Which statements describe a parabola? Check all that apply.

A parabola is the set of all points equidistant from the directrix and focus.
The fixed line is called the vertex of a parabola.
The focus is a fixed point inside the parabola.
The line of symmetry intersects the focus and directrix.
The line of symmetry and the directrix are perpendicular.
The parabola intersects the directrix.

Answer:

The graph of [tex]g(x) = (x - 1) (x + 4)^3(x +5)^2[/tex] crosses the x-axis at (1,0) and (-4, 0). It touches the x-axis at (-5, 0).

Step-by-step explanation:

g(x):

[tex]g(x) = (x - 1) (x - (-4))^3(x - (-5)^2[/tex].

There are three factors:

The first and second factors are raised to odd powers. The graph will cross the x-axis at all these two points:

The third factor is raised to an even power. The graph will touch the x-axis at that point.

Answer:

crosses at (1,0)

crosses at (-4,0)

touches at (-5,0)

Got correct on ed

Step-by-step explanation:

Answer:

= 5.196 i

Step-by-step explanation:

The problem tells us to find the square root of -98 +71

√(-98 + 71)

= √(-27)

Which is an imaginary number

=√(-3^3)

Lets remember that, √(-1) = i

= i*3√(3)

= 5.196 i

Please see attached image for more information

Answer:

Counting by hand

Dividing 15 by 2

Step-by-step explanation:

Answer:

The product is -x³ - 2x² + 13x + 26

Step-by-step explanation:

* Lets revise how to find the product of two binomials

- If (ax ± b) and (cx ± d) are two binomials, where a , b , c , d are constant

 their product is:

# Multiply (ax) by (cx) ⇒ 1st term in the 1st binomial and 1st term in the

  2nd binomial

# Multiply (ax) by (d) ⇒ 1st term in 1st binomial and 2nd term in

  2nd binomial

# Multiply (b) by (cx) ⇒ 2nd term in 1st binomial and 1st term in

  2nd binomial

# Multiply (b) by (d) ⇒ 2nd term in 1st binomial and 2nd term in

  2nd binomial

# (ax ± b)(cx ± d) = cx² ± adx ± bcx ± bd

- Add the terms adx and bcx because they are like terms

* Now lets solve the problem

- There are two binomials (13 - x²) and (x + 2)

- We can find their product by the way above

∵ (13)(x) = 13x ⇒ 1st term in the 1st binomial and 1st term in the

  2nd binomial

∵ (13)(2) = 26 ⇒ 1st term in 1st binomial and 2nd term in

  2nd binomial

∵ (-x²)(x) = -x³ ⇒ 2nd term in 1st binomial and 1st term in

  2nd binomial

∵ (-x²)(2) = -2x² ⇒ 2nd term in 1st binomial and 2nd term in

  2nd binomial

∴ The product of (13 - x²)(x + 2) = 13x + 26 - x³ - 2x²

- There is no like terms

- Lets arrange the terms from greatest power to smallest power

∴ The product is -x³ - 2x² + 13x + 26

Answer:

[tex]\large\boxed{V=\dfrac{75\sqrt3}{2}\approx64.95}\\\boxed{S.A.=\dfrac{160+25\sqrt3}{2}}[/tex]

Step-by-step explanation:

The formula of a volume of a prism:

[tex]V=BH[/tex]

B - base area

H - height

In the base we have the equilateral triangle. The formula of an area of an equilateral triangle with side a:

[tex]A=\dfrac{a^2\sqrt3}{4}[/tex]

Substitute a = 5:

[tex]B=\dfrac{5^2\sqrt3}{4}=\dfrac{25\sqrt3}{4}[/tex]

H = 6.

Calculate the volume:

[tex]V=\left(\dfrac{25\sqrt3}{4}\right)(6)=\dfrac{75\sqrt3}{2}[/tex]

The formula of a Surface Area:

[tex]S.A.=2B+PH[/tex]

B - base area

P - perimeter of a base

H - height

Calculate P:  [tex]P=5+5+5=15[/tex]

Substitute:

[tex]S.A.=2\left(\dfrac{25\sqrt3}{4}\right)+(15)(6)=\dfrac{25\sqrt3}{2}+80=\dfrac{160+25\sqrt3}{2}[/tex]

Answer: $116,000

Step-by-step explanation:

Set up a ratio and then cross multiply and divide. See paper attached. (:

Final answer:

Ava's salary is calculated based on the given salary ratio of Paul to Ava (3:4). By dividing Paul's salary by 3, we find out how much one part of the ratio is worth and then multiply by 4 to find Ava's salary to be $116,000.

Explanation:

The question provided asks us to calculate Ava's salary based on the ratio of Paul to Ava's salaries which is 3:4. If Paul's salary is $87,000, we determine Ava's salary using the given ratio. Here is the step-by-step process:

Step 1: Understand the ratio, which tells us that for every 3 parts of Paul's salary, Ava gets 4 parts. This does not tell us the total amount, but how they share the total amount.

Step 2: Since Paul's salary is $87,000, and that represents 3 parts of the total, we divide $87,000 by 3 to find out what 1 part is: $87,000 / 3 = $29,000.

Step 3: Now that we know 1 part is $29,000, we can calculate Ava's salary which is 4 parts: $29,000 X 4 = $116,000.

Ava's salary is therefore $116,000.

Answer:

2p, since twice as long would hint to multiplication.

Answer:

176

Step-by-step explanation:

To find a number from a known percentage and a number, divide the given number by the percent.

[tex]\frac{v}{p}[/tex]

Where [tex]v[/tex] is the value given and [tex]p[/tex] is the percentage.

[tex]\frac{44}{0.25}=176[/tex]

Answer:

176

Step-by-step explanation:

Answer:

Step-by-step explanation:

45% off $25.60

= [tex]\frac{45}{100}[/tex] x $25.60

= $11.52 (Ans)

Answer:

$11.52

Step-by-step explanation:

$25.60 is 25.6 and 40% is 0.40

So do 25.6 * 0.40 and you get your answer of $11.52

Hope this helped ^-^

Answer:

Option A. [tex]LN^{2}=33^{2}-11^{2}[/tex]

Step-by-step explanation:

we know that

In the right triangle MNL

Applying the Pythagoras Theorem

[tex]MN^{2}=ML^{2} +LN^{2}[/tex]

substitute the values

[tex]33^{2}=11^{2} +LN^{2}[/tex]

[tex]LN^{2}=33^{2}-11^{2}[/tex]

Step-by-step explanation:

If the zeros are 5 and 9, then the equation will have the form:

y = a (x–5) (x–9)

We know the point (0, 90) is on the curve, so we can use this to find the coefficient a:

90 = a (0–5) (0–9)

90 = 45a

a = 2

y = 2 (x – 5) (x – 9)

Answer:

y = 2 (x-5) (x-9)

Step-by-step explanation:

Edge

Answer:

[tex]\large\boxed{\dfrac{5}{4}}[/tex]

Step-by-step explanation:

[tex]a_1=20\\\\a_2=\dfrac{20}{2}=10\\\\a_3=\dfrac{10}{2}=5\\\\a_4=\dfrac{5}{2}\\\\a_5=\dfrac{\frac{5}{2}}{2}=\dfrac{5}{2}\cdot\dfrac{1}{2}=\dfrac{5}{4}[/tex]

Answer: 72

Step-by-step explanation:

Rewriting input as fractions if necessary:

8/9, 7/8

For the denominators (9, 8) the least common multiple (LCM) is 72.

LCM(9, 8)

Therefore, the least common denominator (LCD) is 72.

Rewriting the original inputs as equivalent fractions with the LCD:

64/72, 63/72

Step-by-step answer:

Given:

In a triangle ABC, AD is the bisector of angle A ....If AB=5.6cm ,AC=4cm and DC=3cm, find BD and DC

This problem can be solved by direct application of the angle bisector theorem, which states that the division of the side opposite to the bisected angles is proportional to the respective sides.

Here we have:

Bisector: AD

Side divided: DC = 3 cm

Length of AB = 5.6

Length of AC = 4.0

Then BD = AB/AC * DC = 5.6/4.0 * 3 = 4.2

BC = BD+DC = 4.2+3 = 7.2

Answer:

B. Rectangle

Step-by-step explanation:

All rectangles are parallelograms.

Answer:

Step-by-step explanation:

D is correct.  The idea here is to ensure that the point on the post is equidistant from the bottom of the post (where it meets the ground), which in turn ensures that the angle between ground and post is 90° in at least two places on the ground.

The step that Sam must take first in order to make sure that the post of the fence is ⊥ to the bottom of the ground would be:

D). "Place the compass at the point off the ground, and swing an arc that intersects the ground in two places."

Learn more about 'arcs' here:

brainly.com/question/16765779

Answer: Last option

[tex]p = (0.9801) ^ {30}[/tex]

Step-by-step explanation:

the probability of a jaywalker being hit is

[tex]P = \frac{1}{100} = 0.01[/tex].

So the probability of a jaywalker not being hit is:

[tex]P '= 1-0.01[/tex]

[tex]P '= 0.99[/tex]

As in this experiment the probability of each trial is independent then, the probability that it is not a jaywalker will not be hit if it makes a round trip is:

[tex]P '= (0.99) (0.99) = 0.9801[/tex]

[tex]P '= 0.9801[/tex]

If this experiment is repeated for 30 days then the probability that it is not a jaywalker will not be hit if it makes a round trip is:

[tex]p = (0.9801) ^ {30}[/tex]

[tex]x=\ln 403.429[/tex]

Answer:

D. R0, 360°

Step-by-step explanation:

Since the transformation is from (x,y) to (x,y), the values stay the same...

It's just like a 360 degrees rotation then, since the end position is identical to the start position.

All other answers would affect at least one of the values to change sign like (-x,y), (x,-y) or (-x,-y)... but a 360 degrees rotation would not.

Gregory has 2/3 of a pizza and gives 1/4 of an entire pizza to Marlene. By converting the fractions to a common denominator, we find that he gives away 3/8 of his portion of the pizza to Marlene.

Understanding fractions can sometimes be as easy as picturing how you would slice a pie and share it with friends.

Gregory has 2/3 of an entire pizza and decides to give 1/4 of an entire pizza to his friend Marlene.

To solve how much of his portion Gregory gives to Marlene, we need to figure out what fraction 1/4 represents out of the 2/3 that Gregory has.

If we think of the pizza being cut into 12 slices (since 12 is a common multiple of both 3 and 4), Gregory's 2/3 is equivalent to 8/12 of the pizza because (2/3) × (12/1) = 8/12.

Similarly, 1/4 of the pizza is equivalent to 3/12 of the pizza because (1/4) × (12/1) = 3/12.

Now we know that Gregory aims to give away 3/12 of the pizza, but we want to express this as a part of his original 8/12.

To find out what fraction of his part he gives away, we then calculate (3/12) ÷ (8/12).

When we divide these fractions, we can multiply by the reciprocal of the second fraction:

(3/12) × (12/8), which simplifies to 3/8.

Therefore, Gregory gives away 3/8 of his 2/3 of the pizza to Marlene.

Squares 1 and 2 have the same area because they're both (a+b) on a side.

Each of these squares is covered by four identical right triangle tiles, legs a,b, hypotenuse c.  

In the first picture we see the uncovered part of the square, not covered by triangular tiles, is two squares, area [tex]a^2+b^2[/tex].

In the second picture the uncovered part of the square is a smaller square, area [tex]c^2[/tex].

We just moved the tiles around on the square, so the uncovered part is the same in both cases.  So

[tex]a^2 + b^2 = c^2[/tex]

--------

The rectangular prism has a bottom rectangular base 6 by 8.  So  the diagonal is [tex]\sqrt{6^2+8^2}=\sqrt{100}=10[/tex].

