When is it helpful to convert from point-slope to slope-intercept form?

Answer:

[tex] \boxed{\sf (8x + y)(2x + 3y)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies {(5x + 2y)}^{2} - {( 3x - y)}^{2} \\ \\ \sf Factor \: the \: difference \: of \: two \: squares. \\ \sf {(5x + 2y)}^{2} - (3x - y)^{2} = ((5x + 2y) + (3x - y)) \\ \sf ((5x + 2y) - (3x - y)) : \\ \sf \implies ((5x + 2y) + (3x - y))((5x + 2y) - (3x - y)) \\ \\ \sf Grouping \: like \: terms, \: 5x + 2y + 3x - y = \\ \sf (5x +3x) + (2y - y) : \\ \sf \implies \boxed{ \sf( (5x +3x) + (2y - y))}((5x + 2y) - (3x - y) \\ \\ \sf 5x + 3x = 8x : \\ \sf \implies (\boxed{ \sf 8x} + (2y - y))((5x + 2y) - (3x - y)) \\ \\ \sf 2y - y = y : \\ \sf \implies (8x + \boxed{ \sf y})((5x + 2y) - (3x - y)) \\ \\ \sf - (3x-y)=y-3x: \\ \sf \implies (8x + y)(5x + 2y + \boxed{ \sf y - 3x}) \\ \\ \sf Grouping \: like \: terms, \: 5x + 2y + y - 3x = \\ \sf (5x - 3x)(2y + y) : \\ \sf \implies (8x + y) + \boxed{ \sf ((5x - 3x)(2y + y))} \\ \\ \sf 5x - 3x = 2x : \\ \sf \implies (8x + y)( \boxed{ \sf 2x} + (2y + y)) \\ \\ \sf 2y + y = 3y : \\ \sf \implies (8x + y)(2x + \boxed{ \sf 3y})[/tex]

Answer:

(8x+y)(2x+3y)

Step-by-step explanation:

see attached

Answer:

Area of ΔDEF = 12 in²

Step-by-step explanation:

Since they are similar, we have to find the scale factor

Scale Factor = [tex]\frac{Side OfDilated Triangle}{Side of Original Triangle}[/tex]

Scale Factor = 4/2

Scale Factor = 2

This means The area of ΔABC is 2 times the area of ΔDEF

So,

ΔABC = 2(ΔDEF)

Where Area of ΔABC = 24 in²

24 = 2(ΔDEF)

Dividing both sides by 2

=> Area of ΔDEF = 12 in²

Answer:

You use the facts about a 30, 60, 90 triangle.

Step-by-step explanation:

The angles in a triangle add up to 180.

90+30+x=180

120+x=180

x=60

This is a 30-60-90 right triangle.

The side opposite the 30 degree angle is a.

The side opposite the 90 degree angle (hypotenuse) is 2a.

The side opposite the 60 degree angle is a[tex]\sqrt{3}[/tex]

We know the side opposite the 90 degree angle.

2a = 12[tex]\sqrt{3}[/tex]

Divide by 2.

a=6[tex]\sqrt{3}[/tex]

a is the side opposite the 30 degree angle (y)

Because we know a, we can find a[tex]\sqrt{3}[/tex].

6[tex]\sqrt{3 } (\sqrt{3})[/tex]

The square roots cancel, leaving 3.

6 times 3 is 18.

Therefore, the side opposite the 60 degree angle (x) is 18.

Answer: Graph C

Step-by-step explanation:

The correct graph is C.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given : On a piece of paper, graph y - 3 > 2x + 2.

To find : determine which answer choice matches the graph you drew,

y - 3 > 2x +  2

y > 2x + 5

x = 0

y > 5

x = - 3

y > - 1

at x = 0,  y = 5

0 < 5

origin does not lie in the shaded region,

as y > 2x + 5

line y = 2 x+ 5 is not part of solution (dotted line)

Hence Graph C is correct

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Answer:

C

Step-by-step explanation:

Factor: -7x^2 -5x+18

Factor -1 out of 7x^2 -5x +18:

−(7x^2+5x−18)

Factor.

