expand the square of a binomial (y^7-11)^2​

Answer:

7.61

Step-by-step explanation:

Sum all of the values

2.22+2.97+2.42=7.61

Answer:

761

Step-by-step explanation:

Answer:

D. c/6 - x

Step-by-step explanation:

Rearranging with subject '6y':

6y = c - 6x

Dividing the above equation by 6 to get subject 'y':

y = c/6 - x

Feel free to mark this as brainliest and hope this helps! :)

Extract the common factor 6.

\(\bf{6(x+y)=c }\)

Divide both sides by 6.

\(\bf{x+y=\dfrac{c}{6} }\)

Subtract x from both sides.

\(\bf{y=\dfrac{c}{6}-x \ \ \to \ \ \ Answer }\)

Therefore, the correct option is "D".

The solutions to the linear function are;

1. The soccer team makes more money per car ($8) than the French club ($5).

2. The graph that demonstrates Arnold's journey is graph 3

3. The graph that demonstrates Francisco's journey is graph 1

4. The graph that demonstrates Celia's journey is graph 2

To determine which group makes the most money per car, we can calculate the slope of the linear function representing the amount earned per car washed for both the French club and the soccer team. The slope of a linear function is the change in the dependent variable (y) divided by the change in the independent variable (x).

Let's calculate the slope for the soccer team. We can choose any two points to calculate the slope. Let's use the points (3, 24) and (6, 48):

Slope (m) = (change in y) / (change in x) = (48 - 24) / (6 - 3) = 24 / 3 = 8

The soccer team earns $8 per car washed.

We can choose any two points to calculate the slope for the French club. Let's use the points (2, 10) and (4, 20):

(20 - 10) / (4 - 2) = 10 / 2 = 5

The French club earns $5 per car washed

The above answer is dependent on the questions below;

The french club and soccer team are washing cars to earn money. The amount earned, (y) dollars for washind (x) cars is a linear function.  Which group makes the most money per car? explain

                                      French club

Number of cars (x)                       Amount earned (y)

2                                                         10

4                                                          20

6                                                          30

8                                                         40

10                                                         50

Soccer team

Number of cars (x)                       Amount earned (y)

3                                                      24

6                                                       48

9                                                      72

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Mario is left with 3/10 lb of the salt at the end of the basketball game.

Salt in the concession stand with Mario at the beginning of the basketball game  = 8/10 lb

Salt used by Mario while making 20 batches of popcorn during the game = 1/2 lb

Salt remaining at the end of the game = 8/10 - 1/2

Multiplying the numerator and denominator by 5 and subtracting it from 8/10 we get:

8/10 - 5/10 = 3/10

Therefore, the salt left with Mario at the end of the game is 3/10 lb

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The minimum number of books she must sell to make a profit is given as follows:

1862 books.

The profit function is given by the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

The revenue and cost functions for this problem are given as follows:

Hence the profit function is given as follows:

P(x) = 6.53x - 10125 - 1.11x

P(x) = 5.44x - 10125.

She makes a profit when P(x) > 0, hence:

5.44x - 10125 > 0

x > 10125/5.44

x > 1861.2 books.

Hence the must sell at least 1862 books to make a profit, as the number of books is a countable amount, hence it must have an integer value.

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Answer: Focus, Vertex, Axis, and Directrix.

Step-by-step explanation:

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

Answer: 17.4

Step-by-step explanation:

There isn't much to it... it's basic addition.

I guess if you were not using a calculator you would set it up like this:

3.1

+7.4

+6.9

---------

17.4

Answer:

17.4

Step-by-step explanation:

if you estimate all of these you get 3,7, and 7, these(added together) are 17,

9514 1404 393

Answer:

  a) 2.038 seconds

  b) 5.918 meters

  c) 1.076 seconds

Step-by-step explanation:

For the purpose of answering these questions, it is convenient to put the given equation into vertex form.

  h = -4.9t² +9.2t +1.6

  = -4.9(t² -(9.2/4.9)t) +1.6

  = -4.9(t² -(9.2/4.9)t +(4.6/4.9)²) +1.6 +4.9(4.6/4.9)²

  = -4.9(t -46/49)² +290/49

__

a) To find h = 0, we solve ...

