Find the equation of a straight line which passes through the point (3, 2) and is perpendicular to the line 3x + 5y =10. Hence, determine the gradient and y-intercept of the equation.​

For all rectangles, the area is the length multiplied by the height. For squares (a special type of rectangle), the length and height are the same, so you just use [tex]s^2[/tex], where [tex]s[/tex] is the side length.

[tex]A=s^2=16^2=\boxed{256}[/tex]

The formula for the area of the circle is [tex]\pi r^2[/tex], where [tex]\pi[/tex] is pi, a constant, and [tex]r[/tex] is the radius of the circle, or the length from the center point to the edge.

We're given the side length of the square, which is the same as the diameter of the circle (length from edge to edge going through the center point). Divide the diameter by [tex]2[/tex] to get the radius of [tex]8[/tex] kilometers.

[tex]A=\pi r^2=\pi8^2=\boxed{64\pi}\approx201.1[/tex]

The area of the blue section is simply the area of the square minus the area of the circle since we just want what's left over.

[tex]A=\boxed{256-64\pi}\approx54.9[/tex]

You can keep the answer exact (the boxed expression) or use the approximate value of 54.9, depending on the instructions for the assignment.

Answer:

20

Step-by-step explanation:

-3(-6+4)+2y(-6+-4)

18 - 12 - 12y - 8y

6 +-20y

The solution to When asked to find the sum of two mixed numbers with different denominators, you should before you add, find a common denominator.

For instance,

4 1/3 + 3 2/5

= 13/3 + 17/5

find common denominator

= (65+51) / 15

= 116/15

= 7 11/15

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I don't know please help me

Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

the sides of a 30 60 90 triangle are x, 2x, and [tex]x\sqrt{3}[/tex], with [tex]x\sqrt{3}[/tex] being opposite to the 60 degree angle, and x being adjacent to the 60 degree angle. If [tex]x\sqrt{3}[/tex] = 15 (as given from the image), you can calculate x to be [tex]5\sqrt{3}[/tex].

To achieve the goals, he needs to make 29.75 sales and 30 sales as add-on sales.

Since we have given that,

A total number of sales = 35

According to the question, his goal is to make add-on sales during 85% of sales.

So, His added sales would be 85% of sales,

A percentage calculator computes a number of values involving percentages, including the percentage difference between two given values.

85  percent of 35

[tex]=(\frac{85}{100}) \times 35\\[/tex]

=29.75

To achieve the goals, he needs to make 29.75 sales and 30 sales as add-on sales.

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Using the Fundamental Counting Theorem, there are 240 ways to choose general education courses from these 4 areas.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Considering the number of options for each course, the parameters are given as follows:

[tex]n_1 = 5, n_2 = 4, n_3 = 4, n_4 = 3[/tex].

Hence the number of ways is given by:

N = 5 x 4 x 4 x 3 = 240.

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The simplified function of [tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex] is [tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]

The function is given as:

[tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex]

Expand 108

[tex]f(x) = \frac 14(\sqrt[3]{27 * 4})^x[/tex]

Take the cube root of 27

[tex]f(x) = \frac 14 * 3^x(\sqrt[3]{4})^x[/tex]

Evaluate the product

[tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]

Hence, the simplified function of [tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex] is [tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]

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The answer to this question is choice C

Answer:

3.) b) The straight line that divides the parabola into half.

4.) b) 1/11^4

Explanation:

3. The axis of the symmetry is the straight line that divides the parabola into half.

Note down: the image below which shows a parabola (red line) and axis of symmetry (blue line).

4. Formula's: [tex]a^{-1} = \dfrac{1}{a}[/tex] , same with [tex]a^{-4 } = \dfrac{1}{a^4}[/tex]

So here: [tex]11^{-4}[/tex] is equivalent to [tex]\dfrac{1}{11^4}[/tex] which later equals to [tex]\dfrac{1}{14641}[/tex]

B and C are the letters from the table which have like terms which is denoted as option B.