1. 18 is negative, so a negative number multiplied by a postive number.

2. You can't factor 7, so 7x times x.

(7x−9)(x+2)

Answer: the correct answer is C

Step-by-step explanation:

Answer:

Dependent = cost

independent = number of DVDs

Discrete

Function :f(x) = 16 x  = 16 (6)

Solution = $96

Step-by-step explanation:

Hi, to answer this question we have to write a function:

The cost (f(x)) must be equal to the price per DVD (16) multiplied by the number of DVDs (x)

Function: f(x) = 16 x  

Dependent = f (x) =(cost)

Independent = x (number of DVDs)

Solution for x=6

f(6) = 16 (6)

Cost = $96

Since the number of DVDs can't be fractional it's a Discrete function.

Answer:

u have insta

Step-by-step explanation:

Answer: y=-4/3x-(34/3)

Step-by-step explanation:

Since we want to find the equation of a parallel line, we know the slope is going to stay the same. If the slope is changed, the lines will intersect at one point. All we need to do is to find the y-intercept. We can do that by using the point provided.

[tex]2=-\frac{4}{3} (-10)+b[/tex]

[tex]2=\frac{40}{3} +b[/tex]

[tex]b=-\frac{34}{3}[/tex]

Now that we know the y-intercept, we can complete the equation.

y=-4/3x-(34/3)

Answer:

Given:

Number of yards of red fabric purchased by Jane = 50

Number of yards of gold fabric purchased by Jane = 110

We need to find the largest number of curtains she can make if she wants all the curtains to be exactly the same length.

For this we will find H.C.F. of 50 and 110.

Factors of 50 = 1, 2, 5, 10, 25, 50.

Factors of 110 = 1, 2, 5, 10, 11, 22, 55, 110.

So, Highest common factor of 50 and 110 is 10.

So, there are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.

Number of yards of red fabric is given by:

50/10=5

Number of yards of gold fabric is given by

110/10=11

Hence, there are 5 red fabrics and 11 gold fabrics that would be used for each curtain.

Answer:

x = 1

Step-by-step explanation:

This is a 30-60-90 triangle, which means that if the long leg is the square root of 3, the hypotenuse is 1.

Answer:

X=1

Step-by-step explanation:

Answer:

1

Step-by-step Explanation

Step-by-step Explanation

[tex] \huge{ \red{ \csc \: \frac{\pi}{2}} = \purple{ 1}} \\ [/tex]

Answer:

733.04

Step-by-step explanation:

Cylinder:

V=3.14x5x5x7

=549.78

Cone:

V=3.14x5x5x7/3

=183.26

TOTAL:

549.78+183.26=733.04

Answer:

Step-by-step explanation:

"Four times a number" in symbols is "4n."

Answer:

Minimum 5 socks needs to be selected.

Step-by-step explanation:

Given that there are four different colors of socks.

So, if you pick 4 socks , in worst case it will be all four of different color.

now if you pick 5th socks it will be either of those four colors.

Hence, minimum 5 socks must be taken to ensure that  a pair of matching-color socks is selected.

______________________________________________

To elaborate it more,

let four colors be red, yellow, blue , green

if you pick 5 socks, then in worst case four will be all of different color

red, yellow, blue , green but fifth will be

Hence. minimum 5 socks needs to be selected.

_______________________________________

In general, if you have n objects of different colors then you need to take minimum n+1 number of object to have at least two object of same color.

Answer:

Option B.

Step-by-step explanation:

The given triangle is a right angle triangle.

In a right angle triangle,

[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]

In the given triangle,

[tex]\tan (45^{\circ})=\dfrac{v}{7}[/tex]

[tex]1=\dfrac{v}{7}[/tex]

[tex]7=v[/tex]

Using Pythagoras theorem, we get

[tex]hypotenuse^2=Perpendicular^2+Base^2[/tex]

[tex]u^2=v^2+7^2[/tex]

[tex]u^2=7^2+7^2[/tex]

[tex]u^2=2(7^2)[/tex]

Taking square root on both sides, we get

[tex]u=\sqrt{2(7^2)}[/tex]

[tex]u=7\sqrt{2}[/tex]

Therefore, the correct option is B.