The diagonal and the 7 cm side make a right triangle whose hypotenuse is the diagonal of the rectangular prism we seek.

[tex]\sqrt{10^2 + 7^2} = \sqrt{149}[/tex]

Answer: √149

Answer:

The answer would be B. 2x+4 / x

For this case we have that by definition of composition of functions that:

[tex](f_ {0} h_ {0} g) = f (h (g (x)))[/tex]

So:

[tex]h (g (x)) = 4 (x-2) -1 = 4x-8-1 = 4x-9[/tex]

So:

[tex]f (h (g (x))) = \frac {4x-9 + 4} {4x-9} = \frac {4x-5} {4x-9}[/tex]

ANswer:

[tex](f_ {0} h_ {0} g) = \frac {4x-5} {4x-9}[/tex]

Option D

Answer:

Step-by-step explanation:

[tex]14\leq2t+18\leq20\qquad\text{subtract 18 from all sides}\\\\14-18\leq2t+18-18\leq20-18\\\\-4\leq2t\leq2\qquad\text{divide all sides by 2}\\\\\dfrac{-4}{2}\leq\dfrac{2t}{2}\leq\dfrac{2}{2}\\\\-2\leq t\leq1\\\\\text{The third graph.}[/tex]

Answer:

{x | x ≤ -20}

Step-by-step explanation:

x + 17 ≤ -3

Subtract 17 from each side

x + 17-17 ≤ -3-17

x  ≤ -20

Answer:

{x | x ≤ -20}

Answer:

x^3-1

Step-by-step explanation:

f(x)=g(x)-1 since was shifted down 1 unit                                        x^3-1

f(x)=g(x)+1 would have been a shift up of 1 unit                             x^3+1

f(x)=g(x-1) shifted right 1 unit                                                            (x-1)^3

f(x)=g(x+1) shifted left one unit                                                        (x+1)^3

Anyways the answer is f(x)=x^3-1

Answer:

The value of x is -3

Step-by-step explanation:

We need to solve the given equation and find value of x

5(x-4)+3x-9x=6-(2x+5)+8x

First solving the brackets

5x-20+3x-9x = 6-2x-5+8x

Now combining the like terms,

5x+3x-9x-20 = -2x+8x+6-5

8x-9x-20 = 6x +1

-x-20=6x+1

Now moving x terms on one side and constants on other

6x+x=-20-1

7x = -21

Dividing both sides by 7

7x/7 = -21/7

x = -3

So, the value of x is -3

Answer:

The graph of his initial step in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=3(4)^{x}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

r is the rate of change

In this problem

a=3 ---> the initial value ( value of the function when the value of x is equal to zero)

b=4

b=1+r ----> 4=1+r ----> r=3 ---> r=300%

therefore

The initial value is the point (0,3)

The graph of his initial step in the attached figure

Calculista · Quality Assurance - seems pretty accurate i was looking at their answer and he went as far as actually graphing it out for everyone... it shure as **** helped me not get confused. Thanks  Calculista you got big brain lol!

1- Writing the system of equations:

The price of a cup of coffee is denoted by c while the price of a spaghetti is denoted by s

We are given that:

4 cups of coffee and 6 spaghetti cost $20.5

This means that:

4c + 6s = 20.5 ................> equation 1

We are also given that:

1 cup of coffee and 3 spaghetti cost $8.75

This means that:

c + 3s = 8.75 .................> equation 2

2- Solving the equations using substitution methods:

From equation 2:

c = 8.75 - 3s ................> I

Substitute with I in equation 1 and solve for s as follows:

4c + 6s = 20.5

4(8.75 - 3s) + 6s = 20.5

35 - 12s + 6s = 20.5

35 - 6s = 20.5

6s = 14.5

s = $2.41667

Substitute with s in I to get c:

c = 8.75 - 3s

c = 8.75 - 3(2.41667) = 1.4999 = $1.5

3- getting price for 1 cup of coffee and 1 spaghetti:

c + s = 1.5 + 2.41667 = $3.91667

Hope this helps :)