Z. Find an equation of a parabola satisfying the given conditions. a Focus (0 directrix y T b) Focus (3,2), directrix x 4

Answer:

17/24

Step-by-step explanation:

This expression simplifies to the following:

-7     15        1          1

---- * -----  -  -----  +  -----

18     -7        4          8

Reducing the product, we get

  15        1

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

  18        8

and this simplifies further:

 5       1

----- - -----

 6       8

The LCD is 24.  Thus, we have:

20      3         17

------ - -----  =  -----

24      24       24

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▹ Answer

-3

▹ Step-by-Step Explanation

1.25 + (-1.75) = -0.5

Opposite of 2.5 = -2.5

-2.5 + (-0.5) = -3

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

*The dot plot is shown in the attachment below

Answer:

2

Step-by-step explanation:

Interquartile range is the difference between the upper median (Q3) and the lower median (Q1).

First, let's write out each value given in the data. Each dot represents a data point.

We have:

2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7

=>Find the median:

Our median is the middle value. The middle value is the 6th value = 4

==>Upper median Q3) = the middle value of the set of data we have from the median to our far right.

2, 3, 3, 4, 4, |4,| 4, 5, [5], 6, 7

Our upper median = 5

==>Lower median(Q1) = the middle value of the data set we have from our median to our far left.

2, 3, [3], 4, 4, |4,| 4, 5, 5, 6, 7

Lower median = 3

==>Interquartile range = Q3 - Q1 = 5-3 = 2

Answer:

2

Step-by-step explanation:

Answer:

I just answered this question lol but the answer is 2^0*3^0*7^47=329. Hope this helps!!

Step-by-step explanation:

Answer:

[tex]\frac{3x^{4} }{2y^{4} }[/tex]

Step-by-step explanation:

[tex]\frac{21x^{6}y^{5} }{14x^{2}y^{9} }[/tex]

→ First simplify the numbers

[tex]\frac{3x^{6}y^{5} }{2x^{2}y^{9} }[/tex]

→ Now simplify the x powers, remember when dividing indices, you subtract them away from each other so,

[tex]\frac{3x^{4}y^{5} }{2y^{9} }[/tex]

→ Now simplify the y powers, remember when dividing indices, you subtract them away from each other so,

[tex]\frac{3x^{4} }{2y^{4} }[/tex]

Answer:

simplify.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To evaluate the derivative of this function you need the chain rule. The pattern I teach to my calculus students is to find

u =

u' =

f(u) =

f'(u) =

First pick your "u". u will be the inner function, the one inside the parenthesis.

u' will then be the derivative of u.

f(u) is the function in terms of u, and

f'(u) is the derivative of the function in terms of u.

The derivative then, finally, will be u' * f'(u). Let's begin.

Our u, or the part of the function inside the parenthesis is 3 - 2x; hence,

u = 3 - 2x

The derivative, u', then is

u' = -2

f(u) is the function in terms of u, so

f(u) = [tex]u^{-\frac{1}{2}[/tex] and the derivative in terms of u is

f'(u) = [tex]-\frac{1}{2}u^{-\frac{3}{2}[/tex]

u' * f'(u) then is

[tex]-\frac{1}{2}u^{-\frac{3}{2}*(-2)[/tex] Simplify that by subbing back in for u and multiplying -2 by -1/2 to get

[tex]y'=(3-2x)^{-\frac{3}{2}[/tex]

Answer:

ordered pairs for the

x-intercept : (6,0)

 y- intercepts :(0,9)

Step-by-step explanation:

Given equation : 3x-2y=18

X- intercept on coordinate plane is point where the line intersect the x- axis.

The coordinate of point y is 0 for x-intercept.

Based on this let the coordinate of X- intercept be (x,0)

we will plug this value in equation 3x-2y=18, to find value of x and hence we will get x-intercept

3x-2y=18

3x -2*0 =18

=> 3x = 18

=> x = 18/3 = 6

Thus, coordinate of x-intercept is (6,0)

________________________________________________

Y- intercept on coordinate plane is point where the line intersect the y- axis.

The coordinate of point x is 0 for y-intercept.

Based on this let the coordinate of X- intercept be (0,y)

we will plug this value in equation 3x-2y=18, to find value of y and hence we will get y-intercept

3x-2y=18

3*0 -2y =18

=> 2y = 18

=> y = 18/2 = 9

Thus, coordinate of y-intercept is (0,9)

Answer:

irrational

Step-by-step explanation:

pi itself is an irrational number, pi/2 will also be an irrational number

Answer:

irrational

Step-by-step explanation:

it's an irrational number divided by a rational so therefore it is irrational

Answer:

Step-by-step explanation:

1. A given chord on a circle is perpendicular to a radius through its center, and it is at a distance less that the radius of the circle.