Answer:

x = 6.5

Step-by-step explanation:

Since all angles in a triangle adds up to 180°, we have:

10x - 10 + 10x + 8 + 8x = 180

28x - 2 = 180

28x = 182

x = 182/28 or 6.5

Answer:

6.5

Step-by-step explanation:

Sum of three angles of triangle = 180

10x - 10 + 8x + 10x + 8 = 180

28x - 2 = 180

28x = 180 + 2

28x = 182

x = 182/28

x = 6.5

Answer:

[tex] 12^{11} [/tex]

Step-by-step explanation:

Count the number of factors of 12. The number is 11. There are 11 factors of 12, so the base is 12, and the exponent is 11.

Answer: [tex] 12^{11} [/tex]

Answer:

12¹¹

Step-by-step explanation:

12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12

12 is being multiplied by itself 11 times.

= 12¹¹

= 743008370688

Answer:

250

Step-by-step explanation:

245 / 0.98 = 250

Start by making a table for ordered pairs.

X in the left column and y in the right column.

Now find the change in y and change in x.

This 1/5.

So our slope is 1/5.

Image is below.

Answer:

1/5  (Answer D)

Step-by-step explanation:

Going right from (-1, 2) to (4, 3), we see x increasing by 5; this is the "run;"

we also see y increasing by 1; this is the "rise."

Thus, the slope of this line is m = rise / run = 1/5  (Answer D)

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the SURFACE AREAS AND VOLUMES.

Since the given section is a Sector of a Circle with length as, 8πcm .

Thus then it's folded veltically at an axis to make a cone.

since we know that, The Curved surface area of a cone is given as formula,

C.S.A = πrl

where, r = radius and l = slant height.

also 2πr = circumference of a circle,

we get as, radius = 4 cm.

Answer:

r = 4 cm

Step-by-step explanation:

AB is actually the circumference of the circle

So,

Circumference = 8π cm

Whereas,

Circumference = 2πr

8π = 2πr

Dividing both sides by 2π

=> r = 4 cm

→Answer:

8T - 7lb - 6oz

→Step-by-step explanation:

So 17T 13lb 3oz - 9T 20lb 9oz

This information is asking us to simplify the expression.

To do that we need to combine like terms meaning If t and t are alike variables they go together.

And in this expression we have 3 pairs of alike variables which are T, lb, and oz.

So we need to subtract all the like terms.

_____________

17T - 9T is 8T

13lb - 20lb is -7lb

3oz - 9 oz is -6oz

______________

So,

The expression now shows 8T - 7lb - 6oz.

___________________I do hope this helps!________________

_____________Brainliest is always appreciated!_____________

Answer:

The length of the side PC is 34 cm.

Step-by-step explanation:

We are given that BP is the perpendicular bisector of AC. QC is the perpendicular bisector of BD. AB = BC = CD.

Suppose BP = 16 cm and AD = 90 cm.

As, it is given that AD = 90 cm and the three sides AB = BC = CD.

From the figure it is clear that AD = AB + BC + CD

So, AB = [tex]\frac{90}{3}[/tex] = 30 cm

BC = [tex]\frac{90}{3}[/tex] = 30 cm

CD = [tex]\frac{90}{3}[/tex] = 30 cm

Since the triangle, BPC is a right-angled triangle as [tex]\angle[/tex]PBC = 90°, so we can use Pythagoras theorem in this triangle to find the length of the side PC.

Now, the Pythagoras theorem states that;

[tex]\text{Hypotenuse}^{2} = \text{Perpendicular}^{2} +\text{Base}^{2}[/tex]

[tex]\text{PC}^{2} = \text{BP}^{2} +\text{BC}^{2}[/tex]

[tex]\text{PC}^{2} = \text{16}^{2} +\text{30}^{2}[/tex]

[tex]\text{PC}^{2} = 256+900[/tex] = 1156

[tex]\text{PC}=\sqrt{1156}[/tex]

PC = 34 cm

Hence, the length of the side PC is 34 cm.