  0 = -4.9(t -46/49)² +290/49

  290/240.1 = (t -46/49)² . . . . subtract 290/49 and divide by -4.9

  √(2900/2401) +46/49 = t ≈ 2.0378 . . . . seconds

The ball takes about 2.038 seconds to fall to the ground.

__

b) The maximum height is the h value at the vertex of the function. It is the value of h when the squared term is zero:

  290/49 m ≈ 5.918 m

The maximum height of the ball is about 5.918 m.

__

c) We want to find t for h ≥ 4.5.

  h ≥ 4.5

  -4.9(t -46/49)² +290/49 ≥ 4.5

Subtracting 290/49 and dividing by -4.9, we have ...

  (t -46/49)² ≥ 695/2401

Taking the square root, and adding 46/49, we find the time interval to be ...

  -√(695/2401) +46/49 ≤ t ≤ √(695/2401) +46/49

The difference between the interval end points is the time above 4.5 meters. That difference is ...

  2√(695/2401) ≈ 1.076 . . . . seconds

The ball is at or above 4.5 meters for about 1.076 seconds.

__

I like a graphing calculator for its ability to answer these questions quickly and easily. The essentials for answering this question involve typing a couple of equations and highlighting a few points on the graph.

_____

Additional comment

I have a preference for "exact" answers where possible, so have used fractions, rather than their rounded decimal equivalents. The calculator I use deals with these fairly nicely. Unfortunately, the mess of numbers can tend to obscure the working.

"Vertex form" for a quadratic is ...

  y = a(x -h)² +k . . . .  where the vertex is (h, k) and 'a' is a vertical scale factor.

In the above, we have 'a' = -4.9, and (h, k) = (46/49, 290/49) ≈ (0.939, 5.918)

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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The required area of the sector of the circle with radius 5 yards and central angle 3.8 radians is approximately equals to  47.500 square yards (rounded to three decimal places).

Radius of the circle is equal to 5 yards

Central angle of the sector of the circle is equal to 3.8 radians.

Let us consider θ be the central angle in radians,

And r be the radius of the circle.

Let 'A' be the area of the sector of a circle.

The formula for the area of a sector of a circle is equal to,

A = (θ/2) r^2

Substitute the values in the formula of the area of the sector we have,

⇒ A = (3.8/2) × 5^2

⇒ A = 1.9 × 25

⇒A = 47.500 square yards (rounded to three decimal places)

Therefore,  the area of the sector of the circle is approximately equals to  47.500 square yards (rounded to three decimal places).

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1. The quadratic function for the Area in terms of x: A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is 0.

3. The maximum cross-sectional area is square inches 0.

To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.

1. Write a quadratic function for the area in terms of x:

The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is:

To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.

3. The maximum cross-sectional area is square inches:

Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.

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Answer:

10.50

Step-by-step explanation:

5+5.5=10.5............

Answer:

The answer is B $10.50 :)

To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.

First, let's find the multiplicative inverse of (4/3 - 4/9):

Multiplicative inverse = 1 / (4/3 - 4/9)

To simplify the expression, we need a common denominator:

Multiplicative inverse = 1 / ((12/9) - (4/9))

= 1 / (8/9)

= 9/8

Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:

Subtracted value = (7/12 + 7/8) - (9/8)

To perform this calculation, we need a common denominator:

Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)

= (14/24 + 21/24) - (9/8)

= 35/24 - 9/8

To simplify further, we need a common denominator:

Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)

= 35/24 - 27/24

= 8/24

= 1/3

Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).

The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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Answer:

AB = 28 , BC = 17.5 , X = 13.2

Step-by-step explanation:

since the figures are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{AB}{PQ}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{AB}{8}\) = \(\frac{14}{4}\) ( cross- multiply )

4 AB = 8 × 14 = 112 ( divide both sides by 4 )

AB = 28

and

\(\frac{BC}{QR}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{BC}{5}\) = \(\frac{14}{4}\) ( cross- multiply )

4 BC = 5 × 14 = 70 ( divide both sides by 4 )

BC = 17.5

similarly for the 2 similar figures

\(\frac{x}{6}\) = \(\frac{11}{5}\) ( cross- multiply )

