6. The height of Martin's rectangular door is 8
inches more than 3 times the width. If w
represents the width of the door, write an
expression
to represent the area of the door.

The equation f(x) = (x - 2)² + 6 in the standard form will be f(x) = x² - 4x + 10.

What is  function in math ?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

                         Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.

The function is given below.

f(x) = (x - 2)² + 6

Convert the equation into a standard form. Then we have

f(x) = (x - 2)² + 6

f(x) = x² - 4x + 4 + 6

f(x) = x² - 4x + 10

The equation f(x) = (x - 2)² + 6 in the standard form will be f(x) = x² - 4x + 10.

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Answer:

Step-by-step explanation:

If Sara is making 3 batches of chocolate chip cookies using 2 1/4 cups of flour per batch, then the total amount of flour she uses for the chocolate chip cookies is:

3 batches x 2 1/4 cups per batch = 6 3/4 cups of flour

Since she will use 12 3/4 cups of flour for all six batches, the amount of flour used for the oatmeal cookies can be found by subtracting the amount of flour used for the chocolate chip cookies from the total amount of flour:

12 3/4 cups - 6 3/4 cups = 6 cups

To determine how many cups of flour are needed for each batch of oatmeal cookies, we can divide the total amount of flour used for the oatmeal cookies by the number of batches:

6 cups ÷ 3 batches = 2 cups per batch

Therefore, the equation that can be used to determine how many cups of flour are needed for each batch of oatmeal cookies is:

Flour needed per batch of oatmeal cookies = Total flour needed for oatmeal cookies ÷ Number of oatmeal cookie batches

Or, in this case:

Flour needed per batch of oatmeal cookies = 6 cups ÷ 3 batches = 2 cups per batch.

Answer:

A rotation about the origin 180 degrees means that the pre-image essentially rotates half an actual circle

The rule for 180 degrees rotation is (x,y)-->(-x, -y)

So the points of this quadrilateral are now

(1,3) = (-1, -3)

(4,1)=(-4, -1)

(4,4)=(-4, -4)

(1,4)=(-1,-4)

So it moves from 1st to 3rd quadrant

HOPE THIS HELPS

Answer:

How?

Step-by-step explanation:

The true statement of the equation 4+-2=5 is false

From the question, we have the following parameters that can be used in our computation:

4+-2=5

To determine the trie statement, we evaluate the expression 4 + (-2)

Using the above as a guide, we have the following:

The sum of 4 and -2 is:

4 + (-2) = 2

So, we have

2 = 5

The above is not true

Hence, the statement "4 + (-2) = 5" is false.

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Answer: 5

Step-by-step explanation:

Use the Formula d = √((x2 - x1)2 + (y2 - y1)2)

Find the difference between coordinates:

(x2 - x1) = (-3 - 0) = -3

(y2 - y1) = (-2 - 2) = -4

Square the results and sum them up:

(-3)2 + (-4)2 = 9 + 16 = 25

Now Find the square root and that's your result:

Exact solution: √25 = 5

Approximate solution: 5

Answer:

300 feet

Step-by-step explanation:

A square has 4 equal sides and the area of a square is length x length which is also the square of the length i.e 10²

So one of the square's area = 10 x 10

=100

So the three squares have a square of 100 +100+100

300² feet

The distance between points A and B is: A. 4√5 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-4))² + (-2 - 2)²]

Distance = √[(8)² + (-4)²]

Distance = √(64 + 16)

Distance = √80

Distance = √16 × √5

Distance = 4√5 units.

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Answer:

none of them are right it is 4 to the 10

Step-by-step explanation:

2 quart of blue paint and 5/4 quart of red paint is needed to make 3 1/4 quart purple paint

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

2/5 quart of blue paint is mixed with 1/4 quart of red paint to make purple paint. Hence:

Ratio of blue paint to red paint = (2/5) : (1/4) = 8 : 5

Therefore for 3 1/4 quart of purple paint:

Amount of blue paint = (8/13) * 3 1/4 = (8/13) * 13/4 = 2 quart

Amount of red paint = (5/13) * 3 1/4 = (5/13) * 13/4 = 5/4 quart

2 quart of blue paint and 5/4 quart of red paint is needed to make the purple paint

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Answer:

The volume of the ice cream scoop is less than the volume of the cone. So, when the ice cream melts, it will fit in the cone without overflowing.

The inequality Kailyn can use to ensure that she completes at least 25 minutes of Mindplay each day over 4 days to complete a total of 100 minutes is x ≥ 25.

What is inequality ?

An inequality is a mathematical statement that compares two values or expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

To split the 100 minutes evenly over 4 days, Kailyn would need to complete at least 25 minutes each day.

To express this mathematically as an inequality, you can use the greater than or equal to symbol (≥) to indicate that Kailyn must complete at least 25 minutes each day:

Let x be the number of minutes Kailyn completes each day. Then the inequality would be:

x ≥ 25

This means that Kailyn must complete at least 25 minutes of Mindplay each day to ensure that she completes all 100 minutes in the given 4 days.

Therefore, the inequality Kailyn can use to ensure that she completes at least 25 minutes of Mindplay each day over 4 days to complete a total of 100 minutes is x ≥ 25.

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The best interpretation of the y-intercept of the linear function is given as follows:

D. The model indicates that 1-bedroom apartments in New York had an average rent of 800 dollars in 2000.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The variables for this problem are given as follows:

Hence option D gives the correct interpretation of the intercept of the line.

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Answer:

Below

Step-by-step explanation:

If the 'y'-axis is # larvae  and the  'x' axis is °C  then the peak  would show the greatest # larvae (450) would be at 5 °C

Answer:

B) This means that the number of larvae is greatest at 5 degrees Celsius.

Step-by-step explanation:

On the given graph:

The curve is a parabola that opens downwards. Therefore, its vertex is the maximum value.

From observation of the graph, the vertex (peak) is (5, 450).

This means that the number of larvae reaches its maximum value of 450 at a temperature of 5 degrees Celsius.

5[1-[tex](2/3)^{8}[/tex]/1-2/3] can be used to evaluate the series 8 E k=1 5 (2/3) k-1 through geometric series.

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios. In other words, the following term is obtained by multiplying each phrase in a geometric series by a constant.

Hence, a geometric series has the formula a, ar, ar2, where an is the first term and r are the sequence's common-ratio. Either a positive or negative integer can be used to describe the common ratio.

The given series is:

Now,we want to write an expression that can be used to evaluate this series.

Since this is a geometric series, we use the formula for the sum of the first k terms: Sk = a (1-[tex]r^{k}[/tex]/1-r)

From the given series the first term a= 5 is, and the common ratio is r =2/5 and k=8

We substitute the values to obtain:

S8= 5[1-[tex](2/3)^{8}[/tex]/1-2/3]

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Answer:

f=-15

Step-by-step explanation:

f/3 +22=17

take away 22 from both sides

f/3=-5

then times by 3

f=-15

so f=-15

The required number of tubs are 17.55 tubs.

To solve the problem, we need to find the total amount of ice cream used in ounces and then convert it to pounds to find the number of tubs used.

Number of scoops for regular cones = 2 scoops/cone

Number of scoops for large cones = 3 scoops/cone

Total number of scoops of ice cream used for regular cones = 2 scoops/cone x 234 cones = 468 scoops

Total number of scoops of ice cream used for large cones = 3 scoops/cone x 156 cones = 468 scoops

Total number of scoops of ice cream used = 468 scoops + 468 scoops = 936 scoops

Total amount of ice cream used in ounces = 936 scoops x 3 ounces/scoop = 2808 ounces

Total amount of ice cream used in pounds = 2808 ounces / 16 ounces/pound = 175.5 pounds

Number of tubs of ice cream used = 175.5 pounds / 10 pounds/tub = 17.55 tubs

Rounding up to the nearest whole number, we get:

Answer: (C) 17.55 tubs.

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Answer: C

Step-by-step explanation: is closer to 5000

Answer:

the missing ratio is 12

Step-by-step explanation:

essentially all of these ratios should simplify to 3:4

The equation for the function with the described transformations is y(x) = -2f(x+1) + 8.

Starting with the basic function of f(x), we can apply the described transformations in the following order:

Vertical stretching by a factor of 2: We multiply the output of the function by 2. This results in a new function g(x) = 2f(x).

Reflection across the x-axis: We flip the sign of the output of the function. This results in a new function h(x) = -g(x) = -2f(x).

Translation 1 unit left and 8 units up: We shift the graph of the function 1 unit to the left and 8 units up. This can be achieved by replacing x with (x+1) and adding 8 to the output.

This results in a new function y(x) = h(x+1) + 8 = -2f(x+1) + 8.