Answer:

Domain: (-∞, -7) ∪ (-7, ∞)

Step-by-step explanation:

There is a vertical asymptote at x = -7, so the answer would be all real numbers except for when x= -7

Answer: 8568 pounds

poopity scoopity:)))

There are total 8568 pounds in 4 tons and 568 pounds.

A unit conversion expresses the same property as a different unit of measurement.

For example, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

Given that, there are how many pounds in 4 tons plus 568 pounds in total,

So, for the same we will use the concept of unit conversion,

Here, we will convert the unit of 4 tons into pounds then add the extra pounds given to get the total pounds,

Since, we know that, 1 ton = 2000 pounds

So, 4 tons = 4 x 2000 = 8000 pounds

Therefore,

4 tons plus 568 pounds

= 8000 pounds + 568 pounds = 8568 pounds

Hence, there are 8568 pounds in 4 tons plus 568 pounds

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Answer:

D is the correct answer

Step-by-step explanation:

according to the graph you can see that D should be correct.

Good luck! ^_^

Answer:

Step-by-step explanation:

Given data

θ= 10°

Horizontal length is equivalent to the adjacent= 20 m

the height of the ramp is equivalent to the opposite=?

Applying SOH CAH TOA we have

using TOA

Tan θ= opp/adj

Tan 10= opp/20

opp= Tan(10)* 20

opp= 0.64836*20

opp= 12.96

Approximately the maximum height of the ramp is 12 m

Answer:

8

Step-by-step explanation:

8 is greater than 7

Answer:

n = √2/8

Step-by-step explanation:

1/4 × √ 2 = 2n

√2/4 = 2n

√2 = 4×2n

8n = √2

n = √2/8

The value of n in

[tex] \frac{1}{4} \times \sqrt{2} = 2n[/tex]

is n = √2 / 8

The given equation is:

[tex] \frac{1}{4} \times \sqrt{2} = 2n[/tex]

Multiply through by 4

[tex] \sqrt{2} = 4(2n)[/tex]

This can be further simplified as

[tex] \sqrt{2} = 8n[/tex]

[tex] \frac{ \sqrt{2} }{8} = \frac{8n}{8} [/tex]

The like terms cancel out

[tex]n = \frac{ \sqrt{2} }{8} [/tex]

Therefore, the value of n in

[tex] \frac{1}{4} \times \sqrt{2} = 2n[/tex]

is

[tex]n = \frac{ \sqrt{2} }{8} [/tex]

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Answer:

14.86 knots.

Step-by-step explanation:

Given that:

The boats leave the port at noon.

Speed of boat 1 = 12 knots due east

Speed of boat 2 = 8 knots due south

At 2 pm:

Distance traveled by boat 1 = 24 units due east

Distance traveled by boat 2 = 16 units due south

Now, speed of boat 1 changes to 9 knots:

At 3 pm:

Distance traveled by boat 1 = 24 + 9= 33 units due east

Distance traveled by boat 2 = 16+8 = 24 units due south

Now, speed of boat 1 changes to 8+7 = 15 knots

At 5 pm:

Distance traveled by boat 1 = 33 + 2[tex]\times[/tex] 9= 51 units due east

Distance traveled by boat 2 = 24 + 2 [tex]\times[/tex] 15 = 54 units due south

Now, the situation of distance traveled can be seen by the attached right angled [tex]\triangle AOB[/tex].

O is the port and A is the location of boat 1

B is the location of boat 2.

Using pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^{2} = 51^{2} + 54^{2}\\\Rightarrow AB^{2} = 2601+ 2916 = 5517\\\Rightarrow AB = 74.28\ units[/tex]

so, the total distance between the two boats is 74.28 units.

Change in distance per hour = [tex]\dfrac{Total\ distance}{Total\ time}[/tex]

[tex]\Rightarrow \dfrac{74.28}{5} = 14.86\ knots[/tex]

Answer:

Step-by-step explanation:

3/25 = 12%

3/25=0.12

Answer:

12%

.12

Step-by-step explanation:

3/25 * 4/4 = 12/100

Percent means out of 100

12%

12/100

Since it is out of 100, we can move the decimal 2 places to the left

.12