5x = 6 × 11 = 66 ( divide both sides by 5 )

x = 13.2

Answer:

\(\overline{AB}=28\)

\(\overline{BC}=17.5\)

\(x=13.2\)

Step-by-step explanation:

If quadrilateral PQRS is similar to quadrilateral ABCD, their corresponding sides are in the same ratio:

\(\overline{PQ} : \overline{AB} = \overline{QR} : \overline{BC} = \overline{RS} : \overline{CD} = \overline{SP}:\overline{DA}\)

From inspection of the two quadrilaterals, the given side lengths are:

\(\overline{PQ} = 8\)

\(\overline{QR} = 5\)

\(\overline{RS} = 6\)

\(\overline{SP} = 4\)

\(\overline{DA} = 14\)

Substitute these into the ratio equation:

\(8 : \overline{AB} = 5 : \overline{BC} = 6 : \overline{CD} = 4:14\)

Solve for AB:

\(8 : \overline{AB} = 4:14\)

   \(\dfrac{8}{\overline{AB}}= \dfrac{4}{14}\)

 \(8 \cdot 14=4 \cdot{\overline{AB}}\)

   \(\overline{AB}=\dfrac{8 \cdot 14}{4}\)

  \(\boxed{\overline{AB}=28}\)

Solve for BC:

\(5 : \overline{BC} = 4:14\)

  \(5 \cdot 14=4 \cdot \overline{BC}\)

    \(\overline{BC}=\dfrac{5 \cdot 14}{4}\)

   \(\boxed{\overline{BC}=17.5}\)

\(\hrulefill\)

Assuming the two figures are similar, their corresponding sides are in the same ratio. Therefore:

\(x:6=11:5\)

   \(\dfrac{x}{6}=\dfrac{11}{5}\)

   \(x=\dfrac{11 \cdot 6}{5}\)

   \(x=\dfrac{66}{5}\)

  \(\boxed{x=13.2}\)

The distinguishing feature between a square and a rectangle is that all sides of a square are equal in length.

Yes, a square is a special type of rectangle because it possesses all the properties of a rectangle.

The distinguishing feature of a rhombus is that all sides are equal in length, while a parallelogram can have unequal side lengths.

Yes, a rhombus is a special type of parallelogram because it possesses the properties of a parallelogram and has all sides equal in length.

The three features used to describe 3-dimensional objects are faces, edges, and vertices.

The common properties between a square and a rectangle are that both have four sides, four right angles (90 degrees), and opposite sides that are parallel. The distinguishing feature is that all sides of a square are equal in length, while a rectangle can have unequal side lengths.

Yes, a square is a special type of rectangle. A rectangle is defined as a quadrilateral with four right angles, while a square is a specific type of rectangle where all sides are equal in length. Since a square possesses all the properties of a rectangle, including four right angles, it can be considered a special case of a rectangle.

The common properties between a rhombus and a parallelogram are that both have four sides and opposite sides that are parallel. The distinguishing feature of a rhombus is that all sides are equal in length, while in a parallelogram, the opposite sides are equal in length.

Yes, a rhombus is a special type of parallelogram. A parallelogram is defined as a quadrilateral with opposite sides that are parallel. A rhombus possesses this property, but it also has the additional feature of having all sides equal in length. Therefore, a rhombus can be considered a special case of a parallelogram.

The three features used to describe 3-dimensional objects are:

Faces: The flat surfaces that make up the object.

Edges: The lines where two faces intersect.

Vertices: The points where multiple edges meet.

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Answer:

she needs to purchase 33 more bags

The required distance between the points  (−1,6) and (−1,7). is 1 unit.

Given that,
using the distance formula to evaluate the distance between the points  (−1,6) and (−1,7).

Distance is defined as the object traveling at a particular speed in time from one point to another.

Here,
The distance formula is given as,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
Substitute the values in the above equation,
D = √[[-1 + 1]² + [7 - 6]²]
D = √[0 + 1]
D = 1

Thus, the required distance between the points  (−1,6) and (−1,7). is 1 unit.

