What inequality is represented by this graph? 1 34 o O xS6 O XC6 O x26

Answer: Answer choice B

Step-by-step explanation:

Step-by-step explanation:

\(2p + q = 3 \\ p - 5q = 7 \\ \\ multiply \: the \: second \: equation \: by \: 2 \\ 2p - 10q = 14 \\ 2p - 10q - (2p + q) = 14 - 3 \\ 2p - 10q - 2p - q = 11 \\ - 11q = 11 \\ q = - 1 \\ \\ 2p + q = 3 \\ 2p - 1 = 3 \\ 2p = 4 \\ p = 2\)

No, the estimate of 11 × 2 = 22 tells us that 2.6509 is too small and the decimal point is placed incorrectly. The product has four decimal places and should have been 26.5090, but a missing zero on the end caused the decimal to end up in the wrong position.

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Since each term can be written as the previous term divided by three, this is a geometric sequence.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

For this problem, we have that each term can be written as the previous term multiplied by one third or divided by three, hence the division of consecutive terms is always the same and this is a geometric sequence.

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Answer:

After applying the distributive property, Ezra's expression was 8y + 16

After he used the commutative property, his expression was 16 + 8y

Step-by-step explanation:

Distributive property rule: a(x+y) = ax + ay
   Not much to explain here

Commutative property rule: a + b = b + a   or  xy = yx
   We use addition rule in this case, simply place 16 in front of 8y

Answer:

81

Step-by-step explanation:

25​, 36​, 49​, 64​, ...

36 - 25 = 11

49 - 36 = 13 = 11 + 2

64 - 49 = 15 = 13 + 2

64 + 15 + 2 = 81

Answers:

Refer to the graph below.

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Explanation:

If f(x) is an even function, then f(-x) = f(x) for all x in the domain.

What this means is that we have symmetry about the y axis. We can reflect that given curve over the y axis to generate the missing left side.

The graph shows that (1,1) is on the orange curve. It reflects over to (-1,1). This means 1 goes in the first box.

Use the rule \((x,y) \to (-x,y)\) to apply a y axis reflection. We simply just change the sign of the x coordinate from positive to negative, while keeping the y coordinate the same.

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

We can also see that (3,1) is also on the orange curve. It reflects over to (-3, 1) using that rule mentioned earlier.

1 goes in the second box

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The graph your teacher gave you shows that if we plugged in x = 5, then we get y = 3. In other words, the point (5,3) is on the orange graph.

It reflects over to (-5, 3) to show that x = -5 leads to the output y = 3

3 goes in the third box

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

Lastly, the point (6,3) reflects to (-6,3) when reflecting over the y axis.

3 goes in the fourth box.

See the graph below.

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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The first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.

What is the first quartile of the data set?

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

Since we have given a box and whisker plot.

As we know about the box and whisker method that :

Left most part of the box represents the first quartile and the rightmost part of the box represents the third quartile.

And the middle value is for median

so, we can conclude that

First quartile = 20

Third quartile = 40

Median = 25

Hence, the first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.

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Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

Answer:

6.2

Step-by-step explanation:

hope it helpes you in the long run

The difference in the addition of both fractions is that they have different lowest common multiples.

We want to add the fraction expression given as:

¹/₂ + ¹/₄

Taking the Lowest common multiple of 8, we have:

(4 + 2)/8 = 6/8

However, for the second fraction expression, we have:

¹/₂ + ¹/₃

Taking the lowest common multiple which is 6, we have:

(3 + 2)/6 = 5/6

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Answer:

£75.53

Step-by-step explanation:

3tshirt=£17.82

2pauntbrush=£13.94

4bags of pasta=£3.52

toral=£17.82+£13.94+£3.52+£41.25=75.53

Answer:

Either \(c = 12\) or \(c = (-12)\).

Step-by-step explanation:

Find the \(x\)-coordinate of the intersection of the two curves by equating their \(y\)-values and solving for \(x\):

\(x^{2} - c^{2} = c^{2} - x^{2}\).

\(x^{2} = c^{2}\).

\(x = c\) or \(x = (-c)\).

In other words, the two curves intersect both when \(x = c\) and when \(x = (-c)\).

Assume that \(c \ge 0\). The area enclosed would be over the range \((-c) < x < c\). Note that over this range, \(x^{2} \le c^{2}\), so \(x^{2} - c^{2} \le 0 \le c^{2} - x^{2}\). The curve \(y = c^{2} - x^{2}\) would be above \(y = x^{2} - c^{2}\).

Integrate the upper curve minus the lower curve \((c^{2} - x^{2}) - (x^{2} - c^{2})\) over this interval to find the area enclosed:

\(\begin{aligned}& \int\limits_{-c}^{c} \left((c^{2} - x^{2}) - (x^{2} - c^{2})\right)\, dx \\ =\; & \int\limits_{-c}^{c} \left(2\, c^{2} - 2\, x^{2}\right)\, dx \\ =\; & {\left[2\, c^{2}\, x - \frac{2}{3}\, x^{3}\right]}_{-c}^{c} && (\text{power rule}) \\ =\; & \left(2\, c^{2}\, c -\frac{2}{3}\, c^{3}\right) - \left(2\, c^{2}\, (-c) - \frac{2}{3}\, (-c)^{3}\right) \\ =\; & \frac{8}{3}\, c^{3} \end{aligned}\).