2. A circle of center O has a radius of 13 units. If a chord AB of 10 units is drawn at a distance, d, to the center of the circle, determine the value of d.

3. From question 2, the radius = 13 units, length of chord = 10 units and distance of chord to center of the circle is d.

A radius that meet the chord at center C, and divides it into two equal parts.

So that;

AC = CB = 5 units

Applying Pythagoras theorem to ΔOCB,

OC = d, CB = 5 units and OB = 13 units

[tex]13^{2}[/tex] = [tex]5^{2}[/tex] + [tex]d^{2}[/tex]

169 = 25 + [tex]d^{2}[/tex]

169 - 25 = [tex]d^{2}[/tex]

144 = [tex]d^{2}[/tex]

⇒ d = [tex]\sqrt{144}[/tex]

       = 12 units

Therefore, the chord is at a distance of 12 units to the center of the circle.

A chord is a straight line joining 2 points on the circumference of a circle.

The line that connects any two points of the circumference of a circle is known as a chord.

Theorem: A radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa.

Converse: The perpendicular bisector of a chord passes through the center of a circle.

Problem: In the given figure the radius of the circle is 5 cms. what is the length of the chord?

Solution:

Given to us,

radius of the circle, r = 5 cms,

RA = 1 cm,

Radius, r = OA = OP = OQ = 5 cms.

Also, OR = OA - OR = 4 cms.

In ΔOPQ,

According to Pythagorus theorum,

OP² = OR² + RP²

5² = 4² + RP²

RP² = 25 -16 = 9

RP = 3,

We know,

A radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa.

A radius (OA) that is perpendicular to a chord divides the chord into two equal parts(RP = RQ).

Therefore, chord = RP + RQ = 3+3 = 6 cms.

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Answer:

She can only make 5/6 of her recipe with the amount of milk that she has.

Step-by-step explanation:

Some data of this problem is missing, the data missing is:

Her recipe calls for 3/4 of a pint of milk and she only has 5/8 of a pint of milk.

Now, to know what's the portion she can do with that amount we need to divide the amount of milk she has by the total amount she needs:

[tex]\frac{5}{8}[/tex] ÷[tex]\frac{3}{4}[/tex]

When we divide we turn the second fraction upside down (the numerator becomes the denominator and viceversa) and multiply, thus:

[tex]\frac{5}{8}[/tex]÷[tex]\frac{3}{4}=\frac{5}{8}[/tex]×[tex]\frac{4}{3} =\frac{20}{24}[/tex]

If we simplify this last expression we have:

[tex]\frac{20}{24}=\frac{10}{12} =\frac{5}{6}[/tex]

Thus, she can only make 5/6 of her recipe with the amount of milk that she has.

Note: In case the data missing is different, you can apply this same procedure with the fractions you have.

Answer:

The college student can spend $15.00 in December.

Step-by-step explanation:

This can be calculated as follows:

Let y represents the amount to spend in December.

The can now us the formula for calculating a mean is as follows:

Mean = Sum of montlhy spending / Number of months ...... (1)

From the question, we have:

Mean = $50

Sum of monthly spending = $100 + $25 + $80 + $30 + y = $235 + y

Number of months = 5

Substituting the values into equation (1) and solve for y, we have:

$50 = ($235 + y) / 5

$50 * 5 = $235 + y

$250 = $235 + y

$250 - $235 = y

$15.00 = y

Therefore, the college student can spend $15.00 in December.

Answer:

This is False.

Step-by-step explanation:

I hope this helped you! :)

Answer: false

Step-by-step explanation:

Answer:

B- 110.5

Step-by-step explanation:

slant height = 17 inches

diameter = 13 inches

If we divide 13/2 = 6.5

then we multiply it by 17

6.5*17 = 110.5 pi in.sq or in other words B

To solve this problem, we have to get the data in the question and then substitute the values into the formula and solve.

The lateral surface area of the cone is 640.874in^2.

Lateral surface area of an object is the sum of the total areas of the object.

The formula of lateral surface area of a cone is given as

[tex]A = 2\pi rh[/tex]

Let's substitute the values into the equation and solve.