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Answer:

Step-by-step explanation:

for circle

diameter = 26 cm

radius = diamtere/2

=26/2

=13 cm

area of circle  = πr^2

=3.14^13^2

=3.14*169

=530.66 cm^2

=531 cm^2   (after round off )

area of square= l^2

=5.1^2

=26.01 mi^2

are of rectangle = l *b

=6*5.1

=30.6 m^2

area of triangle = base*height / 2

=9*6.4 / 2

=57.6 / 2

=28.8 yd^2

An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is

The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

f(x) = a(b)^x

Where:

Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 13 = 87% = 0.87.

By substituting the parameters into the exponential equation, we have the following;

\(f(x) = 95(0.87)^x\)

When x = 12, we have;

\(f(12) = 95(0.87)^{12}\)

f(12) = 17.86 ≈ 18 milligrams.

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Answer:

  x = 9 inches

Step-by-step explanation:

You want the value of x in the similar triangles shown.

Corresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.

  6/4 = (6+x)/10

  15 = 6 +x . . . . . . . . multiply by 10

  9 = x . . . . . . . . . subtract 6

The measure of x is 9 inches.

__

Additional comment

You could also write the proportion ...

  6/4 = x/(10 -4)

  x = 36/4 = 9 . . . . . . . multiply by 6

You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.

<95141404393>

(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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The amount of Bruno's yearly pay deducted for FICA is approximately

A. $4,524.15. The closest option provided is A. $4521.15.

To calculate the amount of FICA deducted from Bruno's yearly pay, we need to consider the specific FICA tax rates for Social Security and Medicare.

As of 2021, the Social Security tax rate is 6.2% on income up to a certain threshold, and the Medicare tax rate is 1.45% on all income.

Given that Bruno's gross income per pay period is $4925 and he is paid monthly, we can calculate the yearly gross income as follows:

Yearly gross income = $4925 * 12 = $59,100

To calculate the FICA deduction, we need to find the sum of the Social Security and Medicare taxes. Using the respective tax rates mentioned earlier:

Social Security deduction = $59,100 * 6.2% = $3,667.20

Medicare deduction = $59,100 * 1.45% = $856.95

Adding these two deductions together:

FICA deduction = $3,667.20 + $856.95 = $4,524.15

Therefore, the amount of Bruno's yearly pay deducted for FICA is approximately $4,524.15.

The closest option provided is A. $4521.15.

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Answer:

41.4 im pretty sure

Step-by-step explanation:

Answer:

I think you put that } by accident so if its 4+2y=6

your answer is y=1

Based on the data, the mean would be the best measure of center to describe a typical value in the data set.

To create a dot plot, we can list the numbers in order and place a dot above the corresponding value on the number line.

20 ••

21 ••

22 •

23 ••••

24 •••••

25 ••

26 ••

27 •

The dot plot shows a relatively symmetric distribution of the data, with the majority of values clustered around the middle. Therefore, the mean would be a good measure of center to describe a typical value of the data set.

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Answer:

the common difference is 2

and a₁ = 2

We need to find the first term given two terms of an arithmetic sequence:

a₆ = 12

a₁₄ = 28

First, we will solve for the common difference 'd'. To do this, we will create a system of equations using the given terms and the following formula:

From the given, we can have:

We will then substitute Eq.2 with Eq.1 to solve for the common difference 'd'

We now have a common difference d = 2

We can now solve the first term of the arithmetic sequence using any of the equations that we had. In this case, let us use Eq.2

Therefore, the first term of the sequence is 2.

We wrote pricing equations and solved them to find that when the number of hats is 2, we found that the cost of both companies is the same and it is $14.

What is an equation?

A mathematical equation is a formula that uses the equals sign (=) to represent the equality of two expressions. The expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side," respectively, of the equation. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

Given,

  Price charged by company S for design = $10

  Price charged by company S for one hat = $2

Price charged by company OF for design = $6

  Price charged by company S for one hat = $4

Let the total price be P and the number of hats be n.

1) For company S the price equation is,

   P = 10 + 2n

 For company OF the price equation is,

 P = 6 + 4n

3) When the cost is the same, the equations become equal

  10 + 2n = 6 + 4n

  4 = 2n

 n = 2

P = 6 + 4 * 2 = 6 + 8 = $14

Therefore after solving the above equations, when the number of hats is 2, we found that the cost of both companies is the same and it is $14.

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