The following are the ages (years) of 5 people in a room:
21, 24, 18, 15, 15
A person enters the room.
The mean age of the 6 people is now 16.
What is the age of the person who entered the room?

Answer:

f(x) = |x + 2|

General Formulas and Concepts:

Transformations Graph: f(x) = a|bx - c|+ d

Step-by-step explanation:

Step 1: Define

We see a transformation from a parent function of the absolute value.

Parent Graph: f(x) = |x|

Step 2: Find equation of graph

We see the transformation moving horizontally 2 units to the left.

c = -2

f(x) = |x + 2|

Answer:

y=-2x+19

Step-by-step explanation:

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:  m= [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

Now we have,

m= 3-7/8-6

m=-2. Since m=-2, the equation is y=-2x+b.

To find b, think about what your (x,y) points mean:

(6,7). When x of the line is 6, y of the line must be 7.

(8,3). When x of the line is 8, y of the line must be 3.

Substitute them to the equation  y=-2x+b.

You can use either (x,y) point you want..the answer will be the same:

(6,7). y=mx+b or 7=-2 × 6+b, or solving for b: b=7-(-2)(6). b=19.

(8,3). y=mx+b or 3=-2 × 8+b, or solving for b: b=3-(-2)(8). b=19.

So, the equation of the line that passes through the points

(6,7) and (8,3)  is  y=-2x+19.

Answer:

Step-by-step explanation:

the formula for calxulating the area if the isosceles triangle is expressed as;

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

b is the base of the triangle

h is the altitude

Given

b = 16ft

h = 10ft

Substitute

A = 1/2 * 16 * 10

A = 8*10

A = 80ft²

Hence the area of the triangle is 80ft²

b) To get the measure of one side of the triangle, we will use the pythagoras theorem. Let s be the slant side

s² = h²+(b/2)²

s² = 10²+(16/2)²

s² = 10²+(8)²

s² =100+64

s² =164

s = √164

s = 12.8ft

Hence one side of the triangle is 12.8ft

Answer:

a. 5

b. 1

c. 132

d. -2

Step-by-step explanation:

a. The square root of 4 is 2, the absolute value of -3 is 3. 2 + 3 = 5

b.  4 - (-3) / -7 = 7/ -7 = 1

c. 2 * 4^3 = 128 + (-3) - (-7) = 132

d. 2 (-7 + 3) = -8, square root to the third power of -8 is -2

I hope this helped, please mark Brainliest, thank you!!

The rate at which the height of water tank changing is [tex]0.4244 \; \text {ft./hr}[/tex]

Step-by-step explanation:

Given information:

[tex]\text{\bold{The diameter of cone}}=10\;\rm{ ft.}[/tex]

[tex]\rm{The\; height\; of\; the\; cone}= 15\;\rm{ ft.}[/tex]

[tex]\text{The rate at which the water is leaking }= 12 \; \rm ft^3/hr.[/tex]

[tex]\text{Volume of water tank}=27 . \pi \; \rm ft^3[/tex]

Now,

If ,we take a right circular cone with radius r and height h , its volume

[tex]\text{volume (V)} = (1/3) \times \pi \times \rm{r^3 \times h[/tex]

Now, the radius of cone when the volume of water tank is given

[tex]\frac{1}{3}\times \pi \rm\times{r^2 \times h = 27 \times \pi[/tex]

The ratio of height to radius of the cone :

[tex]\text {h/r} =3[/tex]

[tex]\text r = \text h/3[/tex]

Now calculate :

[tex]dV/dt= dV/dh \times dh/dt[/tex]

Which gives:

[tex]12 = \frac{d(\text h^3/27 \pi)}{dh} \times \frac{d\text h}{dt} \\\\\frac{d\text h}{dt} = \frac{12}{\pi \text h^2/9}[/tex]

As ,

[tex]27=\frac{1}{27 \times h}[/tex]

[tex]\text h^3=27^2\\\text h= 9\\[/tex]

Now,

[tex]dh/dt=12/(\pi.\text h^2/9)\\dh/dt=4/3\pi\\dh/dt=0.4244\\[/tex]

Hence, The rate at which the height of water tank changing is [tex]0.4244 \; \text {ft./hr}[/tex]

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Answer:

A.

Step-by-step explanation:

your equation has no exponents, it is linear.

Answer:

A

Step-by-step explanation:

Answer:

When you add polynomials, you combine only like terms together. When you multiply polynomials, you multiply all pairs of terms together.

Step-by-step explanation:

.