This is referred to a type of polynomial which has two terms and is the sum or difference of a monomial.

From the table we can deduce the following:

B and C have a degree of 1 which means they are like terms thereby making them the most appropriate choice.

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Answer:

option 2 is correct

Step-by-step explanation:

[tex] \frac{2}{5} \: \: and \: \: \frac{3}{2} [/tex]

L.C.M. of 5 and 2 = 10

[tex] \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \\ \\ \frac{3 \times 5}{2 \times 5} = \frac{15}{10} [/tex]

[tex] \frac{5}{10} , \frac{6}{10} , \frac{7}{10} , \frac{8}{10} , \frac{9}{10}, \frac{10}{10} , \frac{11}{10} , \frac{12}{10} , \frac{13}{10} , \frac{14}{10} [/tex]

The 10 rationals numbers are :

[tex] \frac{1}{2} , \frac{3}{5} , \frac{7}{10} , \frac{4}{5} , \frac{9}{10} , \frac{1}{1}, \frac{11}{10} , \frac{6}{5} , \frac{13}{10} , \frac{7}{5} .[/tex]

The function is (c) (f.g)(x) = 24x^2 - 36x - 24; domain of all set of real numbers

The given parameters are:

f(x) = 3x - 6; g(x) = 8x +4

The composite function is calculated as:

(f.g)(x) = f(x) * g(x)

This gives

(f.g)(x) = (3x - 6) * (8x + 4)

Expand

(f.g)(x) = 24x^2 + 12x - 48x - 24

Evaluate the difference

(f.g)(x) = 24x^2 - 36x - 24

The above function is a quadratic function;

Quadratic functions have a domain of all set of real numbers

Hence, the function is (c) (f.g)(x) = 24x^2 - 36x - 24; domain of all set of real numbers

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Answer:

0.8 hrs it take to drive 80 km at 100 km an hour

Step-by-step explanation:

Hello,

Answer:

48 min

Step-by-step explanation:

Cross product :

80 km   ⇒  x h

100 km  ⇒ 1 h

x = (1 × 80)/100 = 8/10 = 0,8 h    

                                   = 0,8 × 60 min

                                  = 48 min

The attached graph represents a histogram that has a range of 55

The range is given as:

Range = 55

The range is calculated as:

Range = Maximum - Minimum

So, we have:

Maximum - Minimum = 55

Rewrite as:

Maximum = Minimum + 55

Let the minimum be 10.

So, we have:

Maximum = 10 + 55

Evaluate

Maximum = 65

The following dataset can be used to create the histogram

Score   Frequency

10           2

15            5

45          3

65         1

This is so because it has a range of 55

See attachment for the histogram

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The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the number of individual songs and y represent the number of albums, hence:

x + 8y ≤ 50   (1)

x ≤ 30    (2)

y > 2   (3)

The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.

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This exercise is about Linear Functions. From the values given, we can state that:

Given that the table represents a  linear function, so the function is a straight line.

Taking two points

(-12, 17)

(-10, 19)

To determine the slope between (-12, 17) and (-10, 19), we need to use the formula:

Slope = (y2-y1)/(x2 - x1)

Recall that:

(x1, y1) = (-12, 17); and

(x2, y2) = (-10, 19)

m = 19 -17/-10 -17

m = 1

Leveraging the point-slope to create the linear equation, we have:

y-y1 = m(x-x1)

where m is the slope of the line and (x₁, y₁) is the point substituting the values m = 1 and the point (-12, 17). Hence, we have:

y-y1 = m(x-x1)

→ y-17 = 1 (x-(-12))

→ y - 17 = x +12

y = x + 12 + 17

y = x + 29 ..................................Linear Equation

Next, we substitute x = -8 into the Linear Equation

y = (-8) + 29
y = 21

Hence, the missing y = 21; and

The missing x = -8

If we substitute y = 23 into the equation, we have:

y = x + 29
23 = x + 29
x = 29 - 23

x = 6

Thus, when the value of y = 23, the missing x is = 6

Conclusively,

The value of missing x = 6

The value of missing y = 21

Full Question

Determine any data values that are missing from the table, assuming that the data represent a linear function.

