In XYZ, what is the cosine ratio of X?

Answer:

Ok, our function is:

f(x) = 3*(x - 1)^2 + 2.

First, domain:

We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.

In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)

Then the domain is the set of all real numers.

Vertex:

Let's expand our function:

f(x) = 3*x^2 - 3*2*x + 1 + 2

f(x) = 3*x^2 -6*x + 2

The vertex of a quadratic function:

a*x^2 + b*x + c is at:

x = -b/2a

here we have:

a = 3 and b = -6

x = 6/2*3 = 6/6 = 1.

And the value of y at that point is:

f(1) = 3*(1 - 1)^2 + 2 = 2

Then the vertex is at: (1, 2)

Range:

The range is the set of all the possible values of y.

Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.

Then the minimal value of our quadratic function is the value at the vertex, y = 2.

This means that the range can be written as:

R = y ≥ 2

So the range is the set of all real numbers that are larger or equal than 2.

Answer: False, this is not the graph of f(x) = 3^x

=====================================================

Explanation:

Plug in x = 0 to get

f(x) = 3^x

f(0) = 3^0

f(0) = 1

That means (0,1) is on the graph. So far so good.

-------

But let's try x = 1

f(x) = 3^x

f(1) = 3^1

f(1) = 3

Meaning (1,3) should be on the graph of y = 3^x. Instead, the graph shows (1,4) is on the red curve. We don't have a match.

The red curve shows the equation y = 4^x.

Answer:

see below

Step-by-step explanation:

Complementary means that they add to 90 degrees

<A + <B = 90  given

<B + <C = 90  given

<A + <B = <B + <C  substitution property of equality.

<A = <C  subtraction property of equality

Answer:

L=110

d=110

b=70

a=70

c=110

Answer:

30w-51

Step-by-step explanation:

6+8(4w-7)-(2w+1)

Distribute

6 + 32w-56 -2w-1

Combine like terms

32w-2w  +6-56 -1

30w-51

Answer:W=1.7

Step-by-step explanation: Simplifying

0 = 6 + 8(4w + -7) + -1(2w + 1)

Reorder the terms:

0 = 6 + 8(-7 + 4w) + -1(2w + 1)

0 = 6 + (-7 * 8 + 4w * 8) + -1(2w + 1)

0 = 6 + (-56 + 32w) + -1(2w + 1)

Reorder the terms:

0 = 6 + -56 + 32w + -1(1 + 2w)

0 = 6 + -56 + 32w + (1 * -1 + 2w * -1)

0 = 6 + -56 + 32w + (-1 + -2w)

Reorder the terms:

0 = 6 + -56 + -1 + 32w + -2w

Combine like terms: 6 + -56 = -50

0 = -50 + -1 + 32w + -2w

Combine like terms: -50 + -1 = -51

0 = -51 + 32w + -2w

Combine like terms: 32w + -2w = 30w

0 = -51 + 30w

Solving

0 = -51 + 30w

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-30w' to each side of the equation.

0 + -30w = -51 + 30w + -30w

Remove the zero:

-30w = -51 + 30w + -30w

Combine like terms: 30w + -30w = 0

-30w = -51 + 0

-30w = -51

Divide each side by '-30'.

w = 1.7

Simplifying

w = 1.7

Answer:

(7, 5)

Step-by-step explanation:

(x+5)/2, ( y-3)/2)=(6,1)

(x+5)/2=6, x= 7

( y-3)/2=1, y=5

Answer:

(7-d)(7+d)

Step-by-step explanation:

49 - d^2

Rewriting

7^2 - d^2

We know that a^2 - b^2 = (a-b)(a+b)

(7-d)(7+d)

The answer you are looking for is -(d+7)(d-7).

Answer:

75 students and 13 buses are just 75 x 13

975 students

Step-by-step explanation:

75 x 13 = 975

Answer:

x+3x-15=13

4x=28

x=7

......

Answer:

[tex]y = 3x - 15 \\ \\ to \: find \: x \: substitute \: y \: into \: 0\\ \\ 0 = 3x - 15 \\ - 3x = - 15 \\ divide \: both \: sides \:by \: - 3 \\ \\ x = 5[/tex]

Answer:

f(1) = 11

Step-by-step explanation:

f(x) = 3x + 8

Let x=1

f(1) = 3(1) +8

    = 3+8

   = 11

Hi there!  

»»————-　★　————-««

I believe your answer is:  

4

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the Answer...}}\\\\15+(-11)\\----------------\\\rightarrow 15 +1(-11)\\\\\rightarrow 15 - 11\\\\\rightarrow \boxed{4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

your answer will obviously be 4

Answer:

50%

Step-by-step explanation:

We are given this set of data: Age of professors in years

47, 44, 48, 43, 35, 65, 56, 37, 73,51

We can firstly rearrange the years properly in ascending order.

Hence we have:

35, 37, 43, 44, 48, 51, 53 56, 65, 73

The number of the professor given = 10 professors

The number of professors younger 50 years = 5

Therefore, the percentage of these professors who are younger than 50

Is:

5/10 × 100 = 50%

Therefore, 50% of the professors are younger than 50

Answer:

Linear f(x) = 2·x + 3

Quadratic f(x) = x² + 2·x - 3

Exponential f(x) = 3ˣ - 2

Step-by-step explanation:

1) Linear function

The general form of the linear equation is of the form, f(x) = y = m·x + c

Where;

m = The slope

c = y-intercept (Constant)

The linear function is therefore, f(x) = 2·x + 3

2) Quadratic function

The general form of the quadratic function is f(x) = a·x² + b·x + c

Where;

a, and b are the coefficients of x² and x respectively and c is the constant term

Therefore,  f(x) = x² + 2·x - 3, is a quadratic function, with a = 1, b = 2, and c = -3

3) Exponential function

The general form of the exponential function is f(x) = a·bˣ + k

Where;

a = The initial

b = The multiplier (growth or decay value)

k = vertical shift

Therefore, the function f(x) = 3ˣ - 2 is an exponential function with the initial = 1, b= 3, and k = -2

Answer:

8 lb box

Step-by-step explanation:

Find which laundry detergent has a lower unit price

The unit price is how much something costs for a single unit

In this case, it is how much the detergent costs for 1 pound

7.4/8 lbs = 0.925 dollars per lb

5.38/4 lbs = 1.345 dollars per lb

Since 1.345 > 0.925, the 8 lb box is a better buy

Case 1

Cost of 8 pound detergent = $7.40

So, cost of 1 pound detergent

= $7.40 ÷ 8

= $0.925

Case 2

Cost of 8 pound detergent = $5.38

So, cost of 1 pound detergent

= $5.38 ÷ 4

= $1.345

$0.925 < $1.345

$0.925 < $1.345So, cost per pound in 8 pound box < cost per pound in 4 pound box

So, buying the 8 pound box is better.

Answer:

I will assume that ABCD is a parallelogram.

1. In a parallelogram, opposite sides are congruent so 3x = 18 which means x = 6.

2. The diagonals of a parallelogram bisect each other so BE is half of BD, therefore, BD = 7.5.

3. Consecutive angles of a parallelogram are supplementary so m∠ADC = 180° - 135° = 45°.

4. Consecutive angles of parallelograms are supplementary so 2x + 10 + 135 = 180 → 2x + 145 = 180 → 2x = 35 → x = 17.5°.

5.  Again, the diagonals bisect each other so -6 + 8v = 9v - 10 → v = 4.

6. DA || BC so ∠DAC and ∠ACB are (congruent) alternate interior angles, therefore, m∠DAC = 37°.

7. The area of a parallelogram is base * height; we know base = 18 and height = 21 u so area = 378 u.

Answer:

Below

Step-by-step explanation:

Let m be the average rate of change.

