Phoebe took a survey of her classmates' favorite sport. The results are in the table below:

Step-by-step explanation:

From the question given above, the following data were obtained:

f(x) = x³ – 6x² – 11x + k

Factor => x + 2

Next, we shall obtained the value of x from x + 2. This can be obtained as follow:

x + 2 = 0

Collect like terms

x = 0 – 2

Finally, we shall determine the the value of k. This can be obtained as  illustrated below:

f(x) = x³ – 6x² – 11x + k

x = –2

f(–2) = 0 since x + 2 is a factor

x³ – 6x² – 11x + k = 0

(–2)³ – (–2)² – 11(–2) + k = 0

–8 – (4) + 22 + K = 0

–8 – 4 + 22 + K = 0

10 + k = 0

Collect like terms

k = 0 – 10

Therefore, the value of k is –10

Learn more: https://brainly.com/question/13587979

Answer:

yes both chances are 1/2 = equal

Step-by-step explanation:

Answer:

See explanation

Question has been corrected

Step-by-step explanation:

Given:

3x² + 11x + 30

To factorise, multiply the coefficient of x² by 30

= 3 * 30

= 90

Find two numbers that have a product of 90 and a sum of 11

** There are no such two numbers, therefore the question can't be solved using factorization

Correcting the error in the question:

x² + 11x + 30

To factorise, multiply the coefficient of x² by 30

= 1 * 30

= 30

Find two numbers that have a product of 30 and a sum of 11

6 and 5

6 + 5 = 11

6 * 5 = 30

x² + 11x + 30

= x² + 6x + 5x + 30

= x(x + 6) + 5(x + 6)

= (x + 6) (x + 5)

Answer:

The domain of the function is (-2,&)

Answer:

379

Step-by-step explanation:

4(-9)²+73-18

4(81)+55

324+55

379

Answer:

Exact Form:

235235

Decimal Form:

4.64.6

Mixed Number Form:

4 3/5

Answer:

5649

Step-by-step explanation:

4^3=64

64^5=5649

Step-by-step explanation:

An=-6+(20-1)×2

=-6+19(2)

=-6+38

=32

Answer:

y = 5x-11

Step-by-step explanation:

The slope intercept form of a line is y =mx+b where m is the slope

y = -1/5 x-3

The slope is -1/5

Lines that are perpendicular have negative reciprocal slopes

-1 /(-1/5)

-1 * -5/1

5

The slope of the line that is perpendicular is 5

y=5x+b

Using the point (4,9)

9 = 5(4)+b

9 = 20+b

9-20 =b

-11

y = 5x-11

Answer:

The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is approximately 125.66 square units

Step-by-step explanation:

The given parameters are;

The radius of the circle with center G, r = 15

The measure of the given angle, m∠AGB = 64°

The area of a sector is given as follows;

Area of a sector of a circle = (θ/360°) × π × r²

Therefore;

The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is given as follows;

The area of the sector in circle G  = (64°/360°) × π × 15² ≈ 125.66 square units

Answer:

A number s plus 21

Step-by-step explanation:

s+21

A number s plus 21

It is hard to find out question cn u pls take a pic and upload so it will more easier to find out the question

Answer:

a) yes

b) y = -x

c) yes it goes thru the origin (0,0)

Step-by-step explanation:

a) x**2 + y**2 = 17

(-4)**2 + (-1)**2 = 17

16 + 1 = 17 YES

b) the slope of DE is

(y1 - y2)/(x1 - x2)

(-1 -4)/(-4 -1) = -5/-5 = 1,  so a perpendicular segment will have a

slope of - 1/current slope or -1.

The midpoint of DE is

x = (x1 + x2)/2 = (-4 +1)/2 = -3/2

y = (y1 + y2)/2 = (-1 +4)/2 = 3/2 so

y = mx + b

y = -x + b plug in the point (-3/2,3/2)

3/2 = -(-3/2) + b

b = 0 SO y = -x

c) The circle equation dictates that it has no offset so centers around the origin (0,0) and the equation of the bisector y = -x indeed fits (0,0).

