please include graph if you can thanks!

The equation of the line that passes through the points (6,0) and (2,-7) is '7x - 4y = 42' when transformed into the standard form.

In mathematics, especially in linear algebra, the standard form of the line is a way of describing a specific line on the plane. We can get this by using two points through which the line passes. In this case, we have the points (6,0) and (2,-7).

First, we calculate the slope using the formula (y2 - y1) / (x2 - x1). Substituting our values, we have (-7 - 0) / (2 - 6) = -7 / -4 = 7/4. So, the slope is 7/4.

Next, we find the y-intercept (b) by substituting one of the points into the equation y = mx + b. Using the point (6,0), we get 0 = 7/4 * 6 + b. Solving for b, we find that b = -21/2.

The equation is then y = 7/4x - 21/2. To convert this to the standard form, we multiply all parts by 4 to remove the fraction. The equation then becomes 4y = 7x - 42. After arranging, we obtain our final equation: 7x - 4y = 42.

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[tex]\bf 2\sqrt{54}+5\sqrt{24}\qquad \begin{cases} 54=2\cdot 3\cdot 3\cdot 3\\ \qquad 2\cdot 3\cdot 3^2\\ \qquad 6\cdot 3^2\\ 24=2\cdot 2\cdot 2\cdot 3\\ \qquad 2^2\cdot 6 \end{cases}\implies 2\sqrt{6\cdot 3^2}+5\sqrt{2^2\cdot 6} \\\\\\ 6\sqrt{6}+10\sqrt{6}\implies \stackrel{\textit{adding like-terms}}{16\sqrt{6}}[/tex]

The simplest radical form of the equation [tex]2\sqrt{54} + 5\sqrt{24}[/tex] is [tex]16 \sqrt{6}[/tex].

We have to determine, the simplest radical form [tex]2\sqrt{54} + 5\sqrt{24}[/tex].

To convert the given equation into radical form following all the steps given below.

Equation; [tex]2\sqrt{54} + 5\sqrt{24}[/tex].

                   [tex]= 2\sqrt{54} + 5\sqrt{24}\\\\=2 \sqrt{2 \times 3 \times 3 \times 3} + 5\sqrt{2 \times 2 \times 2\times 3}[/tex]

        [tex]=2 \sqrt{2 \times 3 \times 3 \times 3} + 5\sqrt{2 \times 2 \times 2\times 3}\\\\= 2 \sqrt{2 \times 3 \times 3^2} + \sqrt{2^2\times 2 \times 3} \\\\[/tex]

                   [tex]= 2\times 3\ \sqrt{2 \times 3 } + 5 \times 2 \sqrt{2 \times 3}\\\\= 6 \sqrt{6} \ + 10 \ \sqrt{6}\\\\= 16\sqrt{6}[/tex]

Hence, The required simplest radical form of the equation [tex]2\sqrt{54} + 5\sqrt{24}[/tex] is [tex]16 \sqrt{6}[/tex]

To know more about the Radical form click the link given below.

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I think it is 1.6m but I'm not sure

Answer:

A. 4.26 in^2

Step-by-step explanation:

Step 1: Find the area of the sector DBC. Here we have to use the formula.

Area of a sector = Central Angle/360 *π[tex]r^{2}[/tex]

The area of the sector DBC = (54/360)*3.14*[tex]8^{2}[/tex]

= 30.16

Step 2: Area of segment CFD = Area of the sector DBC - Area of the ΔCBD

= 30.17 - 25.9

Area of segment CFD = 4.27in^2

Answer:

4.24 in ^2

Step-by-step explanation:

extra added: Use 3.14 for the value of π. Round your answer to the nearest hundredths if necessary.

1) 15/5 = 3 .  

2) 27/3= 9

3)48/8 = 6

4) 84/7=  12

5)32/4= 8

6) 90/9 =10

7) 30/5= 6

8) 22/2 = 11

9) 60/12= 5

10) 21/3= 7

11) 44/11= 4

12) 54/6 = 9

13) 132/12 = 11

14) 70/ 10= 7

15) 99/9 = 11

HOPE THIS HELPS XD

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All you have to do is add 31300000+23200000 which equals 54500000. Next subtract  54500000 from 193800000 which equals 139300000. So plant 2 is 139.3 million miles away from the sun

Let Planet 2 = X

Planet 1 = X + 31.3

Planet 3 = x +(31.3+23.2) = x + 54.5

Add the 3 distances together:

x + x +31.3 + x + 54.5 = 193.8

3x + 85.8 = 193.8

Subtract 85.8 from each side:

3x = 108

Divide both sides by 3:

x = 108 / 3

X = 36

Planet 2 = 36 million miles

Planet 1 = 36 + 31.3 = 67.3 million miles

Planet 3 = 36 + 54.5 = 90.5 million miles

36 + 67.3 + 90.5 = 193.8

Answer:

p^2 + 3p - 10

Step-by-step explanation:

Use the so-called "foil" method of multiplication of binomials:

p^2 -2p + 5p - 10, or p^2 + 3p - 10

Given:-

... ( p+5 )( p-2 )

When we have an equation like,

( a + b ) ( a - c )

... a² + ba - bc - ac

We have,

( p+5 )( p-2 )

... p² - 2p + 5p - 10

... p² + 3p - 10 Is the answer.

