to be positive 1 which in this case is 4 and -3.

-12=4(-3) while 1=4+(-3).

So the factored form of [tex]x^2+x-12[/tex] is [tex](x+4)(x-3)[/tex].

The zeros of [tex]x^2+x-12[/tex] are therefore x=-4 and x=3.  We know those are zeros of [tex]x^2+x-12[/tex] by the factor theorem.  

So x=-4 and x=3 are also zeros of [tex]x^3+ax^2-10x-b[/tex] because we were told that [tex]x^2+x-12[/tex] was a factor of it.

This means that when we plug in -4, the result will be 0. It also means when we plug in 3, the result will be 0.

Let's do that.

[tex](-4)^3+a(-4)^2-10(-4)-b=0[/tex]  Equation 1.

[tex](3)^3+a(3)^2-10(3)-b=0[/tex]  Equation 2.

Let's simplify Equation 1 a little bit:

[tex](-4)^3+a(-4)^2-10(-4)-b=0[/tex]

[tex]-64+16a+40-b=0[/tex]

[tex]-24+16a-b=0[/tex]

[tex]16a-b=24[/tex]

Let's simplify Equation 2 a little bit:

[tex](3)^3+a(3)^2-10(3)-b=0[/tex]

[tex]27+9a-30-b=0[/tex]

[tex]-3+9a-b=0[/tex]

[tex]9a-b=3[/tex]

So we have a system of equations to solve:

16a-b=24

9a-b=3

---------- This is setup for elimination because the b's are the same. Let's subtract the equations.

16a-b=24

9a-b=   3

------------------Subtracting now!

7a    =21

Divide both sides by 7:

 a   =3

Now use one the equations with a=3 to find b.

How about 9a-b=3 with a=3.

So plug in 3 for a.

9a-b=3

9(3)-b=3

27-b=3

Subtract 27 on both sides:

   -b=-24

Multiply both sides by -1:

    b=24

So a=3 and b=24

Answer:

Look at the picture

Hope it helps ;)