A family smoothie recipe calls for strawberry juice and apple juice. This equation represents the proportional relationship between the number of cups of strawberry juice (s) and apple juice (a) in the recipe.​

The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,

⇒ x²+ (y - 6)² = 36

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Now, We know that;

The standard form for finding the equation of a circle is expressed as;

⇒(x - a)² + (y - b)² = r²

where; (a, b) is the center of the circle and r is the radius of the circle.

Here, we have;

⇒ Diameter = 12 units

⇒ Radius = 12/2 = 6 units

Since, The center lies on the y-axis,

Hence, the center will be at (0, 6).

Substituting into the formula, we will have;

⇒ (x - 0) + (y - 6)² = 6²

⇒ x² + (y - 6)² = 36

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Answer:

Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.

Step-by-step explanation:

Out of 50 people, there are 50C5 = 50!/(5!*45!) ways to select 5 of them.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

How many of those methods involve picking a particular person (you)? If you are selected, there are only 4 more options left out of the remaining 49. There are thus 49C4 = 49!/(5!*44!) ways to select both you and the other 4 individuals.

Therefore, (49C4)/(50C5) = 1/10 is the probability.

The probability that you are one of the five individuals chosen from 50 is 5/50, or 1/10, as a second check.

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Answer:

Should be right and scalene

Whale is 1628.87 feet far from the shoreline.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the tower = 200 feet

Angle of depression = 7°

Distance of whale from the shore line = x = AB = ?

In the figure

tan 7° = BC/AB = 200/AB

0.1228 = 200/AB

AB = 1628.87 feet = x

Distance of whale from the shoreline = 1628.87 feet.

Hence, Whale and shoreline are 1628.87 feet far from each other.

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Answer:

Using Words: The total area of the house and deck is given by the sum: 40x20 + x(13x) .

Using Symbols: The total area of the house and deck is given by the sum: 800 + 13x^2 ft².

Step-by-step explanation:

A triangle whose any one of the angles is an obtuse angle or more than 90°, then it is called an obtuse-angled triangle or obtuse triangle.

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Answer:(b)7m^4

Step-by-step explanation:
56m^8/8m^4
is can be said as

(7m^4 )(8m^4)/8m^4

8m^4 from both numerator and as well as denominator cancels so the final answer is 7m^4(7 m to the power 4)

Answer:4 individuals

Step-by-step explanation:

Two pairs refers to 2 sets of two things. In general terms, a pair refers to two items and when you have two of them, it would be two sets of two things, or simply "four items".

For example, two pairs of socks would be four socks.

Answer:

Step-by-step explanation:

Karine De Marchand is 54 years

The y-intercept of Y = - 10 is -10.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, b, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Now, if we equate the standard slope-intercept form of the equation with the given equation, we get

y = mx + c

y =  - 10 = 0x -10

m = 0 and c = -10

As we know the c is the y-intercept which is equal to -10.

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The value 255 in pixels means the code for the image is white. Therefore, any image with 255 pixels means it is white color.

Pixel values are the numerical values that make up the matrix in which images are stored in computers. The byte image, the most popular pixel format, stores this number as an 8-bit integer with a possible value range of 0 to 255.

Normally, zero and 255 are considered to be black and white, respectively. The many colors of gray are composed of values in between. This has the tremendous benefit of allowing computers to operate with color values that can be stored in a tidy number of bytes.

It is represented in 8 bits because 2⁸ equals 256 (from 0 to 255).

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The amplitude of a sine or cosine function is the vertical stretch or compression factor of the function. In this case, the function f(x) = sin(x) has been stretched vertically by a factor of 3. Therefore, the amplitude of the function g(x) is A = 3.

