Write the point-slope form of the equation of the line through the given point with the given slope. through: (2, 2), slope = 3

Given:

A polynomial equation with rational coefficients has the roots   [tex]5, \sqrt{6}, 3, -\sqrt{7}[/tex].

To find:

The two additional roots.

Solution:

According to the irrational root theorem, if [tex]a+\sqrt{b}[/tex] is a root of a polynomial, then [tex]a-\sqrt{b}[/tex] is also the root of that polynomial.

It is given that, [tex]\sqrt{6}\text{ and }-\sqrt{7}[/tex] are roots of a polynomial.

By using irrational root theorem, [tex]-\sqrt{6}\text{ and }\sqrt{7}[/tex] are also the roots of that polynomial.

Therefore, the two additional roots are [tex]-\sqrt{6}\text{ and }\sqrt{7}[/tex].

Answer:

k/4 + 3 = 14

k = 44

Step-by-step explanation:

Step 1: k + 12 = 56

Step 2: k = 56 - 12

Step 3: k = 44

Answer:

The answer are

t=4

f=4

e=2

k=44

a=-4

n=11

Answer:

hahdg duchy jejeurur y ed sethi. riruru. udhrhru. ueeh

Answer:

Step-by-step explanation:

Perpendicular lines have negative-reciprocal slopes.

The line contains point P(4, 8)

Point slope form:

Given line:

The slope of the perpendicular line is m = -1/4.

The line in point-slope form is:

Answer:

y - 8 = -1/4(x - 4)

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 4x - 7. Its slope is 4. A line perpendicular to this one will have a slope of -1/4, the reciprocal (opposite) of the given equation.

Plug this value (-1/4) into your standard point-slope equation of y - y₁ = m(x - x₁)

y - y₁ = -1/4(x - x₁)

To find x₁ and y₁, we want to plug in a value that we know is on this line: in this case, it is P (4, 8). Plug in the x and y values into the x₁ and y₁ of the standard equation.

y - 8 = -1/4(x - 4)

This equation is perpendicular to your given equation (y = 4x - 7) and contains point P (4, 8)

Hope this helps!

Answer:

(2x+3)(x+1)

Step-by-step explanation:

6x² + 2x + 9x +3

(6x² + 2x) + (9x +3)

2x (x+1) + 3 (x+1)

(2x+3)(x+1)

Answer:

(3x+1) ( 2x+3)

Step-by-step explanation:

6x² + 2x + 9x +3

Make the groups

6x² + 2x     +   9x +3

Factor 2x out of the first group  and 3 out of the second group

2x( 3x+1)   + 3(3 x+1)

Now factor out the common term inside the parentheses

(3x+1) ( 2x+3)

Answer:

360/9=40

Step-by-step explanation:

Answer:

40

all you have to do is divide the first term by the second term

example: 360 divided by 9 = 40

Answer:

x<8/3

Step-by-step explanation:

Your answer is x is less than 8 over 3

Answer:

Answer is d

Step-by-step explanation:

x<8/

Answer:Nonlinear

Step-by-step explanation:

The ratio is 1:8 meaning if you divide the second part by 8 it should get you the first part but 16/8 is 2 not 3 therefore it is not linear

Answer:

P=130

Step-by-step explanation:

Answer:

37.7359

Step-by-step explanation:

first you visualize the shape created

if you visualize it... it will look like a right angled triangle

and we are looking for the longest side

remember the pythagoras theorem c^2= a^2 + b^2

in this case we are looking for c

a^2= 20^2

b^2= 32^2

400+ 1024= 1424

therefore c^2= 1424

then you square root 1424

to get 37.7359

note- the answer is solely based on the information given

Answer:

4 ft = width of walkway

Step-by-step explanation:

It helps if you can draw a figure.

Let x = width of walkway

Length of pool + walkway = (2x + 15)

Width of pool + walkway = (2x + 15)

area of pool and walkway together = (2x + 15)(2x + 15) = [tex]4x^{2} = 60x + 225[/tex]

Area of the pool = 15(15) = 225

Now,

The area of the walkway = area of pool and walkway together - area of pool

304 = 4[tex]x^{2}[/tex] + 60x + 225 - 225

304 = [tex]4x^{2}[/tex] + 60x

4[tex]x^{2}[/tex] + 60x - 304 = 0

4([tex]x^{2}[/tex] +15x - 76) = 0

4(x - 4)(x + 19) = 0

x = 4    x = -19

-19 must be discarded because a length cannot be negative

Therefore x = 4 ft = width of walkway

Answer:

Please mark brainleiest

Step-by-step explanation:

Answer is B

Step-by-step explanation:

B if you divided all the y values by x you will get 0.9

Answer:

UW = 5

Step-by-step explanation:

use the altitude rule and set up a proportion:

4/UW = UW/6.25

cross-multiply:

UW² = 25

UW = [tex]\sqrt{25}[/tex]

UW = 5

Answer:

A) 1/6

B) 1/3

C)1/2

D) 1/6

Answer:

An ordinary die has numbers from 1 to 6

Number of dots on the face = number that face represent

Dots on face can be 1 , 2 , 3 , 4 , 5 , 6

Probaility = 1/6

Probability = 2/6 = 1/3

Probability = 3/6 = 1/2

Probability = 0

A die is rolled. What is the probability that the number appearing on ...