Using Pythagora's theorem, we can find the height of the cone

[tex]17^2 = 6.5^2 + h^2\\h^2 = 17^2 - 6.5^2\\h^2 = 246.75\\h = \sqrt{246.75} \\h = 15.70[/tex]

Substituting the values into the formula, we can solve for the lateral surface area

[tex]A = 2\pi rh\\A = 2 * 31.14 * 6.5 8 15.70\\A = 640.874in^2[/tex]

The lateral surface area of the cone is 640.874in^2

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Answer:

The missing term is 3x

Step-by-step explanation:

Given

-(x - 1) + 5 = 2(x + 3) - _

Required

Find _

For proper identification of the parameters, represent _ with Z

So, the equation becomes

-(x - 1) + 5 = 2(x + 3) - Z

Open bracket (start from the left hand side)

-x + 1 + 5 = 2(x + 3) - Z

-x + 1 + 5 = 2x + 6 - Z

Solve like terms

-x + 6 = 2x + 6 - Z

Subtract 6 from both sides

-x + 6 - 6 = 2x + 6 - 6 - Z

-x = 2x - Z

Subtract 2x from both sides

-x - 2x = 2x - 2x - Z

-3x = -Z

Multiply both sides by -1

-3x * -1 = -Z * -1

3x = Z

Reorder

Z = 3x

Hence, the missing term is 3x

Answer:

answer is 3x

Step-by-step explanation:

Answer:

£20

Step-by-step explanation:

First you add 1 ,1 ,2 which =4

Next you divide 80 by 4 which give you the answer 20.

Answer:

similar triangles have there corresponding sides proportional and corresponding angles equal

Answer: y+1=-2(x-1)

Step-by-step explanation:

The point-slope formula is [tex]y-y_{1}=m(x-x_{1})[/tex]. Since we know the coordinate and slope, we can directly plug them in.

[tex]y-(-1)=-2(x-1)[/tex]

[tex]y+1=-2(x-1)[/tex]

Answer:

The answer is below

Step-by-step explanation:

Given that, there are only two available choices, which are a black or white duck, this can be represented using a coin: H→White duck, T→Black Duck

Hence, to represent a set of possible outcomes, the coin has to be tossed three times.

Thus, we assume that, at the minimum we have total number of Ducks = 3 Black + 3 White = 6 Ducks

Total Favorable Outcome = 2 White + 1 Black

Total Possible Outcome = Selecting 3 Ducks (2 White +1 Black) from 6 Ducks

Formula to Calculate Probability

     =  Total favourable outcome ÷ Total possible outcome

Use ,C(n,r)= n! / (n - r)! r!

Therefore, the Probability of two white ducks one black duck swimming together

              = ³C² * ³C¹ ÷ 6C3 = 9/20

To use Simulation Coin Flip, we have the following:

H→White duck, T→Black Duck

HHH→Three White Ducks Swimming together

TTT→Three black ducks Swimming together

HHT→Two white duck and a Black Duck swimming together

HTH→Two white duck and a Black Duck swimming together

THH→Two white duck and a Black Duck swimming together

TTH→Two Black duck and a White Duck swimming together

THT→Two Black duck and a White Duck swimming together

HTT→Two Black duck and a White Duck swimming together

Finally, to find the probability, divide the observed desired outcomes by the total number of trials.

Answer:

There are only two choices, a black or white duck, so a coin is the best choice. To represent a set of possible outcomes, toss the coin three times. Repeat the experiment multiple times. To find the probability, divide the observed desired outcomes by the total number of trials.

Step-by-step explanation:

edg2020

Answer:

The answer should be A'(-9,3) B'(12,-6)

Step-by-step explanation:

If you dialate, you multiply every coordinate by 3. -3 x 3= -9. 1 x 3=3. 4 x 3= 12. -2 x 3= -6. So,  the last option is correct.

Answer:

pi is infinite

Step-by-step explanation:

pi rounded ends

In the graph the line shifted down by 3 units, so k=3. Therefore, option B is the correct answer.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

From the given graph,

The coordinates of line red are (0, 5) and (3, 6)

Here, slope (m) = (6-5)/(3-0)

= 1/3

Substitute m=1/3 and (x, y)=(0, 5) in y=mx+c, we get

5=1/3 (0)+c

c=1/3

Now, g(x)=1/3 x

The coordinates of line blue are (0, 2) and (3, 4)

Here, slope (m) = (4-2)/(3-0)

= 2/3

Substitute m=2/3 and (x, y)=(0, 2) in y=mx+c, we get

2=2/3 (0)+c

c=0

So, f(x)=2/3 x

From the graph the line shifted down by 3 units

Therefore, option B is the correct answer.

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Answer:

a)1280 bacteria

Step-by-step explanation:

We find the function in t hours first

Bacteria in a petri dish doubles every 10 minutes. (Express in exponential function)

a) If there are 10 bacteria initially, how many are there after 120 minutes?

b) If there are 10 bacteria initially, when would there be a million bacteria?