X Ix ly |-12 17 -10 19 -8 23

a. Missing x:-6 Missing y:22

b. Missing x:-7 Missing y:22

c. Missing x:-7 Missing y:20

d. Missing x:-6 Missing y:21

Please select the best answer from the choices provided.

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Answer:

Step-by-step explanation:

Answer:

vertex  =  (1/4 , -81/8)

Step-by-step explanation:

f(x) = y

f(x) = 2x²-x-10

a= 2

b= -1

c = -10

-b/2a

-(-1)/(2(2))

1/4

x = 1/4

f(x) = 2x²-x-10

y = 2x²-x-10

y = 2(1/4)²-(1/4)-10

y = 2/16-1/4-10

y = 2/16-4/16-160/16

y = -2/16-160/16

y = -162/16

y = -81/8

Answer:

72

Step-by-step explanation:

The amount of money​ you'll have at the end of 10 years is $3900.

Given that, P=$3000, R=3% and T=10 years.

The formula to find the simple interest is [tex]Interest=\frac{P \times T \times R}{100}[/tex].

Now, simple interest [tex]=\frac{3000 \times 10 \times 3}{100}=\$900[/tex].

Amount=Simple Interest+Principal

=900+3000=$3900

Therefore, the amount of money​ you'll have at the end of 10 years is $3900.

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Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).

From the graph;

Using midpoint formula;

[tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

We substitute in our values

[tex]( \frac{0+2}{2},\frac{4+(-2)}{2}) \\\\( \frac{2}{2},\frac{4-2)}{2}) \\\\( \frac{2}{2},\frac{2}{2}) \\\\( 1, 1 )[/tex]

Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).

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Answer:

Step-by-step explanation:(-4, -1) --> (4, -1). Translating two units to the right means adding two units to the x-coordinate: (4, -1) --> (6, -1). This is our final point

Answer:

Step-by-step explanation:

Formula

c^2 = a^2 + b^2

Givens

Solution

c^2 = 3^2 + 8^2                 Substitute givens

c^2 = 9 + 64                       Combine

c^2 = 73                             Take the square root of both sides

√c^2 = √73  

c = √73                        \

Exact answer

c = √73                                73 is prime. It will break down no further

Approximate answer

c = 8.54400                         Both zeros must be entered

Answer:

A. there is exactly one solution. the solution set is {(2, 0)}.

Step-by-step explanation:

3x + 8y = 6

3x - 8y = 6

when we add these 2 equations, we get

6x + 0 = 12

6x = 12

x = 2

now we use one of the original equations to get y :

3×2 + 8y = 6

6 + 8y = 6

8y = 0

y = 0

The expression that can be used to find the area of the tiled floor is 4w² + 200w

Length = 70 Meters

Width = 30 meters

Area = length × width

= 70 × 30

= 2100

Length = 70 + 2w meters

Width = 30 + 2w meters

Area = length × width

= (70+2w) (30+2w)

= 2100 + 140w + 60w + 4w²

= 4w² + 200w + 2100

Area of the tiled floor = Area of new rectangle - area of old rectangle

= (4w² + 200w + 2100) - 2100

= 4w² + 200w + 2100 - 2100

= 4w² + 200w

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The system of equation that will represent her situation is as follows:

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

At store A she will pay a total sum of $50.73 for bread and milk.

At store B she will pay a total sum of $51.63  for bread and milk.

Therefore, the system of equation that will represent her situation is as follows:

where

Therefore,

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

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Answer:

(c - 2d) (3a - 2b)

Step-by-step explanation:

if you need the steps just ask me in the comments and I’ll type them lol

Answer:

c

Step-by-step explanation:

y=[tex]\sqrt{x+7}[/tex]

Answer: Addition Rule

Step-by-step explanation:This is the probability that either one or both events occur. a. If two events, say A and B, are mutually exclusive - that is A and B have no outcomes