Hope it helps!

The x- intercept would be (3,0) or 3

The y-intercept would be (0,-4) or -4

Answer:

[tex]\huge\boxed{\{x|x\in\mathbb{R},\ x<-2\}}[/tex]

Step-by-step explanation:

[tex]5>x+7\qquad|\text{subtract 7 from both sides}\\\\5-7>x+7-7\\\\-2>x\to x<-2}[/tex]

0.98  0.0 = tenths 0.00 = hundredths 0.000 = thousandths

Final answer:

Alice hit 10 home runs and Peter hit 8 home runs that season. The width of the parallelogram is 16 meters and the length is 20 meters.

Explanation:

To solve this problem, we need to set up an equation. Let's say that Alice hit x home runs. Then, Peter hit twice the difference of home runs Alice hit and 6, or 2(x - 6). Together, they hit 18 home runs. Setting up the equation, we have x + 2(x - 6) = 18. Solving for x, we get 3x - 12 = 18, 3x = 30, and x = 10. So, Alice hit 10 home runs and Peter hit 2(10 - 6) = 8 home runs that season.

To find the length and width of a parallelogram, we need to use the information given in the problem. Let's say the width of the parallelogram is W. The length of the parallelogram is then 4 meters more than the width, or W + 4. The perimeter of a parallelogram is given by the formula 2(length + width), so we have 2(W + W + 4) = 72. Simplifying the equation, we get 4W + 8 = 72. Subtracting 8 from both sides, we get 4W = 64. Finally, dividing both sides by 4, we find that the width of the parallelogram is 16 meters and the length is 16 + 4 = 20 meters.

y + 4 = - 56(x - 8)

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 56 and (a, b) = (8, - 4)

y  + 4 = - 56( x - 8 ) ← in point-slope form

Hello!

[tex]7d + 12 -4d -3\\[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓

First this problem it should be the group like terms.

[tex]7d-4d+12-3[/tex]

Then you add similar elements.

[tex]7d-4d=3d[/tex]

[tex]3d+12-3[/tex]

You can also add or subtract by the numbers.

[tex]12-3=9[/tex]

[tex]=3d+9[/tex]

Answer⇒⇒⇒3d+9

Hope this helps!

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Have a great day!

-Charlie

we can solve this by first combining like terms: our like terms in this equation are d and plain numbers

so, this means that we can combine the d's with the d's and the plain numbers with the plain numbers

so,

7d + 12 - 4d - 3 = 0

3d+ 9 = 0

next, we have to get our plain numbers on one side of the equal sign, and our numbers with the d's on the other side of the equal sign: we do this by doing the opposite of what the number is doing on the side it is on, since the 9 is being subtracted from the left hand side, we will subtract it from both sides:

3d = -9

next, we want to get rid of the 3 next to the d

to do this, we would divide the 3 on both sides since it is being multiplied to the d on the left hand side:

d = -3

this is our final answer: d = -3

Matthew charges $25 for each haircut, and earned $325

Divide 325 with 25

325/25 = 13

13 haircuts were given.

hope this helps

13 because 325/25 = 13

An expression equal to 3/4 - 1/2 would be 6/8 - 2/4.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

The expression is given as

[tex]\dfrac{3}{4}-\dfrac{ 1}{2} = \dfrac{-1}{4}[/tex]

Also,

[tex]\dfrac{-1}{4}-\dfrac{ 1}{2} = \dfrac{3}{4}[/tex]

Any equation that equals 1/4 will work in this situation.

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The given angles are known as alternate interior angles.

For line L and M to be parallel, the two given angles must be the same.

Set them to equal each other and solve for X.

7x - 7 = 4x +14

Add 7 to each side:

7x = 4x +21

Subtract 4x from each side"

3x = 21

Divide both sides by 3:

X = 21 / 3

X = 7

Answer:

7

Step-by-step explanation:

i need points

3^3 = 27

4^3 = 64

5^3 = 125

The largest cube has volume 64 cubic units, and the sides are 4 units long.

The largest cube Elena can build is of side [tex]5\;units[/tex] having a volume of [tex]64\;unit^3[/tex].