In other words, assuming that \(c \ge 0\), area enclosed between these two curves would be \((8/3)\, c^{3}\). Since this area is given, the value of \(c\) can be found as:

\(\begin{aligned}c &= \sqrt[3]{\frac{3}{8}\, (\text{Area})} = 12\end{aligned}\).

However, note that if \(c < 0\), the order of limits of the integral would need to be reversed:

\(\begin{aligned}& \int\limits_{c}^{-c} \left((c^{2} - x^{2}) - (x^{2} - c^{2})\right)\, dx \\ =\; & \cdots \\ =\; & {\left[2\, c^{2}\, x - \frac{2}{3}\, x^{3}\right]}_{c}^{-c} \\ =\; & \left(2\, c^{2}\, (-c) - \frac{2}{3}\, (-c)^{3}\right) - \left(2\, c^{2}\, c -\frac{2}{3}\, c^{3}\right) \\ =\; & \left(-\frac{8}{3}\, c^{3}\right) \end{aligned}\).

Hence, \(c = (-12)\) would also be a solution to this question.

Answer:

C: 85 + 30x ≥ 500

Step-by-step explanation:

None

Hi!!

Let's solve :

• 45x²-17x-6

Let's calculate delta :

a = 45 ; b= -17 ; -6

∆= b²-4ac

∆= (-17)²-4(45)(-6)

∆= 289 + 1080

∆= 1369

√∆= √1369

√∆= 37

Find x :

x' = (-b-√∆)/2

x' = -(-17-37)/2

x' = -(-54)/2

x' = 54/2

x' = 27

x'' = (-b+√∆)/2

x'' = -(-17+37)/2

x'' = -(20)/2

x'' = -20/2

x'' = -10

S= {-10 ; 27}

Answer:

She will make $793.8.

Step-by-step explanation:

You just divide for example 291.60/9 which gets you 32.4, which is how much she earns an hour

Answer:

$793.8

Step-by-step explanation:

Divide the amount of money earned by the number of hours worked.

For example: 291.60 ÷ 9 = 32.4

Multiply the answer by 24.5

32.4 × 24.5 = 793.8

The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.

To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.

Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).

The formula for sine is:

sin(angle) = opposite / hypotenuse

Rearranging the formula, we have:

hypotenuse = opposite / sin(angle)

In this case, the opposite side is the vertical distance, which is h.

So, the formula becomes:

hypotenuse = h / sin(angle)

To find h, we can use the formula for the length of the zip wire:

h = 25 * tan(angle)

Substituting this into the previous formula, we get:

hypotenuse = (25 * tan(angle)) / sin(angle)

Calculating the value, we have:

hypotenuse = (25 * tan(10°)) / sin(10°)

Using a calculator, we find:

tan(10°) ≈ 0.1763

sin(10°) ≈ 0.1736

Substituting these values, we can calculate the length of the zip wire:

hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters

Therefore, the length of the zip wire is approximately 25.35 meters.

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The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

3x² + 24x + 36 = 0

Step-by-step explanation:

A quadratic equation has the standard form ax² + bx + c = 0.
a, b and c are constants.

The roots of a quadratic equation represent the two solutions to the quadratic equation

Given that the roots are -2 and -6 we have

x = -2 and x = -6 as the solutions

Add 2 to both sides of x = -2 ==> x + 2 = 0
Add 6 to both sides of x = -6 ==> x + 6= 0

So (x+2)(x+6) = 0 is the factored representation of this equation. We have to multiply by a leading coefficient of 3

So the quadratic equation is
3(x+2)(x+6) = 0

Using the FOIL method
(x + 2)(x + 6) = x² + 6x + 2x + 12 = x² + 8x + 12

The leading coefficient is the coefficient of x² and is given as 3

So the quadratic equation in standard form is
3(x² + 8x + 12) = 0

==>  3x² + 24x + 36 = 0

If you solve this equation on a quadratic equation calculator you will get the solutions x = -2 and x=-6

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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Answer:

Step-by-step explanation:

In this scenario, the confidence interval represents the possible range of differences in the proportion of employees who skip breakfast when free breakfast is offered and when it's not. A confidence interval that does not include zero indicates that there is statistically significant evidence to suggest a difference in proportions between these two groups.

Therefore, for the first interval (-0.44,-0.16), since it does not include zero, we can be confident that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.

For the second interval (-0.25, 0.05), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

Similarly, for the third interval (-0.23, 0.15), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

So, the correct answer is:

For the interval (-0.44,-0.16), we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.

For the intervals (-0.25, 0.05) and (-0.23, 0.15), our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

base diameter = 15 inches

hight = 12 inches

diameter = 2(radius)

radius = diameter/2

radius = 15/2

radius = 7.5 inches