Putting it all together, the equation for the function with the described transformations is:

y(x) = -2f(x+1) + 8

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The complete question is below:

Write an equation for f(x) when it is vertically stretched by a factor of 2, reflected across the x-axis, then translated 1 unit left and 8 units up.​

The interval which is function increasing and decreasing is  

A) x = -3.5 and x = -1.5.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here we know that The slope determines if the function is an increasing linear function, a decreasing linear function, or a constant function. f(x)=mx+b is an increasing function if m>0. f(x)=mx+b is an decreasing function if m<0

Then according to the graph ,

The highest point = x=-3.5

The lowest point = x=-1.5

Then the interval which is function increasing and decreasing is  

A) x = -3.5 and x = -1.5.

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Answer:

in image...

if it helped please mark me a brainliest :))

The width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.

What is Area of rectangle ?
Area of rectangle can be defined as product of length and breadth.

We know that the area of the rectangle is given by the function A(x) = x² + 8x, where x is the width of the rectangle. We also know that the area of the rectangle is 33 in². So we can set up the equation:

x² + 8x = 33

To solve for x, we can rearrange the equation and set it equal to zero:

x² + 8x - 33 = 0

We can now use the quadratic formula to solve for x:

[tex]x = (-b\±\sqrt{(b^2 - 4ac)}) / 2a[/tex]

where a = 1, b = 8, and c = -33. Substituting these values, we get:

[tex]x = (-8\±\sqrt{(8^2 - 4(1)(-33))}) / 2(1)[/tex]

[tex]x = (-8\± \sqrt{(256)}) / 2[/tex]

x = (-8 ± 16) / 2

So x = -12/2 or x = 4.

Therefore, the width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.

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Answer:

Inverse Operation

Step-by-step explanation:

The percentage of his paycheck went to paying taxes is, 28.66%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given a paycheck of $466.34.

Now, The amount of the following taxes are,

FCIA MED TAX: $8.70.

FICA SS TAX: $37.20.

FED TAX: $59.57.

MA ST TAX: $28.19.

Therefore, The total amount of tax is, $(8.70 + 37.20 + 59.57 + 28.19).

= $133.66.

So, The percentage of his pay that goes to tax is,

= (133.66/466.34)×100%.

= 28.66%.

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Answer:

(1 , -2)

Step-by-step explanation:

We are told that there is a translation of (x-4 , y-3)

This simply means that the x-axis moves to the left by 4 points and that the y-axis moves down 3 points. (if it was a plus not minus then points would move up and to the right)

1) Move the x-axis

We can see that the x-axis of b is 5. To move it to the left 4 we subtract 5 by 4

2) Move the y-axis

We can see that the y-axis of b is 1. To move it down we subtract 1 by 3

This leaves us with (1 , -2)

Hope this helps, have a lovely day! :)

Step-by-step explanation:

What we do here is divide 43 by 50

[tex] \frac{43}{50} = 0.86 = 86\%[/tex]

5/6 is the value of b.......

The angles on the diagram are vertical angles and the value of x is 25.

The two angles are said to be adjacent angles when they have a common vertex and side.

On the other hand, vertical angles are angles that are opposite of each other when two lines cross and they are conguent.

Therefore, the angles on the diagram are vertical angles.

Now, since vertical angles are congruent.

Angle 75 and angle (4x - 25 ) are equal.

Hence;

4x - 25 = 75

Solve for x

4x - 25 = 75

Add 25 to both sides

4x - 25 + 25 = 75 + 25

4x = 75 + 25

4x = 100

Divide both sides by 4

4x/4 = 100/4

x = 100/4

x = 25

Therefore, the value of x is 25.

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The two functions have equivalent zeros if k = 60.

Here we have two functions which are:

f(x) = 4x - 20

g(x) = -12x + k

We want these two functions to have equivalent zeros, so first let's find the zero of f(x), we will get:

f(x) = 4x - 20 =0

4x  = 20

x = 20/4

x = 5

And that must also be a zero of g(x), then:

-12*5 + k = 0

Solving this for k.

-60 + k = 0

k = 60

That must be the value of k.

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There for the answer is the volume of the pyramid is equal to V = 1/3 (n³ - n²).

What do math lengths mean?

The measurement or size of a thing end to end is referred to as its length. In other words, it is the larger of an object's upper two or three geometric dimensions. The dimensions of a rectangle, for instance, are its length and width.

We know that.

The volume of pyramid is equal to

V =1/3 (area of base) × height

In this problem

Area of base = n² units²

Height = (n - 1) units

Substitute in the formula above

V = 1/3 n² × (n - 1)

V = 1/3 (n³ - n²) units³

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