The function g(x) = 3sin(12x) + (-5)

Answer:

121

Step-by-step explanation:

3x + 94 + x + 36 + 2x - 4 = 180

6x + 126 = 180

6x = 54

x = 9

m<AOC = 3x + 94

m<AOC = 3(9) + 94

m<AOC = 121

An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet​ metal is,

[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]

Given that,

An open box length [tex]l[/tex] = 5 feet

An open box breadth b = 5 feet

An open box height = h

An open box area = 605 cubic feet

A square is a four-sided polygon which has it's all sides equal in length and the measure of the angles are 90 degrees. The shape of the square is such as, if it is cut by a plane from the center, then both the halves are symmetrical. Each half of the square then looks like a rectangle with opposite sides equal.

Area = [tex]l * b * h[/tex]    (Equation - 1)

So,

We can substitute l , b , h values in the equation - 1,

605 = 5 * 5 * h

605 = 25 * h

605/25 = h

24.2 = h

Therefore,

An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet​ metal is,

[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]

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Polynomial [tex]$-1+x^3-\frac{1}{3} x^3$[/tex] and its conventional form, [tex]x^5-\frac{x^2}{3}-1$$[/tex] , are both used.

[tex]$$-1+x^5-\frac{1}{3} x^2=x^5-\frac{x^2}{3}-1$$[/tex]

steps

[tex]$$-1+x^5-\frac{1}{3} x^2$$[/tex]

[tex]\begin{aligned}& \frac{1}{3} x^2=\frac{x^2}{3} \\& =-1+x^5-\frac{x^2}{3}\end{aligned}[/tex]

rephrase in proper grammar

[tex]=x^5-\frac{x^2}{3}-1$$[/tex]

The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial. You must consider each term's degree in order to write any polynomial in standard form.

Next, list each phrase in order of degree, left to right, highest to lowest. An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial.

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If XV =27-2x and VZ =3x+2, then the diagonal of parallelogram XZ = 34 units and VZ = 17 units.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size.

The length of line XV = 27 - 2x.

The length of line VZ = 3x + 2.

According to the properties of a parallelogram the diagonals bisect each other .

Hence, XV = VZ.

Equating the expressions -

27 - 2x = 3x + 2

-2x - 3x = 2 - 27

-5x = -25

x = 5

The value of line XV = 27 - 2x

27 - 2(5)

27 - 10

17 units

The value of line VZ = 3x + 2

3(5) + 2

15 + 2

17 units

The value of line XZ = XV + VZ

17 + 17

34 units

Therefore, the value of VZ = 17 units and value of XZ = 34 units.

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The values of x and y that are solutions to the system of simultaneous equations are; y = 573/25 and x = 17.1

We are given the simultaneous equations;

²/₃x + ³/₅y = 12    -----(eq A)

⁵/₂y - 3x = 6       ------(eq B)

Multiply eq A by 9 and eq B by 2 to get;

6x + ²⁷/₅y = 108    -----(eq C)

5y - 6x = 12       ------(eq D)

Add eq C to eq D to get;

5y + ²⁷/₅y = 120

Multiply through by 5 to get;

25y + 27 = 600

25y = 600 - 27

25y = 573

y = 573/25

Thus;

5(573/25) - 6x = 12

6x = 5(573/25) - 12

6x = 102.6

x = 17.1

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Answer:

12.375 hours

Step-by-step explanation:

We know that car travel

400 miles = 5.5 hours

900 miles = ?

We take 900 times 5.5, then divide by 400 and get 12.375 hours

So, the car take 12.375 hours to travel 900 miles

Answer:

12.375

Step-by-step explanation:

400+400+100=900miles

5.5+5.5=11

5.5÷4=1.375

11+1.375=12.375

The relationship between data items is displayed using tables of values. In science class, you might utilize a table of values. Some  methods are explained.

Tables of values are used by scientists and researchers to record their data, which is then examined for patterns. Then, they can use this pattern to make predictions.

Some steps to prepare the table are-

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f(x) = x⁵ – 8x⁴ + 16x³ at x = 4, does not cross the x-axis. at x = 0, crosses the x-axis. This relates to the x-axis end behavior of a graph of a function.

Let's now find the roots of this function;

f(x) = x⁵ - 8x⁴ + 16x³

Let's factorize it first to get;

f(x) = x³(x² – 8x + 16)(x² – 8x + 16) is a perfect square trinomial and can be expressed as (x – 4)(x - 4).