Answer:

we can use simple equation

Answer:

-15abc - 12ac + 15bc

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

(-5abc - 6ac + 7cb) - (10abc + 6ac - 8bc)

Step 2: Simplify

1. Consider the pyramid ABCDE in the figure 1 attached:

Each side of the square base equals  (units)

Area of 1 lateral side of pyramid ABCDE is

so the total lateral area is  (units squared)

and the total surface area is  (units squared)

2. Now consider the second figure KLMNP, Sydney's pyramid:

The lateral area is

so the total area of the second pyramid is

So 2 things can be said about the areas:

i) the lateral area of Sydney's pyramid is times larger than the lateral area of the original pyramid.

ii) The total area of Sydney's pyramid is units squared larger than the total area of the original pyramid.

Answer: See explanation

Step-by-step explanation:

The equivalent fraction of 45% is solved as follows:

First, we'll change the percentage to fraction which will be:

45% = 45/100

Then, we'll reduce to lowest term which will be:

45/100 = 9/20

Now, we'll convert the fraction to decimal which will be:

9/20 = 0.45

The mistake that Jenny made was that she divided 90 by 20. This will give 4.5.

Answer: The decimal equivalent is not correct. The decimal point is in the wrong position. The decimal point should be to the left of the 4, so the correct answer is 0.45.y-step explanation:

Answer:

120 kg in morning and 240 kg in afternoon

Step-by-step explanation:

x+2x=360 kg

Work:

x + 2x = 360 kg

3x = 360 kg

3x/3 = 360 kg/3

x = 120

2x=2(120 kg) =240 kg

Final Answer:

So, 120 kg in morning and 240 kg in the afternoon.

Hope this helps!

Answer:

x = 29

Step-by-step explanation:

ΔABC ≅ ΔDEC,

So, ∠BAC  ≅∠CDE    {Corresponding parts of congruent triangles}

∠BAC = 74°

InΔABC,

∠ABC + ∠BAC + ∠BCA = 180

2x + 74 + 48 = 180

2x + 122 = 180  

Subtract 122 from both sides

2x = 180 - 122

2x = 58

Divide both sides by 2

x = 58/2

x = 29

Answer:

The answer is below

Step-by-step explanation:

If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel.

If two angles are supplementary to the same angle, then the two angles are congruent.

Statement                                         Reason

1) line p is parallel to line q               Given

2) angle 1 and angle 4 are               Given

supplementary i.e. ∠1 + ∠4

= 180° (definition of supplementary)

3) angle 3 and angle 4 are              consecutive interior angles

supplementary

4) angle 1 congruent to angle 3       congruent supplements theorem

supplementary

5) line r parallel to line s                  corresponding angle converse

f-¹(x)=[tex]\frac{2-7x}{x+2}[/tex]

Answer:

Solution given:

f(x)=[tex]\frac{-2x+2}{x+7}[/tex]

Let f(x)=y

y=[tex]\frac{-2x+2}{x+7}[/tex]

Interchanging role of x and y

x=[tex]\frac{-2y+2}{y+7}[/tex]

doing crisscrossed multiplication

x(y+7)=-2y+2

now solve it:

xy+7x=-2y+2

keep like terms in one side

xy+2y=2-7x

take common

y(x+2)=2-7x

make a value of y

y=[tex]\frac{2-7x}{x+2}[/tex]

So,

f-¹(x)=[tex]\frac{2-7x}{x+2}[/tex]

Answer:

ƒ^-1 (x) = [tex]\frac{2-7x}{2+x}[/tex]

Step-by-step explanation:

Substitute y for f (x)

[tex]y = \frac{-2x+2}{x+7}[/tex]

Interchange x and y

[tex]x=\frac{-2y+2}{y+7}[/tex]

Swap the sides of the equation

[tex]\frac{-2y+2}{y+7} = x[/tex]

Multiply both sides of the equation by y + 7

-2y + 2 = (y + 7)x

Distribute x through the parentheses

-2y + 2 = xy + 7x

Move the expression/constant to the left-hand side and change its sign

-2y - xy + 7x - 2

Factor out  from the expression

(-2 - x)y = 7x - 2

Divide both sides of the equation by -2 - x

[tex]y = \frac{7x-2}{-2-x}[/tex]

Simplify the expression

[tex]y = \frac{2-7x}{2+x}[/tex]

Substitute ƒ ^-1 (x) for y

[tex]f^{-1} (x) = \frac{2-7x}{2+x}[/tex]

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

Explanation:

Focus on triangle TUS. The inner angles here are:

Note how the angle measure for S is the supplement of 2x, which is adjacent to the angle S we have.

