what is the slope of a line perpendicular to the line whose equation is x-3y=-27

Answer:

21 cm²

Step-by-step explanation:

Applying,

A = (a+b)h/2............. Equation 1

Where A = area of the trapezium, a = length of the first parallel side, b = length of the second parallel side, h = height.

From the diagram

Given: a = 5 cm (5 grids), b = 9 cm (9 grids), h = 3 cm (3 grids)

Substitute these values into equation 1

A = 3(5+9)/2

A = 3(14)/2

A = 3×7

A = 21 cm²

Answer:

C. a = 6√3, b = 12, c = 6√2

Step-by-step explanation:

First let's find b using the cos. The cos is the adjacent side if the angle divided by the hypotenuse. We know the value of the adjacent side and we know that cos(60°) = 1/2 = 0.5:

cos(60°) = 6/b

0.5 = 6/b

b = 6/0.5

b = 12

Now we can find a using the Pythagorean theorem:

b² = 6² + a²

12² = 6² + a²

144 = 36 + a²

a² = 144 - 36

a² = 108

a = √108

a = 6√3

And now we can find c using cos again:

cos(45°) = c/b

√2/2 = c/12

c = 12•√2/2

c = 6√2

Answer:

(1,0)

Step-by-step explanation:

y = -3x+3

simple, to find the x-intercept, what does x equal for y to be 0?

when x is 1, y equals 0, so the x-intercept would be at (1,0)

Answer:

<RQS = <RSQ

Step-by-step explanation:

IRQ = RS, then QRS is an isosceles triangle and the base angles are equal

<RQS = <RSQ

Answer:

7000

Step-by-step explanation:

Answer:

Step-by-step explanation:

tan x = 5.6/9.7

tan x = 0.57732

x = 29.9 to nearest tenth

I hope I'm correct if not I tried my best

bye :-)

Answer:

x

Step-by-step explanation:

(x²)³ ÷ x⁶

x⁶ ÷ x⁶

x

Answer:

all real values of x where 1 < x < 4

If there is anything you don't understand let me know.  Also, since the graph is supposedly shown you may even be able to get the information just by looking at the graph.  

Step-by-step explanation:

A graph  goes from being negative to positive (or the other way around) by passing through the x axis.  Or in other words when f(x) = 0.  So the trick is to find all 0s and then test if it is poitive or negative before and after the 0.  

f(x) = (x+2)(x-4) is in factored form, so it gives the 0s.  in factored form the 0s are the negatives of the numbers int he parenthesis.  Or in other words (x+a)(x+b) would have 0s at -a and -b.  Notie it is x+a but the 0 is at -a.  so for (x+2)(x-4) the zeroes would be -2 and 4.

Then checking, we can say it is positive before -2, negative after -2 up until 4, then it is positive again.

For increasing and decreasing for anything other than a quadratic and linear function you need calculus.  Since this is a quadratic though you don't need it.

With quadratics you need to know they have two parts.  An increasing part and decreasing part.  If you draw the graph of x^2 you can see it decreases until (0,0) then it starts increasing.  -x^2 is the opposite.  it won't always have the same changing point, but you can always tell if it increases first or decreases first.  You look at if the coefficient next to x^2 is positive of negative.  

In (x+2)(x-4) We have to expand first.  so it becomes x^2 - 2x - 8.  x^2 has 1 as its coefficent so we know it decreases first then increases.  Also looking at (x+2)(x-4) you could say since the two xs have the same sign we also know it would be that.  is one was positive and one negative, like (2x+1)(-3x+1) we would be able to say it increases first then decreases.  

To know when it switches, since it is in factored form you find the point in the middle of the two zeroes, and that is where it switches.  Since the zeroes are -2 and 4 we can say the middle (called the vertex) is at x=1 since it is 3 away from both 0s.  So it decreases up until 1 then increases.  

The different forms of quadratics have different easy methods of finding the vertex.

We could also actually use this information to say, since it is decreasing first we know it is positive before the first 0, then negative until the second 0, then positive again.  Still would have to find the 0s though.

So now we know it is positive and decreasing until x=-2, negative and decreasing until 1, negative and increasing until 4, then increasing after that.

Since you want negative and increasing, that is 1 < x < 4

Answer:

Hi, today we learned about (the lesson you choose)  and the teacher told me to tell you what to do so you need to do your work or you will get in trouble

Step-by-step explanation:

[tex]a =\dfrac{180\cdot(n-2)}{n}\\~\\a = \dfrac{180\cdot(55-2)}{55}\\~\\a = 173^{\circ} \text{ }27'\text{ }16''[/tex]

Answer:

y-1 = 2(x+2)

Step-by-step explanation:

Point slope form of a line is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y -1 = 2(x - -2)

y-1 = 2(x+2)

Answer:

4 1250 m

Step-by-step explanation:

Hope it helps you.

Answer:

1. The starting point of a ray or line segment

is the endpoint.

Step-by-step explanation:

hope it may help you!

Answer:

The starting point of a ray or line segment is the endpoint.

Step-by-step explanation:

hope it may help you

Answer:

Angle A: 28 degrees

Angle B: 24 degrees

Step-by-step explanation:

Hi there!

The angle that measures 52 degrees (angle DCA) is one of the exterior angles of a triangle. An exterior angle of a triangle is equal to the sum of the opposite interior angles, which in this case would be angles A and B. Knowing this, we can set up the following equation:

[tex]4y-4+3y=52[/tex]

1) Solve for y

[tex]4y-4+3y=52[/tex]

Combine like terms

[tex]7y-4=52[/tex]

Add 4 to both sides to isolate 7y

[tex]7y-4+4=52+4\\7y=56[/tex]

Divide both sides by 7

[tex]\frac{7y}{7}=\frac{56}{7} \\y=8[/tex]

Therefore, y is equal to 8.

2) Solve for angles A and B

Angle A:

[tex]4y-4\\=4(8)-4\\=32-4\\=28[/tex]

Angle B:

[tex]3y\\=3(8)\\=24[/tex]

I hope this helps!

Answer:

profit(n) = n * .50

Profit(10) = 5.00

Step-by-step explanation:

Profit = amount of candy bars sold * profit per candy bar

profit(n) = n * .50

Let the number of candy bars sold be 10  ( n=10)

Profit(10) = 10 * .50

               = 5.00

When you added you only added 9  .50 terms which is why you only got 4.50 for your answer.

Answer:

P = 20 and A = 24

Step-by-step explanation:

6+6+4+4 = 20

6*4 = 24

Hope this helps

Answer:

second option : the side length was multiplied by 5.

Step-by-step explanation:

a = side length of the original square

A² = a×a

(a+5)×(a+5) = a² + 10a + 25

and that should be equal to a²×25

a² + 10a + 25 = 25a² ?

10a + 25 = 24a²

no, that is not true for all a

a×5 × a×5 = a²×25 = 25A²

this is the correct solution, as it is true for all a.

For the area to be  25a², the side length was increased by 5.

Let a be the side length of the original square, hence:

A = a²

Increasing the length by 5 will give:

(a+5)×(a+5) = a² + 10a + 25

Factorizing the result

a² + 10a + 25 = (a+5)²

a² + 10a + 25 = 25a²

This shows that for the area to be  25a², the side length was increased by 5.

Learn more on area of square here: https://brainly.com/question/25092270

Step-by-step explanation:

everything can be found in the picture

Step-by-step explanation:

Let the increase in the size of the length and breath be 'x'.

The area of the rectangle = 12in × 8in

=96 in²

From the question,

(12+x)(8+x)=96×2 in²

or, 96+12x+8x+x²= 192

or, x²+20x+96-192=0

or, x²+20x-96=0

or, x²+24x-4x-96=0

or, x(x+24)-4(x+24)=0

or, (x-4)(x+24)=0

Either, Or,

x-4=0 x+24=0

Therefore, or, x= –24 (Which is impossible)

x=4

So the new dimensions are 12+4=16 inch and 8+4=12 inch.

Answer:

Santos should run approximately 36.145 meters along the shore

Step-by-step explanation:

The given parameters are;

The distance along the shore of the child = 50 meters

The distance from the shore of the child = 60 meters

The rate at which Santos can run = 4 m/s

The rate he can swim = 0.9 m/s

Let 'x' represent the distance he runs along the shore

We have;

The time he spends running on the shore, t₁ = x/4

The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9

The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9

To find the maximum, we have;

dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

Simplifying using a graphing calculator gives;

[tex]\dfrac{x - 2000}{9} = \sqrt{x^2-100\cdot x+6,100}[/tex]

1519·x² - 151900·x + 3505900 = 0

x = (151900 ± √((-151900)² - 4×1519×3505900))/(2 × 1519)

x ≈ 63.86 m or x ≈ 36.145 m

We note that the distance from a point x = 63.83 meters and 36.145 meters from where Santos spots the girl to the location of the girl are the same

Therefore, Santos should run approximately 36.145 meters along the shore before jumping into to the water in order to save the child

Answer 20%

Step-by-step explanation:

Answer:

2015-2010=5

50÷5=10

120-50=70

2017-2015=2

2*10=20

70-20=50mg

2018=50mg

Answer:

75 %

Step-by-step explanation:

Answer:

$1.50

Step-by-step explanation:

25% of 6 is basically just 6/4, which is 1.5.

This is money we're talking about, so the answer is $1.50

Answer and Step-by-step explanation:

1.

First, combine everything in the first parenthesis, then multiply by the number on the outside.

Primero, combine todo en el primer paréntesis, luego multiplique por el número en el exterior.

[tex]\frac{8}{5} +\frac{6}{5} -\frac{4}{5} =\\\\\frac{14}{5} -\frac{4}{5} = \frac{10}{5} = 2\\\\\\[/tex]

2 × [tex]\frac{5}{6}[/tex] = [tex]\frac{10}{6} = A) \frac{5}{3}[/tex]   <- This is the answer. Esta es la respuesta.

2. First, combine everything in the first parenthesis, then multiply by the number on the outside.

Primero, combine todo en el primer paréntesis, luego multiplique por el número en el exterior.

[tex]\frac{20}{11} + \frac{12}{11}- \frac{19}{11} =\\\\\frac{32}{11} -\frac{19}{11} = \frac{13}{11} \\\\\\[/tex]

[tex]\frac{13}{11}[/tex] × [tex]\frac{11}{13}[/tex] = B) 1  <- This is the answer. Esta es la respuesta.

3. Make the fractions have the same denominator, then add, then multiply by 40.

Haz que las fracciones tengan el mismo denominador, luego suma y luego multiplica por 40.

[tex]\frac{3}{8} ->\frac{15}{40} \\\\\frac{4}{5} ->\frac{32}{40} \\\\\frac{15}{40}+ \frac{32}{40} = \frac{47}{40} \\\\\\[/tex]

[tex]\frac{47}{40}[/tex] × 40 = E) 47  <- This is the answer. Esta es la respuesta.

I hope this helps! #TeamTrees #PAW (Plant And Water)

¡Espero que esto ayude! #TeamTrees #PAW (Planta y agua)

Answer:

$35

Step-by-step explanation:

1-2/7=5/7 (remaining money left after shopping)

2/5×5/7=2/7 (amount of money lost)

5/7-2/7=3/7 (amount of money she has now)

3/7=$15

1/7=$5

7/7=$35

Hence, total amount of money she has before she went shopping=$35

hope it helps:))))

Answer

IS 2/4

Step-by-step explanation:

1/3 = 4/12  1/4 = 3/12  4/12+3/12= 6/12 = 2/4