Thus; f(x) = x³ (x – 4)(x - 4)

C) Since we have found the factorized form to be;

f(x) = x³ (x – 4)(x - 4)

The roots are at f(x) = 0;

The roots are; x³ = 0; (x – 4) = 0 ; (x - 4) = 0

This indicates that x=0 and x=4 are f(xroots. )'s x = 4

As a result, the graph will touch the x-axis but not the repeated root of 4, which indicates that the graph has a repeated root.

D) The graph will cross at x = 0 because it is a root and does not cross at x = 4.

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The value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]

The Integral is [tex]$$\int \frac{t}{t^4+5} d t$$[/tex]

Indefinite integrals are not defined using the upper and lower limits. The indefinite integrals represent the family of the given function whose derivatives are f, and it returns a function of the independent variable.

Let [tex]$t^2=u= > t d t=\frac{d u}{2}$[/tex]

The above Integral becomes

[tex]$\frac{1}{2} \int \frac{1}{u^2+(\sqrt{5})^2} d u=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{u}{\sqrt{5}}\right)+C$$[/tex]

Substitute u In terms of t

[tex]$$\int \frac{t}{t^4+5} d t=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]

Therefore, the value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex].

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The result for the error interval has already been rounded to the nearest integer, which is 4.8.

The numbers 10.3 and 10.5 are below and above, respectively (to 1 decimal place)

For the lower bound, we need to look halfway between 10.3 and 10.4 and for the upper bound, we need to look halfway between 10.4 and 10.5.

For the number to be rounded to 10.4 with one decimal point, it has to be between 10.35 and 10.45.

An inequality can be used to describe this.

10.35 ≤ x < 10.45

Thus, the error interval with the lower bound and upper bound are: 10.35 ≤ x < 10.45.

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If a certain store is selling packages of 10 pencils and 4 pens for back to school . The number of pencils that are in the larger package is 25 pencils.

First step is to find the  number of pencils per pen

Number of pencils per pen = 10 / 4

Number of pencils per pen = 2. 5

Now let find the number of pencils  that are in the larger package

Number of pencils = Number of pens x Pencils per pen

Number of pencils  = 10 x 2.5

Number of pencils = 25 pencils

Therefore we can conclude that the number of pencils is 25 pencils.

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Recursive  equation :

Thus,

For the given question;

Common ratio or difference : 90% or 0.9.

first term  = $26,500.

Thus, Recursive equation : f(n) = f(n - 1) + 9

Explicit  equation :

Thus,

Explicit equation : f(n) = 26,500 + (n - 1)(0.9).

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A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the period of time the tournament took place was $132,000. This means the tournament took place throughout is 12 days

How to find the number of members ?

When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.

A stadium brought in an average revenue of $11,000 per night for a professional sports tournament.

Total receipts for the period of time the tournament took place was $132,000.

This means the tournament took place throughout how many days?

since total divide by per night is equal to number of days

now 132000/11000= 12

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Answer:

$11.90

Step-by-step explanation:

.85(9.86 + 2.15 + 1.99)

.85(14)

11.90

If we take off 15% from 100%, that leaves 85%.  85% as a decimal is .85

Answer:

$11.90 total bill after discount.

Step-by-step explanation:

the original amount is $14.00 with 15% discount it will come down to $11.90. Your discount was $2.10.

Answer:

x=10 guests and $250

Step-by-step explanation:

Cater A=15x+100

Cater B=20x+50

2x+50=15x+100

5x=50

x=10

Answer: x=7.6

Step-by-step explanation:

x-2.6=5

Step 1: Move 2.6 to another side of the equation with addition

X-2.6+2.6=5+2.6

X=7.6

Check your answer!

7.6-2.6=5 Correct!

Answer:

Step-by-step explanation:

x - 2.6 = 5    

x = 5 + 2.6

x =  7.6

--------------------------

7.6 - 2.6 = 5        

5 = 5