Answer:

adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about

Answer:

Me

Step-by-step explanation:

Because I am really good at math

Answer: 64 fluid ounces

Step-by-step explanation:

Amount of water in the container = 128 fluid ounces

Amount drank by Toya every hour = 8 fluid ounces

For 8 hours, Toya would have drank:

= 8 × 8 fluid ounces

= 64 fluid ounces

To calculate the amount of fluid ounces

thataree in the container after 8 hours, we then subtract 64 fluid ounces from 128 fluid ounces. This will be:

= 128 fluid ounces - 64 fluid ounces

= 64 fluid ounces

Answer:

y-3x=4

Step-by-step explanation:

1-4/-1-0=3

1 = 3(-1)+b

1=-3+b

b=4

The equation of linear equation in standard form consisting points (-1, 1) and (0, 4) is,

⇒ y = 3x + 4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-1, 1) and (0, 4)

Now,

Since, The equation of line passes through the points (-1, 1) and (0, 4).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 1) / (0 - (-1))

m = 3 / 1

m = 3

Thus, The equation of line with slope 3 is,

⇒ y - 1 = 3 (x - (-1))

⇒ y - 1 = 3 (x + 1)

⇒ y - 1 = 3x + 3

⇒ y = 3x + 3 + 1

⇒ y = 3x + 4

Therefore, The equation of linear equation in standard form is,

⇒ y = 3x + 4

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Answer:

224 ounces

Step-by-step explanation:

Answer:

The correct answer is:

Option A: [tex](14.\frac{1}{7})\frac{2}{5}[/tex]

Step-by-step explanation:

Associative property is applied on three numbers which states that when two numbers are being added or multiplied the order of addition and multiplication doesn't matter i.e. the answer is same.

If a,b and c are three numbers then associative property for multiplication can be given as:

a.(b.c) = (a.b).c

The given expression is:

[tex]14(\frac{1}{7}.\frac{2}{5})[/tex]

Applying the associative property for multiplication we get

[tex](14.\frac{1}{7})\frac{2}{5}[/tex]

Hence,

The correct answer is:

Option A: [tex](14.\frac{1}{7})\frac{2}{5}[/tex]

Answer:

130 degrees

Step-by-step explanation:

ABF and BFE are alternate angles. So BFE is 65

BG=FG so FBG is 65. x the exterior angle is 65+65=130 degrees

Answer:

width equals fifteen times one hundred sixty five

is that right or is that ok or good enough?? sorry if i am wrong....

Answer:

W = 2475

Step-by-step explanation:

I am not sure if you want the answer or not but I hope this helps

Answer:

x-int: (3, 0)

y-int: (0, -3)

General Formulas and Concepts:

Alg 1

Slope-Intercept Form: y = mx + b

The y-intercept is the y value when x = 0.

Another way to reword that is when the graph crosses the y-axis.

The x-intercept is the x value when y = 0.

Another way to reword that is when the graph crosses the x-axis.

Step-by-step explanation:

Step 1: Define equation

x - y = 3

Step 2: Convert to slope-intercept form

Step 3: Find x/y-intercepts

x-int

y-int

Answer:

x=3

y=-3

Step-by-step explanation:

Answer:

Price of Mira Breakfast = 9 $ before tip

Step-by-step explanation:

Let say Mira's breakfast Price = B $

Tip she left = 20 %

20 % Tip amount =  (20/100) B =  0.2B $

Tip Amount She left = $ 1.8

Equating Tip Amount

0.2B = 1.8

=> B = 9

Price of Mira Breakfast = 9 $ before tip

Step-by-step explanation:

Answer:

b) simplify the constant

c)isolate the variable by dividing the coefficient

Step-by-step explanation:

Answer:

I am sorry. To answer a test is against the Honor Code, I cannot help you.

Step-by-step explanation:

Remember PEMDAS :)

Answer:

2.125

Step-by-step explanation:

Answer:

Step-by-step explanation:

2

Answer:

if she walks 2 miles in 30 minutes, she will walk 8 miles in 120 minutes.

Step-by-step explanation:

Can i get brainliest plzzz?

Answer:

8

Step-by-step explanation:

They can walk 8 miles in 120 minutes she can walk 1 mile in 15 minutes and 120/15 is 8.

Answer:

corresponding angles

Alternate angle

cointerior angle

Answer:

[tex]\frac{80}{1.94}[/tex]

Step-by-step explanation:

I hope this helps!

Answer:

I believe the answer is p = -7/5

Step-by-step explanation:

Here's the equation and the workthru of my logic:

-5 (p + 3/5) = -4

Divide both sides by -5 to remove the -5 from the left side of the equation,

p + 3/5 = -4/5,

Subtract 3/5 from both sides to solve for p,

p = -4/5-3/5

p = -7/5

Solution is -7/5

Hope this helps.

Good luck!

Answer:

10x⁵ + 8x⁴

Step-by-step explanation:

Answer: x=10 y=5 = 15xy

Step-by-step explanation: