Which can be the first step in finding the equation of the line that passes through the points (5.-4) and (-1,8) in
slope-intercept form?

The area of one base of the triangular prism is given as 16√3 square cm, and since the base is equilateral, the sides of the triangle are of equal length.

The formula to calculate the area of an equilateral triangle is (sqrt(3)/4) * s^2 where s is the length of a side of the triangle.

So, plugging in the given area of base, 16√3, we can find the length of a side of the equilateral triangle, s.

16√3 = (sqrt(3)/4) * s^2

s = (4*16√3)/sqrt(3) = 16√3 cm

Now we can use the height of the prism, which is given as 30 cm, to find the area of the rectangular surface.

Area of the rectangular surface = 2 * base area * height = 2 * 16√3 * 30 cm²

This simplifies to:

960√3 cm²

So the total area of the rectangular surface of the prism is 960√3 square cm.

The answer to this question will  t = 8. The first step to solving this equation is to combine the like terms by adding the two numbers together.

In this case, 5t + 35 = 40t. The next step is to divide both sides of the equation by the coefficient of the variable, which in this case is 5. When you do this, you get 40t/5 = t. Therefore, the answer to 5t + 35 is t = 8.

A coefficient is an integer that is either multiplied by the variable it is associated with or written alongside the variable. A coefficient is, in other words, the numerical factor of a term that contains both constants and variables. For instance, the coefficient in the expression 2x is 2.

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Answer:

a = 3 or -3

Step-by-step explanation:

a^2 -8 = 1

a^2 = 1 + 8

a^2 = 9

a = -  [tex]\sqrt{9}[/tex] or [tex]\sqrt{9}[/tex]

a = 3 or -3

Answer: a = 3, -3

Step-by-step explanation:

      Since we want to find what values of a, or x when substituted into the function, equal 1, we will set the function equal to 1 and solve for x.

     Given:

f(x) = x² - 8

     Set equal to 1:

1 = x² - 8

     Subtract 1 from both sides of the equation:

x² - 9 = 0

     Difference of squares factoring:

(x - 3)(x + 3) = 0

     Answers:

x = 3, -3

     So,

a = 3, -3

Answer:

  4.6 km

Step-by-step explanation:

You want to know how many kilometers east Santos walked to end up 5 km from his starting position after walking 2 km south.

The distance Santos is from his starting position will be the hypotenuse of a right triangle with one leg 2 km. Using the Pythagorean theorem, we can find the length of the other leg.

  c² = a² + b²

  5² = 2² + b²

  21 = b²

  b = √21 ≈ 4.583

Santos walked about 4.6 km east.

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Answer:

Gain: $415

Loss: $10

Step-by-step explanation:

money earned - money spent = gain/loss

The gain is when the participant wins the telescope:

telescope = $425  ==> money earned

10 tickets * $1 = $10 for tickets  ==> money spent

$425 - $10 = $415

Loss is when the participant doesn't get the telescope:

$0 ==> money earned (No money earned)

10 tickets * $1 = $10 for tickets  ==> money spent

$0 - $10 = -$10 gained

-$10 gained ==> $10 lost

Answer:

   - A bag of rice is $16.9

   - A bag of flour is $5.20

Step-by-step explanation:

Let R and F stand for the price of a bag of Rice and Flour, respectively.

We can use the information provided to set an equation that will predict the total cost for that restaurant, given the quantities of rice and flour received (Restaurants A and B)

A) 4R + 2F = 78   [4 bags of rice and 2 bags of flour, when multiplied by the prices per bag, R and F, will result in a total cost of $78.

B)  3R + 4F = 71.5  [Now it is 3 bags of rice and 4 of flour, for a total cost of $71.50

We have 2 equations and 2 unknowns.  We can use substitution to find the answers.  Take one of the equations and reorganize it to isolate one of the variables (R or F).  We'll take the equation for A and isolate F

---

A) 4R + 2F = 78

     2F = 78-4R      [subtract 4R from both sides]

       F = 39-2R      [divide both sides by 2]

We've isolated F, and we can use this definition of F in the second equation:

===

B)  3R + 4F = 71.5

3R + 4(39 - 2R) = 71.5  [Use the definition of F derived above.  In this manner, we have legally eliminated one of the two variables.  (Sneaky, effective, and fun)]

3R + 156 - 8R = 71.5   [Multiply, combine like terms, and simplify]

-5R = -84.5                  [Isolate R]

R = $16.9                      A bag of rice costs $16.9

Now use the price of rice (R=$16.9) in one of the equations.  Since the rearranged equation we used above is already conveniently written for F, we'll use it:

F = 39 - 2R

F = 39 - 2(16.9)

F = 39 - 33.8

F = $5.20                     A bag of flour costs $5.20

===

CHECK:

Do these two prices satisfy both equations we first formulated?

Restaurant A:  4R + 2F = 78?

                        4(16.9) + 2(5.20) = 78  YES

Restaurant B:  3R + 4F = 71.5?

                        3(16.9) + 4(5.20) = 71.5  YES

These are the correct answers.

Yes, infinity times 0 is still 0 because if we multiply 0 to any number is 0.

Yes, infinity times 0 is still 0 because if we multiply 0 to any number is 0.

0 * 0 * 0 * 0= 0

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is neither negative nor positive. A number which is not zero is said to be nonzero. A root of a function f is also sometimes known as "a zero of f."

The Schoolhouse Rock segment "My Hero, Zero" (Multiplication Rock, Season 1, Episode 2, 1973) extols the virtues of zero with such praises as, "My hero, zero Such a funny little hero But till you came along We counted on our fingers and toes Now you're here to stay And nobody really knows How wonderful you are Why we could never reach a star Without you, zero, my hero How wonderful you are."

Zero is commonly taken to have the factorization 0=0·1 (e.g., in the Wolfram Language's FactorInteger[n] command). On the other hand, the divisors and divisor function sigma_k(0) are generally taken to be undefined, since by convention, n|0 (i.e., n divides 0) for every n except zero.

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Answer:

44 minutes

Step-by-step explanation:

Kiran reads 5 pages in 20 minutes, if we divide we will know that he reads 1 page in 4 minutes.

Multiply 4 by 11 to find out how long it will take him to read 11 pages.

11 times 4 = 44

It will take Kiran 44 minutes to read 11 pages.

Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.

A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter. There is frequently just one variable, which is also the symbol. example: 2x - 4 = 2.

given

DE = DC + CE

44 = 5n – 30 +  6n – 25

44 = 11n - 55

44 + 55 = 11n

n = 9

Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.

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y = 3x+4 ← equation of linear function.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have,

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = y_2-y_1/x_2-x_1

with (x₁, y₁ ) = (- 3, - 5) and (x₂, y₂ ) = (1, 7) ← 2 ordered pairs from the table

m = 7+5/1+3

  =12/4

   = 3 ,

So, y = 3x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (1, 7 ), we get,

7= 3 + c

⇒ c = 7-3

      = 4

Hence, y = 3x+4 ← equation of linear function

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The exact value is required. In this case, they don't have enough for 1 3/4 cups of flour.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

From the information, the person had 2/3 cup of flour in a bin and 7/8 flour was still in the bag. In this case, it should be noted that they also wanted to know of they had enough for 1 3/4 cups of flour.

This will be calculated thus:

= 2/3 + 7 / 8

= 16/24 + 21/24

= 37 / 24.

= 1 13 / 24

This is not enough for 1 3/4 cups of flour.

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The midpoint of 1 and 2 and 3 and 4 is (2,3).

The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2.

The end of a line at a point that is equally distant from both ends, a time interval between an event's beginning and end.

The point on a graph or figure where the figure stops might be referred to as the endpoint. It can be the point joining the sides of a polygon (the vertex), the common endpoint of two rays making an angle, the two extreme points of a line segment, the one end of a ray.

Use numbers, fractions, mixed numbers, or decimals to enter two points. The midpoint calculator displays the required research:

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Answer:

x=0 and y=36

Step-by-step explanation:

30 + 6 equals 36 but it is negative so you would add 30 to negative thirty to get to zero and go into the positive numbers. So if you add 6 more you would have positive 6. so it it 36 y is 36

Answer:

a₄ = - 2

Step-by-step explanation:

to calculate a term in the sequence subtract 5 from the previous term

give first term a₁  = 13 , then

a₂ = a₁ - 5 = 13 - 5 = 8

a₃ = a₂ - 5 = 8 - 5 = 3

a₄ = a₃ - 5 = 3 - 5 = - 2

The cost of one ticket in Virginia is $8

A System of Linear Equations is when we have two or more linear equations working together.

Given that, 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77, Also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91.

To find the cost of a ticket in Virginia we will establish a system of linear equations and then solve them,

Let V represents the cost in Virginia that of in Maryland be M

Therefore,

4v+5m = 77.......(i)

8v+3m = 91........(ii)

Multiplying the equation eq(i) by 2 and subtracting eq(ii) from eq(i) [Elimination]

(8v+10m = 154)  - (8v+3m = 91)

7m = 63

m = 9

Put m = 9 in eq(i)

4v+5(9) = 77

4v = 77-45

4v = 32

v = 8

Hence, Each ticket in Virginia and Maryland costs $8 and $9 respectively.

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The process to show the vector field V(x,y,z) as conservative is show  below and the scalar potential f is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex]   .

A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .

The Gradient is vector that is made from partial derivatives of potential function .

The Vector function is given as , V(x,y,z) = [tex](yz^{2} )i + (xz^{2} )j + (2xyz)k[/tex] ,

So , we can write the partial derivatives function of potential function as :

[tex]\frac{\partial f}{\partial x} = yz^{2}[/tex] ; [tex]\frac{\partial f}{\partial y} = xz^{2}[/tex] ; [tex]\frac{\partial f}{\partial z} = 2xyz[/tex],

On Antidifferentiating any of the above three partial derivatives ,

we get ; [tex]f=xyz^{2} + C[/tex] , here the constant C can take any value ,

so , we take C as [tex]e^{\pi }[/tex] .

