The focus of a parabola is (3,-7) and the directrix is y = -4.
What is an equation of the parabola?

Answer:

There are 3 intervals as following:

x ≤ 1

1 ≤ x ≤3

x ≥ 3

Combining the all, we get:

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: 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:

by observation we get to know

highest is 28

lowest is 4

hence difference = 28 - 4 = 24

brainliest plsss

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:

1/16

Step-by-step explanation:

........ .. .............

Answer:

1/16.

Step-by-step explanation:

If the question says to find the product, it means to multiply these numbers.

1/2✖️1/8.

Because you cannot cancel out any numbers, you can just multiiply the numerator and the denominator, which gives 1/16.

Hope this helped!

Have a nice day:)

Answer:

75 students and 13 buses are just 75 x 13

975 students

Step-by-step explanation:

75 x 13 = 975

Answer:

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

Answer:

+-(1,2,4,5,10,20)

Step-by-step explanation:

well if this is factors of -20 (bc 75-95=-20)

then it will be +-(1,2,4,5,10,20)

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

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

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

Answers

Step-by-step explanation:

1.D

2.A

3. A

4. B

5. B

Answers!

- What is the basic economic problem that societies must solve?

       - How to allocate resources in order to best satisfy the needs and wants of people.

- In which economic system are price signals, resulting from supply and demand forces, the only determining factor for the goods and services that the economy produces?

      - a market economy

- How do property rights influence the exchange of goods and services in the market?

      - Property rights determine ownership of resources among businesses, individuals, and governments.

- A traditional economy is an economy where ____________

      - economic decisions are based on traditions, culture, and beliefs.

- Which economy has the highest level of consumer sovereignty?

      - market economy

Hope this helps! :)

The kind of roots does the equation f(x) is option (C) 3 real roots is the correct answer.

A polynomial equation is a sum of constants and variables. A polynomial is an expression consisting of indeterminate's (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

For the given situation,

The equation [tex]f(x) = x^3 - x^2 - x + 1[/tex]

The roots of the polynomial equation can be found as follows,

Step 1:

Substitute the value of x in which the equation f(x) equals zero.

⇒ Put [tex]x = 1[/tex], the equation becomes

⇒ [tex]f(1) = 1^3 - 1^2 - 1 + 1[/tex]

⇒ [tex]f(1) = 0[/tex]

Thus [tex](x - 1)[/tex] is the one root of the equation.

Step 2:

The other roots can be found by framing the quadratic equation on dividing the equation [tex]f(x) = x^3 - x^2 - x + 1[/tex] by [tex](x - 1)[/tex]

On dividing [tex]f(x) = x^3 - x^2 - x + 1[/tex] by [tex](x - 1)[/tex] we get the quotient,

⇒ [tex](x^{2} -1)[/tex]

Step 3:

Now factorize the quadratic equation, [tex](x^{2} -1)[/tex]

It can be expand using the identity,

⇒ [tex](x^{2} -1^{2} ) = (x+1)(x-1)[/tex]            [∵ (a^2 - b^2) = (a+b)(a-b) ]

Thus the factors of the equation are [tex](x-1)(x+1)(x-1)[/tex]. So the roots are [tex]1,-1,1[/tex].

Hence we can conclude that the kind of roots does the equation f(x) is option (C) 3 real roots is the correct answer.

Learn more about polynomials here

https://brainly.com/question/1869917

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Answer:

f(1) = 11

Step-by-step explanation:

f(x) = 3x + 8

Let x=1

f(1) = 3(1) +8

    = 3+8

   = 11

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:

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

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

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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

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

Answer:

Exact Form: -5/2, -79/15            Decimal form: -2.5, -5.26      mixed number form: -2 1/2,   -5 4/15

Answer:

-7  9/10

Step-by-step explanation:

First, I converted the mixed numbers into improper fractions, which left me with 25/10 plus 79/15. I had to find common denominators for the both of them, and I ended up with 30. 10 goes into 30 3 times, and 3 times 25 is 75. 15 goes into 30 two times, and 2 times 79 is 158. That left me with 75/30 plus 158/30 and my first answer was 237/30. I then had to convert that improper fraction into a mixed number. 237 divided by 30 is 7 with a remainder of 27. My next answer to this problem was

7  9/10. A negative plus a negative equals a negative number, so the final answer is -7  9/10.

Answer:

The value of r is 105

Step-by-step explanation:

Quadratic equation helps us to solve any quadratic equation. The formula is:

(-b ± √b² - 4ac) ÷ 2a

For the quadratic equation ax²+bx+c

For the equation: X² - 9x - 6:

a = 1, b = -9 and c = -6

Replacing in the quadratic formula:

(-(-9) ± √(-9)² - 4(1*-6)) ÷ 2*1

= 9 ± √105 / 2

Answer:

105 is right

Step-by-step explanation:

I took the test

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]

Answer:

A

C

D

Step-by-step explanation:

√54 or√9 *√6 or √27 *√4

are equal to the answer.

You can do that by doing the square of outer number which is 3 which equals to 9 when squared and multiplying that with the number inside the square root.

Answer:

x = 30

Step-by-step explanation:

i hope it help, sorry if its wrong

Answer:

L=110

d=110

b=70

a=70

c=110

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:

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:

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: