Autumn buys 9 bottles of orange juice at the corner store for a total cost of $10.71. If each bottle costs the same amount, how much is each bottle of juice?

Answer:

x=15 cm

Step-by-step explanation:

The two triangles in the diagram are:

ABC and BDC

First we have to find the third side (hypotenuse) of BDC so that we can use it to find the value of x.

Hypotenuse is the largest side of a triangle which is usually in front of the right angle.

So in BDC

[tex]Base = BD =10cm\\Hypotenuse = BC = ?\\Perpendicular = CD = 2\sqrt{11}cm[/tex]

Applying Pythagoras theorem:

[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\\BC^2 = BD^2 + CD^2\\BC^2 = (10)^2 + (2\sqrt{11})^2\\BC^2 = 100+(2^2 * 11)\\BC^2 = 100+(4*11)\\BC^2 = 100+44\\BC^2 = 144\\\sqrt{BC^2} = \sqrt{144}\\BC = 12cm[/tex]

Solving for triangle ABC

[tex]Base = BC = 12 cm\\Perpendicular = AB = 9 cm\\Hypotenuse = AC = x\\[/tex]

Applying Pythagoras theorem

[tex]AC^2 = BC^2+AB^2\\x^2 = (12)^2 + (9)^2\\x^2 = 144+81\\x^2 = 225\\\sqrt{x^2} = \sqrt{225}\\x = 15cm[/tex]

Hence,

x=15 cm

Answer:

Velocity is 20

Step-by-step explanation:

well you divide the meters traveled by the time it took and you should get your answer.

1. divide 1200 by 20

2 answer should be 60

Answer:

30.7

Step-by-step explanation:

Answer:

7 and 5 also 3 probably I guess

Answer:

14 1/3

Step-by-step explanation:

First, you need to do what's in the parenthesis by finding a common denominator, which is 6. Multiply the 1 by 2 because that is what you multiply 3 by to get 6. You end up with 8 7/8 + 5 3/6. You then have to find the common denominator again, which is 24. Now the problem is 8 21/24 + 5 12/24. you get 13 32/24, which is equal to 14 8/24. Simplify, and you have 14 1/3.

Answer:

[tex]f(x)=4x^2[/tex]

Step-by-step explanation:

Quadratic Model

The quadratic function can be expressed in the form:

[tex]f(x)=ax^2+bx+c[/tex]

Where a,b, and c are constants to be determined using the points through which the function passes.

We have the points (-2,16) (0,0) (1,4). To find the values of a,b,c we just substitute the values of x and y and solve the system of equations.

Point (0,0):

[tex]f(0)=a*0^2+b*0+c=0[/tex]

It follows that

c=0

Point (-2,16):

[tex]f(0)=a*(-2)^2+b*(-2)+c=16[/tex]

Operating:

[tex]a*(4)+b*(-2)+c=16[/tex]

Since c=0:

[tex]4a-2b=16[/tex]

Divide by 2:

[tex]2a-b=8\qquad\qquad [1][/tex]

Point (1,4):

[tex]f(1)=a*(1)^2+b*(1)+c=4[/tex]

[tex]a*(1)+b*(1)+c=4[/tex]

Since c=0:

[tex]a+b=4\qquad\qquad [2][/tex]

Adding [1] + [2]:

2a+a=12

3a=12

a=12/3=4

a=4

From [2]

b=4-a

b=4-4=0

b=0

The model is:

[tex]\boxed{f(x)=4x^2}[/tex]

Answer:

Step-by-step explanation:

The sides of a parallelogram are equal. If O is the midpoint of its diagonal AC, them AO+OC = AC

Given

AO = 4x + 12 and

OC = 5x – 6

Required

AC

AC = 4x+12 + 5x-6

AC = 4x+5x+12-6

AC = 9x+6

Hence the length of AC is 9x+6

Answer:

C) -4,4,-6

Step-by-step explanation:

domain is x so plug the domain numbers into the function

4-2(-4)=12

4-2(0)=4

4-2(5)=-6

Therefore Range is (-4,4,-6)

Answer:

Yes

Step-by-step explanation:

Because for every 8 feet of the original rectangles, it will be 3 feet on the scale model, therefore it is reducing.

Answer:

Elias is not correct, A scale factor of 8/3 is an enlargement because it is greater than 1.

A reduction has a scale factor between

0 and 1.

(Verified answer)

Answer: x-12

Step-by-step explanation:

Simplify.

x

−

1

0

−

6

+

4

x−10−6+4

2 Collect like terms.

x

+

(

−

1

0

−

6

+

4

)

x+(−10−6+4)

3 Simplify.

x

−

1

2

x−12

Answer:

86-14x

Step-by-step explanation:

4(x+8)+9(6-2x)

4x-18x+54

4x-18x+86

-14x+86

86-14x

Answer:  First You Have To Simplify The Equation From Both Sides Then Thats how You Will Determine what f is. F = -15

Variable [tex]f[/tex] is isolated as [tex]\boldsymbol{f=-15}[/tex] in the expression [tex]\frac{f}{3}+22=17[/tex].

A variable is a symbol and placeholder for a changing amount or any mathematical object.

An algebraic expression is one that is composed of integer constants, variables, and algebraic operations.

Given expression is [tex]\frac{f}{3}+22=17[/tex]

Transpose [tex]22[/tex] to the right side of the equation.

[tex]\frac{f}{3}=17-22\\\frac{f}{3}=-5[/tex]

[tex]f=-15[/tex]

So, variable [tex]f[/tex] is isolated as [tex]\boldsymbol{f=-15}[/tex]

Find out more information about algebraic expression here:

https://brainly.com/question/2945451?referrer=searchResults

Answer:

rise, run

Step-by-step explanation:

When finding the slope of a line using a slope triangle, the RISE length is divided by the RUN length. (I think. Sometimes the "divided by" makes me confused about which is on top, but I'm pretty sure this is right.)

Answer:

3:2 is the ratio.

Step-by-step explanation:

Answer:

I believe it's C, 0.4 x 0.7

Step-by-step explanation:

Answer:

5x = 3x

4+8t-y=y-t+8

98/r=34t

Step-by-step explanation:

hope this helps!

mark me brainliest plz!

Answer:

Evaluate each given numbers, expressions or equation.

Check the values or numbers.

Now in order to solve we proceed in the manner

Answer:

numbers:letters

5:4 (numbers:letters form)

Step-by-step explanation:

There are 5 numbers in the password and 4 letters

Hopefully this helps :)

Answer:

x = -3

Step-by-step explanation:

First solve it:

Subtract the x's from both sides

2y = -3x +8

2y = -5x +2

Divide by two

y= -1.5x + 4

y = -2.5x +1

set them equal to each other:

-1.5x +4 = -2.5x +1

Add 2.5 x to both sides

1x +4 = 1

x +4 = 1

subtract 4 from both sides

x = -3

Answer:

y = 1/4

Step-by-step explanation:

y⁻⁴ = 256

(1/y)⁴ = 256

y⁴ = 1/256

y =  ⁴√1/256

y = 1/4

Thus, The value of y is 1/4

-TheUnknownScientist

Answer:

z > 4

Step-by-step explanation:

- 2z - 3 < 5

- 2z < 5 + 3

- 2z < 8

z > - 4

Answer:

z > -4

Step-by-step explanation:

Please see the following attachment for step by step

Answer:

water-safety suggestions

Explanation:

We can make this conclusion because we notice this addition from the opening lines of the article, "Summertime is near, the lifeguard's whistle  beckons.."

By such Inclusion, the article in other words is saying that since during summertime many people go swimming, it would be best to follow some water-safety suggestions. Therefore, it is most likely to be included in the magazine.

Answer:

water-safety suggestions

Step-by-step explanation:

Answer:

Irrational: √2 = 1.4

Step-by-step explanation:

Answer:

1.445 × 10³

Step-by-step explanation:

Standard form is a way of writing a small number or a large number easily.

We should give the final answer in standard form.

1) (1.7 × 10⁴) × (8.5 × 10⁻²)

We enter this directly into the calculator to obtain a solution.

= 1445

We write this in standard form we have :

1.445 × 10³

Answer:

1.445 × 10³ hope it helped goodluck!

Answer:

The slope of line is 0 given points (2,8)(7,8)

Step-by-step explanation:

We need to find slope of line given points (2,8),(7,8)

The formula used to find slope of line is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

We are given:

[tex]x_1=2, y_1=8, x_2=7 \ and \ y_2=8[/tex]

Finding slope using formula:

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{8-8}{7-2}\\Slope=\frac{0}{5}\\Slope=0[/tex]

So, the slope of line is 0

Step-by-step explanation:

[tex]{:}\longrightarrow[/tex][tex]\sf (w+4)(3w-2)[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf w(3w-2)+4 (3w-2)[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 3w^2-2w+12w-8[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 3w^2+10w-8 [/tex]

Answer:

$52.71

Step-by-step explanation:

Today's price= $58.63

Yesterday's price= y

Difference= $5.92

y+5.92 = 58.63

y = 58.63 - 5.92

= $52.71

Answer: 22

Step-by-step explanation:

2r - 7 = r + 15

2r - r = 15 + 7

2r = 22

r = 22/2

r = 11