Therefore , the potential Function is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .

The given question is incomplete , the complete question is

Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .

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Answer:

10^11

Step-by-step explanation:

This question helps you practice some exponent rules. To "fix" a negative exponent you push it across the fraction bar. The 10^-3 on the bottom becomes a 10^3 on the top. See image.

Then, when you have 10^8 • 10^3, that is when you are multiplying, you add the exponents.

10 ^ (8+3)

= 10^11

see image

Meaning of the △ is: the given symbol is the representation of the geometrical figure triangle.

Therefore, the meaning of the given symbol △ is the representation of the triangle.

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Answer:

Estimate of difference is 4.

Step-by-step explanation:

10.04 = 10 to nearest whole number

6.3 = 6 to nearest whole number.

10 - 6 = 4.

Answer:

try -5

Step-by-step explanation:

mainly because it says -3 plus 5 and there's only 4 and 5 so It can't really go further

Answer:try -5

Step-by-step explanation:

mainly because it says -3 plus 5 and there's only 4 and 5 so It can't really go further

Answer:

35 [tex]\frac{0}{1}[/tex]

Step-by-step explanation:

The estimated revenue, in dollars, that the club will generate when the bags are priced at $13 each is 3) 1,040.

The revenue formula is the multiplication of the number of units sold and the price per unit.

To determine the total revenue, we must first ascertain the unit price and the quantity sold.

We know that market forces and the competitive environment determine the quantity sold or supplied.

The demand for tote bags at $11 = 100 units

Decrease in demand for every $1 price increase = 10 units

When the price is $13 each, the units to be sold = 80 (100 -10 x 2)

The total revenue at $13 each = $1,040 (80 x $13)

Total revenue at $12 each = $1,080 (90 x $12)

Total revenue at $11 each = $1,100 (100 x $11)

Thus, we can conclude that the club generates less revenue when it increases its price per tote bag from $11 to $13, justifying the interactions between supply, demand, and cost.

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Answer:

C. 50%

Step-by-step explanation:

Since 40 is half of 80, and 50% means half, and 42 out of 80 is close to half, then 42 out of 80 is close to 50%.

Answer: C. 50%

Answer:

b25

Step-by-step explanation:

beacuse that is a rain and reasonable he percentage

The length of the map would be 3 inches.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: length of the road as 6/5 miles and on the map 9/5 inches and thus 1 mile = 1.5 inches and therefore the length of the 2 mile road on the map is 2×1.5=3 inches

Hence, The length of the map would be 3 inches.

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[tex]d-2=4.6[/tex]

Add 2 to both sides:

[tex]d-2+2=4.6+2[/tex]

[tex]\fbox{d = 6.6}[/tex]

Answer:

x= 35⁰ - obtuse triangle

Step-by-step explanation:

since the sum of angles of the triangle = 180⁰

(3x-5) + (x+10) + (x) =180⁰

5x+5= 180

(subtracting 5 from both sides)

5x=180-5

5x= 175

(dividing by 5)

x= 35⁰

so the angles of the triangle are

(3x-5) = 105-5= 100⁰

(x+10) = 45⁰

(x) = 35⁰

then this triangle is an obtuse triangle

[tex]sin(A)+cos(A)=\sqrt{2}\hspace{10em}tan(A)+cot(A)=2 \\\\[-0.35em] ~\dotfill\\\\ tan(A)+cot(A)=2\implies \cfrac{sin(A)}{cos(A)}+\cfrac{cos(A)}{sin(A)}=2 \\\\\\ \cfrac{sin^2(A)+cos^2(A)}{cos(A)sin(A)}=2\implies \boxed{\cfrac{1}{cos(A)sin(A)}=2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]sin(A)+cos(A)=\sqrt{2}\implies (~~sin(A)+cos(A)~~)^2=(\sqrt{2})^2 \\\\\\ sin^2(A)+2sin(A)cos(A)+cos^2(A)=2 \\\\\\ 2sin(A)cos(A)+sin^2(A)+cos^2(A)=2\implies 2sin(A)+1=2 \\\\\\ 2sin(A)cos(A)=1\implies \boxed{2=\cfrac{1}{cos(A)sin(A)}}[/tex]

now, another way to look at this identity will  be as a unified system of equations

[tex]\begin{cases} (~~sin(A)+cos(A)~~)^2=2\\\\ ~~ ~tan(A)+cot(A)=2 \end{cases}\implies (~~sin(A)+cos(A)~~)^2=tan(A)+cot(A)[/tex]

and we'd end up with the same rigamarole.

Step-by-step explanation:

the range is (-32, 28)

note that when the bubble is not filled in it should be an open bracket