The volume of a cube is equals to the length of the side raised to the power of 3. Mathematically, [tex]V=(side)^3[/tex].

According to the question, Elena has 80 unit cubes.

So,

For [tex]side=1\;unit;\;Volume=1\;unit^3[/tex]

For [tex]side=2\;unit;\;Volume=8\;unit^3[/tex]

For [tex]side=3\;unit;\;Volume=27\;unit^3[/tex]

For [tex]side=4\;unit;\;Volume=64\;unit^3[/tex]

For [tex]side=5\;unit;\;Volume=125\;unit^3[/tex]

Hence, the largest cube Elena can build is of side [tex]5\;units[/tex] having a volume of [tex]64\;unit^3[/tex].

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If 98 - 32 = 66,

then x = 66°

ANSWER

The correct answer is A

EXPLANATION

We divide the hallway into 2 rectangles as shown in the diagram attached.

The length of the longer is 25 and the with is 5 feet.

The area of this rectangle

[tex]=25\times 5[/tex]

[tex]=75[/tex] square feet

The smaller rectangle has length 6 feet and width 12 feet

The area of the smaller rectangle

[tex]=6\times 12[/tex]

[tex]=72[/tex] square feet

Adding the two areas gives the area of the hallway

[tex]=125+72=197[/tex] square feet

Answer:

x = -[tex]\frac{17n+r}{n-34}[/tex]

Step-by-step explanation:

We have to solve the equation for the value of x.

n(17 + x) = 34x - r

17n + nx = 34x - r [By Distributive property ]

17n + nx - 17n = 34x - r - 17n [subtracting 17n from both the sides of the equation]

nx = 34x - r - 17n

nx - 34x = 34x - r - 17n - 34x [Subtracting 34x from both the sides of the equation]

x(n - 34) = -(r + 17n) [Division by (n - 34) on both the sides of the equation]  

x = -[tex](\frac{17n+r}{n-34})[/tex]

This is the solution for x in terms of constants n and r is x =  17n + r/34 - n

Solving for x in the equation n(17 + x) = 34x − r

To solve for x, we begin by isolating x on one side of the equation. Given the equation:

n(17 + x) = 34x - r

First, distribute n on the left-hand side:

17n + nx = 34x - r

Next, rearrange the equation to place all terms involving x on one side:

17n + r = 34x - nx

Factor out x on the right side:

17n + r = x(34 - n)

Solve for x by dividing both sides by (34 - n):

x =  17n + r/34 - n

This is the solution for x in terms of constants n and r.

The answer is; 24/75 of the entire cake remained

If 2/5 of the initial cake was eaten, the 3/5 is what remained

MInu ate 1/3 of the 3/5 = 3/15

3/5 – 3/15 = 6/15 remained

Her brother ate; 1/5 of 6/15 = 6/75

6/15 – 6/75 = 24/75 remained

Open that attachment and that should be the answer.

Answer:

1.178 x 10^35 Joule

Step-by-step explanation:

Energy produced by sun in one second = 3.8 x 10^27 J

Energy produced by sun in a year = Energy produced by sun in one second x number of seconds in one year

According to the question, the number of seconds in one year

                                                       = 31,000,000 seconds

Energy produced by the sun in one year = 3.8 x 10^27 x 31,000,000

                                                                    = 1.178 x 10^35 Joule

Thus, the energy produced by the sun in a year is 1.178 x 10^35 Joule.

90/18 equals 5 minutes for each window,so after 3 hours they would paint 36 windows.            180 minutes in three  hours so 180/5=36

To convert the ratio 2.5 metres to 60 centimeters to the form 1:n we first change metres to centimeters, which gives 250 cm to 60 cm, then divide 250 by 60 to get n = 4.1667.

To find the value of n when the ratio is converted to the form 1:n, we need to express both measures in the same unit. We know that 1 metre is equivalent to 100 centimeters, so we can convert 2.5 metres to centimeters:

2.5 metres times 100 cm/metre = 250 cm

Now, we have the two measures in centimeters: 250 cm to 60 cm. Next, we divide both these numbers to find the ratio in the form 1:n.

250 cm / 60 cm = n

We simplify the ratio by dividing both numbers by 60 cm:

n = 250 cm / 60 cm = 4.1667

Therefore, the ratio of 2.5 metres to 60 centimeters expressed as 1:n is approximately 1:4.1667.

(6, 2 )

substitute x = 5 into the equation and solve for y

6y + 8 = 20 ( subtract 8 from both sides )

6y = 12 ( divide both sides by 6 )

y = [tex]\frac{12}{6}[/tex] = 2

the ordered pair is (5, 2 )

plug in 5

4(5)=6y+8

20=6y+8

12=6y

2=y

(5,2)

it will be 1.33= 1 1/3