Add up those three angles and set the sum equal to 180

T+U+S = 180

y+x+180-2x = 180

y-x = 180-180

y-x = 0

y = x

We'll use this later.

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

The diagram shows that angle VTU = y+y = 2y.

Focus your attention on triangle TUV.

Since TU = UV, this means the base angles T and V (which are opposite the congruent sides) are congruent angles. We found that angle T was 2y earlier. This means angle V is also 2y.

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

Now shift your focus to triangle TSV.

This triangle has the inner angles

Recall earlier that we found y = x at the conclusion of the first section. Using that and the fact that the angles of triangle TSV add to 180, we get...

T+S+V = 180

2x+y+2y = 180

2x+3y = 180

2x+3x = 180 .... replace y with x, since y = x

5x = 180

x = 180/5

x = 36

This is the value of y as well.

Answer: 504 ways

Step-by-step explanation:

Given

There are nine different marbles in a bag

For the first time, there are 9 possible ways to draw a marble

After removal of first marble, there are 8 possible ways to draw a marble

for the third time, there are 7 possible ways

so, total ways to draw three marble are

[tex]\Rightarrow 9\times 8\times 7=504\ \text{ways}[/tex]

Answer:

‼️A) 12‼️

Step-by-step explanation:

Key skills needed: Interior Angle Measure Theorem, Equation Creation

Step 1) First, we need to classify this shape. It has 7 sides, which means that we can use the Interior angle Theorem to find out the sum of all the interior angle measures

The theorem is:    S = (n - 2)180S=(n−2)180

S is the sum of all interior angle measures

n is the number of sides of the polygon

Step 2) With this, we can plug in 7 for "n" (Since the figure has 7 sides) and get:

---> S = (7-2)180S=(7−2)180

---> (7-2) is 5 since 7 - 2 = 5 so --> S = 5(180)S=5(180)

---> 5(180) is the same as 5 x 180 which is 900 so --> S = 900S=900

This means that the sum of all interior angles is 900 degrees.

Step 3) Now, we have to find out the sum of all the angles that they gave us so:

---> 10x + 10x + 9 + 133 + 9x + 14 + 12x - 9 + 10x + 5 + 136 = 90010x+10x+9+133+9x+14+12x−9+10x+5+136=900

The left side is the sum of all interior angles in the shape, and the right side is what the sum should be when expressed as a number.

Step 4) We have to combine all like terms on the left side:

---> 10x + 10x + 9x + 12x + 10x = 51x10x+10x+9x+12x+10x=51x

---> 9 + 133 + 14 -9+5+136 = 2889+133+14−9+5+136=288    

Step 5) This means that ---> 51x + 288 = 90051x+288=900

Subtract 288 from both sides  and get:

---> 51x = 61251x=612    (900-288 = 612)

Then divide by 51 from both sides and get:

---> x = 12x=12     (612 ÷ 51 = 12)

Therefore A) 12 is your answer.

I think it should be none of these.

The term on the left has to be even no matter what value of x and the right has to be odd no matter what value of x. Therefore, there shouldn't be an integer value of x that satisfies the equation, let alone the answer choices A-D.

Answer:

infjfkflflfmdbfufifldndndhfififkfnf

Answer:

good evening good evening good evening good evening

9514 1404 393

Answer:

  invalid

Step-by-step explanation:

There is more than one set of dimensions that will give a triangle with an area of 6. The fact that the area is 6 implies nothing about the dimensions (except that their product is 12).

The converse is invalid.

Answer:

The first sentence is valid but the second one is invalid.

Step-by-step explanation:

You can't say just because the area of the triangle is 6, its base is 3 and its height is 4, it might have a base of 1 and a hight of 12 so there are more than one answers for the second one.

Feel free to message me if you still have questions :)

Answer:

Solution given:

Relationship between base and hypotenuse is given by Cos angle

Cos Angle(?)=base/hypotenuse

Angle{?}=Cos-¹(40/58)

Angle{?}=46°

The indicated angle is 46°