● m = (f(3)-f(2)) / 3-2

● m = ( log3 - log2) / 1

● m = 0.176

Round it to the nearest tenth

● m = 0.18

Answer:

y = 4

Step-by-step explanation:

Move all terms not containing  y  to the right side of the equation.

-y = -4

Multiply each term in  − y  =  − 4  by  − 1

y = 4

Hope this can help you

[tex]\frac 1c=\frac1{c_1}+\frac1{c_2} [/tex]

$\frac1c=\frac{c_1+c_2}{c_1c_2}$

$\implies c=\frac{c_1c_2}{c_1+c_2}$

Answer:

Step-by-step explanation:

[tex]-8\left(-10\right)-7 \times \frac{1}{-1}=87\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\\\=8\times \:10-7\times \frac{1}{-1}\\\\8\times \:10=80\\\\7\times \frac{1}{-1}=-7\\\\=80-\left(-7\right)\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\\\=80+7\\\\=87[/tex]

Perimeter is the distance around the outside.

A square has 4 equal sides:

Perimeter = 21 x 4 = 84 yards

Answer: Perimeter = 84 yd

Explanation:

Perimeter of square = 4 × side

Side = 21 yd

Perimeter = 4 × 21

= 84 yd

Must click thanks and mark brainliest

Answer:

-9

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

i hope it help, sorry if its wrong

Answer:

There are 3 intervals as following:

x ≤ 1

1 ≤ x ≤3

x ≥ 3

Combining the all, we get:

Answer:

[tex]2a + c \\ a = 2 \\ c = - 1 \\ then \: 2 \times 2 + - 1 \\ = 4 - 1 = 3 \\ thank \: you[/tex]

Step-by-step explanation:

Hi there!

From the given Question, we have;

Diameter (d) = 34ft

Height (h) = 16ft

Now;

Radius (r) = d/2

= 34/2

= 17 ft

Now;

Volume (v) = 1/3(πr²h)

= 1/3(3.14 * 17² * 16) ft³

= 4839.78 ft³

Therefore, the Volume is 4839.78 ft³.

Hope it helps!

Answer:

Hello,

Answer 52/3

Step-by-step explanation:

using the theorem of the bissector :

[tex]\dfrac{x}{13} =\dfrac{20}{15 } \\\\x=\dfrac{20*13}{15} \\\\x=\dfrac{52}{3}[/tex]

The value of x to the nearest tenth is 18.5

To get the value of x, we first need to get the height of the triangle.

[tex]h^2=20^2-15^2\\h^2=400-225\\h^2=175\\h=13.23[/tex]

Next is to get the value of x

[tex]x^2=13^2+13.2^2\\x^2=343.24\\x=18.52[/tex]

Hence the value of x to the nearest tenth is 18.5

Learn more on pythagoras theorem: https://brainly.com/question/343682

Answer:

C. [tex]x[/tex] and $(x-6)$

Step-by-step explanation:

The roots of the quadratic equation are $0$ and $6$.

Hence the equation is $(x-0)(x-6)=x(x-6)$

Answer:

See below

Step-by-step explanation:

Answer:

the slope of the line x+y = 6 is -1.

Step-by-step explanation:

slope = - coefficient of x

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

coefficient of y

slope = -1 /1

slope = -1

Answer:

A: -1

Step-by-step explanation:

Answer:

The fraction filled with water is 7/40

Step-by-step explanation:

Okay.

Here we start by calculating the volume of the cylindrical tank.

Mathematically, that would be;

V = π * r^2 * h

From the question

r = 80 cm = 80/100 = 0.8 meters

h = 1.4 meters

π = 22/7

Plugging these values into the volume equation, we have;

V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3

But mathematically;

1 m^3 = 1000 liters

So 2.816 m^3 = 2.816 * 1000 = 2816 liters

So the fraction filled with water will be;

492.8/2816 = 0.175 = 175/1000 = 7/40