An unbiased die is thrown .what is the probability of getting a ...

Answer:

1 1/3 miles

Step-by-step explanation:

1/3 is for a half-mile, so double it to 2/3 for one mile.

Now double it again for two hours.

2/3 + 2/3 = 1 1/3 miles in two hours

Answer:

The person will walk 1 1/3 miles in 2 hours.

Step-by-step explanation:

There are 4 half-hours in 2 hour

1/3*4=4/3 or 1 1/3 miles

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Factors of 24 and 40

24:  1, 2, 3, 4, 6, 8, 12, 24

40:  1, 2, 4, 5, 8, 10, 20, 40

8 comes as the GCF of both

Multiply out the things in the brackets.

3+7(x+5)=2x+16

3+7x+35=2x+16

Bring the x's over to one side and the numbers to the other side.

7x-2x=16-35-3

5x= -22

Answer: 1/2

Step-by-step explanation:

There are 8 movies in total.

4 of those movies are romance movies.

The probability of picking a romance movie is the proportion of romance movies to the total number of movies.

= Number of romance movies / Number of total movies

= 4 / 8

= 1 / 2

Answer:

1/2

Step-by-step explanation:

Answer:

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

3x - 2x - 2 =-2

x = - 2 +2

x = 0

hope it helps

Answer:

the answer is 56.25

Step-by-step explanation:

.32x=18

×=56.25

Answer:

d/24

Step-by-step explanation:

Answer:

56000 milliliters

1 liter = 1000 milliliters

56(1000)=56000

Step-by-step explanation:

Answer:

1424.81 square meters

Step-by-step explanation:

20.21 m * 70.5m = 1424.805 square meters

So then you round it to the nearest hundredth so then..

1424.81 square meters

Step-by-step explanation:

A of a parallelogram = Base ×height

= 20.21×70.5= 1424.805m

nearest hundreth = 1424.81 m

Answer:

Step-by-step explanation:=(1+sinA)2+cos2A/cosA(1+sinA)

=1+sin2 A+2sin A+cos2 A/cos A(1+sin A)

=1+2sin A+1/cos A(1+sin A)

=2(1+sin A)/cos A(1+ sin A)

=2sec A

Answer:

see explanation

Step-by-step explanation:

Consider the left side

[tex]\frac{1+sinA}{cosA}[/tex] + [tex]\frac{cosA}{1+sinA}[/tex] ← combine into a single fraction

= [tex]\frac{(1+sinA)^2+cos^2A}{cosA(1+sinA)}[/tex] ← expand and simplify numerator

= [tex]\frac{1+2sinA+sin^2A+cos^2A}{cosA(1+sinA)}[/tex] [ sin²A + cos²A = 1 ]

= [tex]\frac{1+2sinA+1}{cosA(1+sinA)}[/tex]

= [tex]\frac{2+2sinA}{cosA(1+sinA)}[/tex] ← factor out 2 on the numerator

= [tex]\frac{2(1+sinA)}{cosA(1+sinA)}[/tex] ← cancel (1 + sinA) on numerator/ denominator

= [tex]\frac{2}{cosA}[/tex]

= 2secA = right side, thus verified

Answer: 0.7515

Step-by-step explanation:

Binomial probability formula:

[tex]P(X=x)=\ ^nC_xp^x(1-p)^{n-x}[/tex] , where

n = total number of trials.

p= probability of success in each trial.

x= Number of successes.

Let x be a binomial variable that represents the number of jurors come to just decision.

p= 0.65

n= 10

Required probability= [tex]P(x>5)=P(x=6)+P(x=7)+P(x=8)+P(x=9)+P(x=10)\\\\ =\ ^{10}C_6(0.65)^6(0.35)^4+ ^{10}C_7(0.65)^7(0.35)^3+ ^{10}C_8(0.65)^8(0.35)^2+ ^{10}C_9(0.65)^9(0.35)^1+^{10}C_{10}(0.65)^{10}(0.35)^0\\\\=0.75149550912\approx0.7515[/tex]

Hence, the probability more than half come to a just decision = 0.7515

Answer: 4 apples will go into each basket if you want all the baskets to be filled with an equal amount.

Step-by-step explanation:

100x=400

dividing through by 100 we get

x=4

Answer:

Transfer of electrons

Form Crystals

High boiling & melting points

Dissolve in water

Good conductor of electricity

Answer:

9x^5

Step-by-step explanation:

the factors of 45:

1, 3, 5, 9, 15, 45

the factors of 36:

1, 2, 3, 4, 6, 9, 12, 18, 36

Greatest common is 9

Answer:

The answer is 3

Step-by-step explanation:

because I said so