Given the function f(x) = 3x - 21 +6, for what values of x is f(x) = 18?

Answer:

The midpoint is (3,8)

Step-by-step explanation:

To find the x coordinate of the midpoint,  add the two coordinates together and divide by 2

( 4+2)/2 = 6/2 = 3

To find the y coordinate of the midpoint,  add the two coordinates together and divide by 2

( 7+9)/2 = 16/2 = 8

The midpoint is (3,8)

Answer:

[tex]\boxed{\sf \ \ \ x = 5 \ or \ x=-5 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]x^2-25=0\\<=> x^2-5^2=0\\<=> (x-5)(x+5)=0\\<=> x-5 = 0 \ or \ x+5=0\\<=> x = 5 \ or \ x=-5[/tex]

hope this helps

Answer:

97 is a prime number.

Prime[25] = 97

Answer:

31

Step-by-step explanation:

Median is the middle number when you order them ascending.

Answer:

40 million acres.

Step-by-step explanation:

15 ,27, 31, 40, 44. The median number is the middle number(arranged from least to greatest). In 5 numbers, the middle number is the 3rd number(arranged from least to greatest), therefore; the answer is 31.

Answer:

Step-by-step explanation:

The length PN is the diagonal of a rectangle that is 33 m by 60 m. Its length can be found from the Pythagorean theorem.

  PN² = 33² +60² = 4689

  PN = √4689 ≈ 68.476 . . . meters

Diagonal NS is the hypotenuse of triangle PNS. Once again, the Pythagorean theorem can be used to find its measure.

  NS² = PN² +PS² = 4689 +1600 = 6289

  NS = √6289

  NS ≈ 79.3 . . . meters

__

We have the side adjacent (PN) and the side opposite (PS) to angle PNS, so we can use the tangent function to find the angle:

  tan(PNS) = NS/PN = 40/68.476

  ∠PNS = arctan(40/68.476)

  ∠PNS ≈ 30.3°

Answer:

C is closest to the actual result, $1126.03.

Step-by-step explanation:

Use the Compound Amount formula:  A = P(1 + r/n)^(nt), where:

 P is the original principal; r is the interest rate as a decimal fraction; n is the number of compounding periods per year, and t is the number of years.

Then we have A = $1000(1 + 0.04/4)^(4*3), or

                            = $1000(1.01)^12  =  $1126.03

Answer:

y = -2/3x + 1

Step-by-step explanation:

Step 1: Find slope

m = (-1 - 3)/(3 + 3)

m = -2/3

y = -2/3x + b

Step 2: Find b

-1 = -2/3(3) + b

-1 = -2 + b

b = 1

Step 3: Write equation

y = -2/3x + 1

Answer:

2600

Step-by-step explanation:

the number of female : 5000*48%= 2400 female

males =5000-2400=2600 0r 52%

Answer:

25 pounds of mix A

10 pounds of mix B

Step-by-step explanation:

Each pound of mix A takes half a pound of peanuts and each pound of mix B takes one fourth of a pound of peanuts. Total peanuts consumption is:

[tex]0.5A+0.25B=15[/tex]

Each pound of mix A takes half a pound of almonds and each pound of mix B takes three fourths of a pound of almonds. Total almonds consumption is:

[tex]0.5A+0.75B=20[/tex]

Solving the linear system:

[tex]0.5A+0.25B=15\\0.5A+0.75B=20\\0.5B=5\\B=10\ pounds\\0.5A=15-0.25*10\\A=25\ pounds[/tex]

In order to exactly use all of your ingredients, you should make 25 pounds of mix A and 10 pounds of mix B

Answer:

7^15

Step-by-step explanation:

(7^5)^3

We know that a^b^c = a^(b*c)

 (7^5)^3 = 7^(5*3)

              = 7^15

Answer:

x= -4

Step-by-step explanation:

2x+4=6x+20

so 2x-6x=20-4

divide both sides by -4

-4x/-4 = 16/4

=-4

Answer:

The length of the arc is 89 yards

Step-by-step explanation:

Mathematically, to find the length of an arc, we use the formula below;

Length of an arc = Theta/360 * 2 * pi * r

In this case, Theta = 300 and r = 17 yards

Length of the arc = 300/360 * 2 * 22/7 * 17 = 89.047619047583 which is 89 yards to the nearest yard

Answer:

Number of lawns mow in 49 hours = 31.5 lawns

Step-by-step explanation:

Given:

Number of lawns mow = 9

Time taken = 14 hours

Find:

Number of lawns mow in 49 hours

Computation:

Time taken for 1 lawn = 14 / 9

Number of lawns mow in 49 hours = 49 / Time taken for 1 lawn

Number of lawns mow in 49 hours = 49 / (14/9)

Number of lawns mow in 49 hours = 31.5 lawns

Step-by-step explanation:

The point-slope form of an equation of a line:

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

where the slope m is:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (2, -3) and (-6, -1).