The formula to use is given as

y = Ab^t

Where

y = Total Population of bacteria

B= initial population of the bacteria

r =

t = time in hours

The bacteria doubles in the petri dish every 10 minutes, we have 10 bacteria

10 minutes in hours = 10/60= 1/6 hours

10 × 2 = 10b^10/60

20 = 10b ^1/6

2 = b^1/6

Multiply both sides by Power of 6

2^6 = b

b = 64

Hence, y = 10×(64)^t

a) If there are 10 bacteria initially, how many are there after 120 minutes?

120 minutes in hours = 2

y = 10(64)²

y = 1280

There would be 1280 bacteria after 120 minutes

b) If there are 10 bacteria initially, when would there be a million bacteria?

y= 1,000,000

A = 10 bacteria

b = 64

t = ???

1000000 = 10 × (64)^t

Divide both sides by 10

100000 = (64)^t

Answer:

( x-8) ( x+6)

Step-by-step explanation:

x^2 - 2x - 48

What two numbers multiply to -48 and add to -2

-8*6 = -48

-8+6 = -2

( x-8) ( x+6)

Answer:

william's age=x-5, mrs boiler=3 (x-5), mr boiler=4+3 (x-5) the sum=7x-31

Answer:

This is equation 1.

Step-by-step explanation:

Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant.

Conditons that need to be satisfied: B can be 0 in only one question, parabola should open up and have a negative y intercept.

1. The parabola should open upwards: a> 0

2. [tex]3x^2+7x-6[/tex] (a>0), y-int is negative (0s for x's)

                     3(0)^2 + 7(0) -6

                                   y= -6

Step 2:

1. Factor the original equation: (3x-2)(x+3)

x=2/3, -3

2. Strategy used (factor by grouping)

Answer:

El área de la casa es de 1,304 m²

Step-by-step explanation:

De las dimensiones dadas en línea, tenemos que el área del jardín = 640 m²

Las dimensiones del jardín son;

Longitud = 40 m.

Ancho = a m

Por lo tanto, 40 × a = 640

a = 640/40 = 16 m

La dimensión del compuesto es así;

Longitud = 40 + 14 = 54 m

Ancho = 20 + a = 20 + 16 = 36 m

El área del compuesto = Área de la casa + Área del jardín

El área del compuesto = Ancho del compuesto × Longitud del compuesto

El área del compuesto = 36 × 54 = 1,944 m²

∴ 1,944 m² = Área de la casa + Área del jardín

1,944 m² = Área de la casa + 640 m²

Área de la casa = 1,944 m² - 640 m² = 1,304 m²

El área de la casa = 1,304 m².

Answer:

Yes.

Base: 4

Step-by-step explanation:

Since we have 4 to the power of x, we do indeed have an exponent. The -2 just signifies vertical movement down.

Answer:

ΔAKL is congruent to ΔBML by the Side Angle Side rule of congruency and ΔALB is isosceles as two of its sides [tex]\overline {AL}[/tex] and [tex]\overline {BL}[/tex] are congruent

Step-by-step explanation:

The given parameters are;

The given triangle ΔKLM has sides [tex]\overline {KL}[/tex] ≅ [tex]\overline {LM}[/tex],   Given

ΔKLM is isosceles Δ (two equal segments),         Definition of isosceles Δ

∠LKM ≅ ∠LMK,                                                       Base ∠s of isosceles Δ are ≅

Point A is on segment [tex]\overline {KM}[/tex],                                  Given    

Point B is also on segment [tex]\overline {KM}[/tex],                          Given

Segment [tex]\overline {AK}[/tex] ≅ segment [tex]\overline {BM}[/tex],                              Given

ΔAKL ≅ ΔBML,                                                       SAS rule of congruency

Segment [tex]\overline {AL}[/tex] ≅ segment [tex]\overline {BL}[/tex],                                CPCTC

ΔALB is isosceles (two equal segments),            Definition of isosceles Δ

Where:

SAS = Side Angle Side

CPCTC = Congruent parts of congruent triangles are congruent.

Answer:

m∠AKL=m∠BML | Base Angle Theorem (Base ∠ TH.)

Step-by-step explanation:

KL=LM | Given

A ∈ KM | Given

B ∈ KM | Given

AK=BM | Given

m∠AKL=m∠BML | Base ∠ TH.

Answer:

A.9x – 13.2

Step-by-step explanation:

2*(3.5x-7+x+0.4)=2*(4.5x-6.6)=9x-13.2

Answer:

It is A

Step-by-step explanation: