Which of the following equations has only one solution?
x2 - 8x + 16 = 0
x(x - 1) = 8
x2 = 16

A simplification of the expression include the following: B. [tex]2\sqrt{33} +3\sqrt{6}[/tex].

In Mathematics and Geometry, an exponent can be represented or modeled by this mathematical expression;

[tex]b^n[/tex]

Where:

In Mathematics and Euclidean Geometry, an expression is typically used for illustrating the relationship that exist between twoor more variables and numerical quantities, without an equal to sign (symbol).

Based on the information provided above, we can logically deduce the following expression;

[tex]\sqrt{6} (\sqrt{22} +3)\\\\ (\sqrt{6} \times \sqrt{22} + \sqrt{6} \times3)\\\\\sqrt{132} +3\sqrt{6}\\\\\sqrt{4 \times 33} +3\sqrt{6}\\\\2\sqrt{33} +3\sqrt{6}[/tex]

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The simplified expression is [tex]\(\sqrt{132} + 3\sqrt{6}\).[/tex] Hence, the correct answer is (a).

To simplify the expression [tex]\(\sqrt{6} (\sqrt{22} + 3)\)[/tex], you can use the distributive property, which allows you to multiply each term inside the parentheses by [tex]\(\sqrt{6}\)[/tex]. Here's how:

[tex]\(\sqrt{6} (\sqrt{22} + 3) = \sqrt{6} \cdot \sqrt{22} + \sqrt{6} \cdot 3\)[/tex]

Now, simplify each term:

1. [tex]\(\sqrt{6} \cdot \sqrt{22} = \sqrt{6 \cdot 22} = \sqrt{132}\)[/tex]

2. [tex]\(\sqrt{6} \cdot 3 = 3\sqrt{6}\)[/tex]

So, the expression simplifies to:

[tex]\(\sqrt{6} (\sqrt{22} + 3) = \sqrt{132} + 3\sqrt{6}\)[/tex]

The correct answer is (a) [tex]\(\sqrt{132} + 3\sqrt{6}\).[/tex]

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Answer:

They do not form a right triangle

Step-by-step explanation:

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Check the coordinates in each graph.

(0, 4), (1, 4.5), (2, 5), (3, 27.5)

The graph that satisfies the coordinates given above is the answer.

The graph shown is not clearly visible.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Slope = m = 1/2

y-intercept = 4

This means,

The equation of the line is y = (1/2)x + 4.

For x = 0, y = 4

For x = 1, y = 1/2 + 4 = 9/2 = 4.5

For x = 2, y = 1 + 4 = 5

For x = 3, y = 3/2 + 4 = 11/4

The coordinates from the line are:

(0, 4), (1, 4.5), (2, 5), (3, 27.5)

Now,

Check the coordinates in each graph.

The graph that satisfies the coordinates given above is the answer.

The graph shown is not clearly visible.

Thus,

Check the coordinates in each graph.

(0, 4), (1, 4.5), (2, 5), (3, 27.5)

The graph that satisfies the coordinates given above is the answer.

The graph shown is not clearly visible.

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The given linear equation with a slope of 1/2 and a y-intercept of 4 represents a straight line that rises 1 unit vertically for every 2 units it moves horizontally and intersects the y-axis at the point (0, 4).

The given information consists of a slope (m) of 1/2 and a y-intercept (b) of 4. When these values are plugged into the linear equation y = mx + b, we get y = (1/2)x + 4. This equation represents a linear graph with a slope of 1/2 and a y-intercept of 4. The graph would be a straight line that rises 1 unit vertically for every 2 units it moves horizontally and intersects the y-axis at the point (0, 4).

Answer:

5/6

Step-by-step explanation:

Make common dinominator:6

1 3/6-4/6

9/6-4/6

5/6

Answer:

⅚

Step-by-step explanation:

1½ - ⅔

Convert the mixed fraction to improper fraction

³/2 - ⅔

Find the L.C.M of the denominator which is 6

9 - 4

——— = 5/6

6

The answer is

B. -2 and 3

Step-by-step explanation :

Given the expression

x²- 5x + 6 = 0

Firstly we need to find two numbers that when multiplied will give us the constant term 6, and when added will give us the 2nd term 5

These numbers are 3 and 2

Substituting 2x +3x for 5x

x²- (2x+3x)+ 6 = 0

x²-2x-3x+6=0

(x²-2x)-(3x+6)=0

Factoring we have

x(x-2)-3(x-2)=0

x-3=0, x-2=0

x=3, x= 2

By using trigonometric relations, we will see that the difference in height is 14.2 ft.

Here we will have two right triangles, in both, the hypotenuses are equal to 50 ft, but in one, one of the angles measures 25° and in the other, the same angle measures 45°.

The height of the kite would be given by the opposite cathetus to these angles, then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse).

Then we can compute:

sin(25°) = h/50ft

sin(25°)*50ft = h = 21.1 ft

sin(45°) = h'/50ft

sin(45°)*50ft = 35.3 ft

The difference is:

35.36ft - 21.13ft = 14.2 ft

So the correct option is the first one.

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The approximate difference in the height of the kite when the string makes a 25° angle with the ground and when the string makes a 45° angle with the ground is 14.2 feet.

To find the approximate difference in the height of the kite when the string makes a 25° angle with the ground and when it makes a 45° angle, we can use basic trigonometry.

Step 1: Calculate the Height at 25°

When the string makes a 25° angle with the ground:

The height (h) can be calculated using the sine function:

h = L · sin(θ)

where:

- ( L ) = length of the string = 50 feet

- (θ) = angle with the ground = 25°

Calculating this:

[tex]\[ h_{25^\circ} = 50 \cdot \sin(25^\circ) \][/tex]

[tex]\[ h_{25^\circ} \approx 50 \cdot 0.4226 \approx 21.1 \text{ feet} \][/tex]

Step 2: Calculate the Height at 45°

When the string makes a 45° angle with the ground:

Using the same sine function:

h = L · sin(θ)

where:

- θ = 45°

Calculating this:
[tex]\[ h_{45^\circ} \approx 50 \cdot 0.7071 \approx 35.4 \text{ feet} \][/tex]

Step 3: Calculate the Difference in Height

Now, we find the difference in the heights:

[tex]\[ \text{Difference} = h_{45^{\circ}} - h_{25^{\circ}} \][/tex]

Difference = 35.4 - 21.1 ≈ 14.3 feet

Rounding to the nearest tenth, the approximate difference in height of the kite is 14.3 feet.

Therefore, the closest answer choice is 14.2 feet.

Answer:

I might be able to help!

Step-by-step explanation:

I'm bored too.

Answer:

Perpendicular

Step-by-step explanation:

Answer:

the y coordinate is 5

Step-by-step explanation:

In the figure attached, the  directed line segment is shown.

J is located at (-3, 1) and K is located at (-8, 11)

run: x2 -x1 = -8 - (-3) = -5

rise: y2 - y1 = 11 - 1 = 10

Taking J as reference, the coordinate of the point that divides the  directed line segment from J to k into a ratio of 2:3 is:

c = 2/(2+3) = 0.4

(x1 + c*run, y1 + c*rise)

(-3 + 0.4*-5, 1+0.4*10)

(-5, 5)

The next three terms in the sequence 21, 19, 17, 15, are found by continuing the pattern of subtracting 2 from the previous term. They are 13, 11, and 9 respectively.

To find the next three terms of the sequence 21, 19, 17, 15, we should first identify the pattern. Observing the sequence, we see that each term decreases by 2 from the previous term. This is called an arithmetic sequence with a common difference of -2.

Starting with the last given term (15), we subtract 2 to find the next term:

Therefore, the next three terms in the sequence are 13, 11, and 9.

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Answer:

true

Step-by-step explanation:

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, a right line, to emphasize that it has no "wiggles" anywhere along its length.

Answer:

(-6, -2)

Step-by-step explanation:

When trying to find the solution to a system of equations on a graph, the solution is where the lines intersect.

The lines intersect at (-6, -2).  This is the solution.

The solution of the system of equations is,

⇒ (-6, -2)

We have to given that;

Graph of system of equations are shown in image.

Since, We know that;

In the graph the solution of system of equations is the intersection point of system of equations.

Hence, By definition, we get;

The solution of the system of equations is,

⇒ (-6, -2)

Therefore, Option 1 is true.

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Answer:

The dimensions of the bar are width = 4.68099 feet and length = 10.06198 feet

Step-by-step explanation:

A chocolate bar has a rectangular shape, therefore it's area is given by the following formula:

area = width*length

In this case the length is 0.7 feet longer than twice the width, therefore:

length = 2*width + 0.7

Applying the second equation on the first one and using the data from the question we have:

47.1 = width*(2*width + 0.7)

47.1 = 2*width² + 0.7*width

2*width² + 0.7*width = 47.1

width² + 0.35*width = 23.55

width = [tex]\frac{-0.35 \pm \sqrt{0.35^2 -4*1*(-23.55)}}{2*1} = -0.175 \pm 4,85599[/tex]

width = 4.68099 or width = -5.03099

Since the width can't be negative, it can only be 4.68099 feet.

length = 2*4.68099 + 0.7 = 10.06198 feet.

The width of the chocolate bar is 4.68 feet and the length is 10.06 feet.

To find the length and width of the chocolate bar, let's denote the width as w (in feet). According to the problem, the length, l, is 0.7 feet longer than twice the width, so we can express the length as:

l = 2w + 0.7

The area of the chocolate bar is given as 47.1 square feet. The area (A) of a rectangle is calculated by multiplying the length and the width:

A = l × w

Substituting the given values, we have:

47.1 = (2w + 0.7) × w

Expanding and rearranging the equation:

47.1 = 2w² + 0.7w

2w² + 0.7w - 47.1 = 0

This is a quadratic equation in the form ax² + bx + c = 0, where a = 2, b = 0.7, and c = -47.1. We can solve this using the quadratic formula: x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Substituting the values into the quadratic formula:

w = [tex]\frac{-0.7 \pm \sqrt{0.7^2 - 4 \times 2 \times -47.1}}{2 \times 2}[/tex]

w = (-0.7 ± √(0.49 + 376.8)) / 4

w = (-0.7 ± √377.29) / 4

w = (-0.7 ± 19.42) / 4

Taking the positive root (since width cannot be negative):

w = (19.42 - 0.7) / 4

w = 18.72 / 4

w = 4.68

Now, substitute w back into the equation for length:

l = 2w + 0.7

l = 2(4.68) + 0.7 = 9.36 + 0.7 = 10.06

Thus, the width of the chocolate bar is 4.68 feet and the length is 10.06 feet.

Answer

3 -4/5ths

the square root of the mass of the sun times molecular biology of a frog equals 3 -4/5ths

Answer:

-4 1/5

Step-by-step explanation:

3+2/5 = 3 2/5

3 2/5 + (-7 1/5) = -4 1/5

Answer:

{a | 25>a>15}

The elements of A ={16,17,18,19,20,21,22,23,24}

Hope it will help u...

Answer: The answer is 18.

Step-by-step explanation:

Since the average of all 10 players was 75, the total number of baskets made was 10 × 75 = 750. Also, since 8 of the player had an average of 79, they made a total of 8 × 79 = 632 points. The other 2 players, therefore, made 750- 632 = 118 baskets. The most baskets that the player with the highest number could have made was 100, so the player with the lowest number had to have made at least 18.

The smallest number of baskets anyone could have made is 18, computed by first finding the total of all scores, then the total of the 8 middle scores and subtracting, and finally subtracting a maximum possible individual score from the remaining total.

One way to approach this problem is to calculate the total baskets scored initially, then the total scored after removing the highest and lowest scorers. We know that there are 10 people in total, each making an average of 75 baskets. So, the total initial scores is 10 * 75 = 750 baskets.

When the highest and lowest scorers are removed, the remaining 8 players have an average of 79 baskets each, which gives a total of 8 * 79 = 632 baskets. Subtracting the latter total from the initial total, we get 750 - 632 = 118 baskets, which are the combined scores of the highest and lowest players.

To find the smallest number of baskets anyone could have made, we consider a case where the highest score is as high as possible while still being within realistic boundaries. Since each player shot 100 free throws, the maximum score by one player could be 100. Therefore, the smallest number of baskets made by a player, could be 118 - 100 = 18 baskets.

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Answer:

6^5x+2

Step-by-step explanation:

Add exponents when multiplying

Answer:

It would be Table D.

(hope this helped!!)

Answer: D

Step-by-step explanation:

Took the quiz on edge :)

Answer:

Sewage treatment and nitrous oxide

Step-by-step explanation:

Sewage to treatment and nitrous oxide is correctly paired with the greenhouse gases that it increases.

Greenhouse gas refers to gases that has the property of absorbing infrared radiation (net heat energy) emitted from Earth’s surface and reradiating it back to Earth’s surface, thus contributing to the greenhouse effect.

Examples of greenhouse gases and the most important greenhouse gases are methane, carbon dioxide (CO2), and water vapor.

Human activities such as fossil-fuel combustion are responsible for increase in the atmospheric concentration of various greenhouse gases, especially carbon dioxide, methane and ozone.

Answer:  The correct answer is sewage treatment and nitrous oxide

Step-by-step explanation:

The other options for rice cultivation, landfills, and deforestation are not paired with the proper greenhouse gases. However, sewage treatment plants are known for emitting nitrous oxide through their processing.

Answer:

Correct answer is B. (-2,4)

Step-by-step explanation:

Given: y = 2x^2 + 8x + 12

if x = 2,

Use substitution: y = 2(-2)^2 + 8(-2) + 12

                                y = 8 - 16 + 12

                                   y = -8 + 12

                                       y = 4

So, (-2, 4) would be your answer.

I hope this helps!!!

Answer

660

Step-by-step explanation:

to find the distance covered in one revolution, we need to find the circumference of the circle.

Radius of wheel is  

=  2.1 / 2

=  1.05 m

Distance traveled when 100 revolutions are completed :  

=  100 x circumference of the wheel

=  100 x 2 x (22/7) x (1.05)

=  100 x 2 x 22 x 0.15

=  660 m

Distance traveled when it completes 100 revolutions is 659.4 meter

Diameter of a cart wheel = 2.1 m

Distance traveled when it completes 100 revolutions

Radius of wheel = 2.1 / 2

Distance traveled when it completes 100 revolutions = [2πr]100

Distance traveled when it completes 100 revolutions = [2(3.14)(2.1 / 2)]100

Distance traveled when it completes 100 revolutions = [(3.14)(2.1)]100

Distance traveled when it completes 100 revolutions = 659.4 meter

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Answer:

The two below equations or so equivalent because they both lie on the x-axis

Step-by-step explanation:

Answer I need help wit this

Answer:

35

Step-by-step explanation:

The angle formed by two secants = 1/2(difference of intercepted arcs)

A = 1/2(100-30)

A = 1/2 (70)

= 35

Answer:

1. 2/3

2. doesn't exist

3. 2

4. x ≥ 0

5. y ≥ 2

Step-by-step explanation:

If we were to take any two points on the line and divide the difference of the y-coordinates by the difference of the x-coordinates, we'd get the slope. So, take any two points: (0, 2) and (3, 4). The slope is:

(4 - 2) / (3 - 0) = 2/3

The x-intercept is where the line crosses the x-axis, but since the line only starts at (0, 2), the x-intercept doesn't exist.

The y-intercept is where the line crosses the y-axis, which is at point (0, 2) so the y-intercept is 2.

The domain is the possible x-values. Here, because the smallest x-value is 0 (from the point (0,2)), and there is no largest x-value (the arrow at the end of the line indicates the graph goes on to infinity), the domain is: x ≥ 0.

The range is the possible y-values. Here, the smallest possible y value is 2 (from (0, 2)) and the largest is infinity, so the range is: y ≥ 2.

If you do this step by step, you will see it is actually easy! So first, the slope is found by rise over run!

rise = 2; run = 3

Slope = 2/3

The graph doesn't extend to the x axis!

X intercept = Not there

The y intercept is where the function touches the y axis, this is already evident on the graph!

Y intercept = (0,2)

The domain is all possible x values, the function starts at (0,2) and can't go past that point which makes our domain...

Domain =  [tex]0\leq x[/tex]

The range is all possible y values, and since the function's vertical limit is 2, then our range is...

Range =  [tex]2 \leq y[/tex]

Answer:

That equation is in slope intercept form, the slope is equal to -2 and it has a constant of 1. Its starting point would be (0,1)

Step-by-step explanation:

I don't really understand your question, but if you need any help I would be glad to help.

Answer: . y=mx+c is one of them. y=2x−1 is in this form, therefore it is a linear equation. It has an x term, a y term and a constant.

Step-by-step explanation:

Answer:

If I got this wrong im sorry but I think its sometimes

Answer:

32

Step-by-step explanation:

32

my answer is right

Answer:

ffrrv3rv4tg

Step-by-step explanation:

Final answer:

The total amount of money saved in the shoebox over time is best described by a linear model since a fixed amount is added each month, creating a straight line when graphed over time.

Explanation:

The model that best describes the total amount of money in a shoebox over time, assuming you consistently save half of your allowance each month, is a linear model. This is because with each month that passes, you add the same fixed amount to the total you've already saved, creating a straight line when graphed over time. A linear model is represented by the equation y = mx + b, where m is the slope (the fixed amount saved each month) and b is the y-intercept (the initial amount in the shoebox, if any).

If you were earning interest on the savings, or if the amount you saved each month changed, you might consider a quadratic or exponential model, respectively. However, without these factors, the growth of your savings is constant and linear.