Substitute:

[tex]m=\dfrac{-1-(-3)}{-6-2}=\dfrac{2}{-8}=-\dfrac{1}{4}[/tex]

[tex]y-(-3)=-\dfrac{1}{4}(x-2)\\\\y+3=-\dfrac{1}{4}(x-2)\to\text{point-slope form}[/tex]

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

[tex]y+3=-\dfrac{1}{4}(x-2)[/tex]

[tex]y+3=-\dfrac{1}{4}x+\dfrac{1}{2}[/tex]         subtract 3 from both sides

[tex]y=-\dfrac{1}{4}x-2\dfrac{1}{2}\to\text{slope-intercept form}[/tex]

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

[tex]y+3=-\dfrac{1}{4}(x-2)[/tex]      multiply both sides by 4

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

[tex]4y+12=-x+2[/tex]        subtract 12 from both sides

[tex]4y=-x-10[/tex]           add x to both sides

[tex]x+4y=-10\to\text{standard form}[/tex]

Answer:

About 157 meters

Step-by-step explanation:

The circumference of a circle is [tex]2\pi r[/tex]. In this case, this means that one loop around the roundabout would be a distance of:

[tex]2\cdot \pi \cdot 12.5\approx 78.5[/tex]

Multiplying this by 2, you get a distance of about 157 meters. Hope this helps!

Answer:

Solution,

1 round = circumference

[tex]2\pi \: r[/tex]

[tex] = 2 \times \frac{22}{7} \times 12.5[/tex]

[tex] = \frac{44}{7} \times 12.5[/tex]

Required distance covered:

[tex]2 \times \frac{44}{7} \times 12.5 \\ = \frac{88 \times 12.5}{7} \\ = 157.14 \: m[/tex]

hope this helps..

Good luck on your assignment...

Answer:

120 m

Step-by-step explanation:

LCM of 1.6 and 15 will give us the distance

Put 1,6 and 15 in same format:

LCM= 2*2*2*2*3*5*5/10= 120 m

So the next point is 120 m apart

Answer:

6 + 6y + 6 = 12 + 6

Step-by-step explanation:

2(3) + 6y = 12

Multiply 2(3).

6 + 6y = 12

Subtract 6 on both sides, so y variable is isolated.

6 + 6y - 6 = 12 - 6

6y = 6

Divide by 6 on both sides.

6y/6 = 6/6

y = 1

Answer:

x² + 13x + 50 + [tex]\frac{57}{x-5}[/tex]

Step-by-step explanation:

Using Synthetic division

divisor is (x - 5) , thus evaluate at h = 5

5 | 1  8  - 25  - 193

        5     65   250

  -----------------------------

    1  13   50     57 ← remainder = 57

The coefficients of the quotient are 1, 13,  50 , that is

x² + 13x + 50

Thus

[tex]\frac{x^3+8x^2-25x-193}{x-5}[/tex] = x² + 13x + 50 + [tex]\frac{57}{x-5}[/tex]

Hey there!

Let's think of this with a simpler example. Let's say one package is 4 pounds and one is 2 pounds. How many times heavier is the first than the second?Well, two, because the first package is double the weight of the second package! It's twice as heavy! And to get to that number, we divide four by two!

So, in our actual problem, we just divide 3.92 (bigger package) by 2.8 (smaller package).

3.92÷2.8=1.4

So, the first package is 1.4 times heavier than the first one!

Have a wonderful day!

Answer:

$1.33

Step-by-step explanation:

let the cost of apple be $x .

now according to question the two shoppers spend the same amount

4.75x+4=5.5x+3

0.75x=1

x= 4/3= $1.33

therefore,  pound of apples cost = $1.33

Answer:

x³ - 4x² - 25x + 28

Step-by-step explanation:

Step 1: Write out binomial linear factors

(x - 1)(x - 7)(x + 4)

Step 2: Expand

(x²  - 8x + 7)(x + 4)

Step 3: Expand

x³ - 4x² - 25x + 28

Answer:

I think it's 1/2 because it might be right

Answer:

The answer is D.

Step-by-step explanation:

The lateral surface area of a 3-D figure is the area of each face that is NOT a base.

Answer:

a) Cost of flying from A to B = $425

b) Total distance travelled by Piravena during the complete trip = 7,500 km

c) To minimize cost and arrive at the final cost given, she must have travelled by bus from B to C and then travelled by taking an airplane from C to A.

Step-by-step explanation:

The complete question is presented in the attached image to this question.

Full Question

a) To begin her trip she flew from A to B. Determine the cost of flying from A to B.

b) Determine the distance she travels for her complete trip.

c) Piravena chose the least expensive way to travel between cities and her total cost was $1012.50. Given that she flew from A to B, determine her method of transportation from B to C and her method of transportation from C to A.

Solution

a) The distance from A to B is given as 3250 km.

To take an airplane, it costs her a $100 booking fee, plus $0.10 per kilometer.

So, to fly 3250 km, she will pay

100 + (0.10×3250) = $425

b) For her complete journey, she is to make a trip from A to B then from B to C, then from C to A.

Her complete distance travelled = AB + BC + CA

But it is given that the three cities form a right angled triangle as given in the question with AB serving as the hypotenuse side.

Pythagoras theorem gives that the square of the hypotenuse side is equal to the sum of the respective squares of the other two sides

AB² = BC² + CA²

3250² = BC² + 3000²

BC² = 3250² - 3000² = 1,562,500

BC = √1,562,500 = 1,250 km

Total distance covered by Piravena during the entire trip = AB + BC + CA = 3250 + 1250 + 3000 = 7,500 km

c) Her total cost of travel = $1012.50

But she definitely flew from A to B at a cost of $425

This means she spent (1012.50 - 425) on the rest of the journey, that is, $587.5

Note that to travel by bus, it is $0.15 per kilometre and to travel by airplane is $100 + $0.10 per kilometre. Indicating that the airplane saves cost on long distance travels while the bus saves cost on short distance travels.

To confirm this, we calculate the two options (bus or airplane) for each route.

If she travels B to C by bus, cost = 0.15 × 1250 = $187.5

If she travels B to C by airplane, cost = 100 + (0.10×1250) = $225

Hence, the bus obviously minimizes cost here.

If she travels from C to A by bus, cost = 0.15 × 3000 = $450

If she travels from C to A by airplane, cost = 100 + (0.10×3000) = $400

Here, travelling by airplane minimizes the cost.

So, if we confirm now that she travelled from B to C by bus and then from C to A by airplane, total cost = 187.5 + 400 = $587.5

which is the remaining part of her total cost is she minimized expenses!

Hope this Helps!!!

Answer:

The distance is 7500 kilometers

Step-by-step explanation:

I got the answer wrong myself and the website told me that it’s 7500 kilometers

Answer:

140 square units

Step-by-step explanation:

The areas of the three right triangles are subtracted from the area of the entire box. This gives you 140 square units.

Step-by-step explanation:

it's simple:

none of the above

Step-by-step explanation:

Answer:

option c

Step-by-step explanation:

Answer: angles EBA and HBI are congruent

Step-by-step explanation:

they are the congruent because they are verticle angles

Answer:

The reason is because linear functions always have real solutions while some quadratic functions have only imaginary solutions

Step-by-step explanation:

An asymptote of a curve (function) is the line to which the curve is converging or to which the curve to line distance decreases progressively towards zero as the x and y coordinates of points on the line approaches infinity such that the line and its asymptote do not meet.

The reciprocals of linear function f(x) are the number 1 divided by function that is 1/f(x) such that there always exist a value of x for which the function f(x) which is the denominator of the reciprocal equals zero (f(x) = 0) and the value of the reciprocal of the function at that point (y' = 1/(f(x)=0) = 1/0 = ∞) is infinity.

Therefore, because a linear function always has a real solution there always exist a value of x for which the reciprocal of a linear function  approaches infinity that is have a vertical asymptote.

However a quadratic function does not always have a real solution as from the general formula of solving quadratic equations, which are put in the form, a·x² + b·x + c = 0 is  [tex]\dfrac{-b \pm \sqrt{b^{2} - 4\cdot a\cdot c}}{2\cdot a}[/tex], and when 4·a·c > b² we have;

b² - 4·a·c < 0 = -ve value hence;

√(-ve value) = Imaginary number

Hence the reciprocal of the quadratic function f(x) = a·x² + b·x + c = 0, where 4·a·c > b² does not have a real solution when the function is equal to zero hence the reciprocal of the quadratic function which is 1/(a·x² + b·x + c = 0) has imaginary values, and therefore does not have vertical asymptotes.