Given matrices
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0
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X=[
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0
​
] and
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=
[
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2
−
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Y=[
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The sum of the solutions for the equation 4x²- 8x - 12 = 0 will be 2. The correct option is C.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

To find the sum of the solutions of the equation 4x^2-8x-12=0, we first need to find the solutions of the equation. We can start by factoring in the left-hand side of the equation:

4x²-8x-12=0

4(x²-2x-3)=0

4(x-3)(x+1)=0

So the solutions of the equation are x=3 and x=-1. The sum of these solutions is:

3 + (-1) = 2

Therefore, the answer is C) 2.

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Answer: 38

Hope this helps!

The volume of the sphere according to the question will be approximately 7232.752cm³.

What is a sphere?

A geometric shape with a sphere-like appearance. In three dimensions, the sphere is defined. The sphere is a three-dimensional solid with a volume and surface area.

What is the Volume of sphere?

A sphere is a perfectly round geometrical 3D object. The formula for its volume equals:

              Formulae of  Volume of sphere = (4/3) × π × r³

So according to the question:

                            r = 12cm(given)

Substitute in above formulae:

                    =(4/3)×3.14×12×12×12 cm³           [Here 4/3= 1.333, π=3.14,r=12]

                    = 1.333×3.14×12×12×12 cm³

      Volume of sphere will be =7232.752 cm³

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Answer: It doesn't really matter

Step-by-step explanation: This is more of an opinion question, but failing math tests doesn't mean you aren't good at math, some people have different reasons why they don't try at math. Math tests don't define how good or bad you really are in math. You can fail a math test and be good at math, but not passing math tests might also create a lot of issues in the careers you're trying to persuade in because math is one of the most useful subjects. If colleges see your math scores and how badly you performed in them, they won't pick you, which is why is always nice to try no matter how easy or hard it is.

The easiest way to solve problems involving "two unit multipliers" is to use a technique called unit conversion or dimensional analysis.

To solve such problems, you need to convert the given value from one unit to another by multiplying it by a series of conversion factors or unit multipliers. A conversion factor is a fraction that has the same value as one, but its numerator and denominator are expressed in different units.

For example, to convert 10 meters to feet, you can use the conversion factor:

1 meter = 3.28 feet

To convert 10 meters to feet, you would multiply 10 by the conversion factor:

10 meters * (3.28 feet/1 meter) = 32.8 feet

The meters unit cancels out, leaving you with the desired unit of feet.

In some cases, you may need to use multiple conversion factors to get from one unit to another. In these cases, you can multiply or divide the conversion factors to cancel out the unwanted units until you get to the desired unit.

Using unit conversion or dimensional analysis is an effective way to solve problems involving two unit multipliers because it ensures that the units cancel out correctly, and you end up with the desired unit in your final answer.

Answer: 8 5/7

Step-by-step explanation:

Well, first you make the common denominator between the two, which would be 46/14 and 76/14. Now you add 46 and 76 and receive 122/14. You can simplify that and get 61/7, and now you turn it into a mixed number:

8 5/7

The experimental probability of choosing a nickel based on 13 trials would be 4 / 13

The experimental probability can be found by the formula ;

= ( ( Probability of picking a Nickel x Number of trials ) + 1 ) / 13 trials

Probability of picking a Nickel - 1 / 4

Number of trials - 13 trials

The experimental probability for Landon picking a Nickel on the 13th trial is :

= ( ( 1 / 4 x 12 ) + 1 ) / 13

= ( 3 + 1 ) / 13

= 4 / 13

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Answer:

(1/48)ax

Step-by-step explanation:

We can use the proportion of the lengths of the model and the actual locomotive to determine the scale factor for this similarity transformation.

The model is 18 inches long, which is equivalent to 1.5 feet (since 1 foot = 12 inches). The actual locomotive is 72 feet long. So, the scale factor can be calculated as:

scale factor = actual length / model length

scale factor = 72 feet / 1.5 feet

scale factor = 48

This means that each measurement on the model is 1/48th the size of the corresponding measurement on the actual locomotive. We can express this similarity transformation using the notation x* ax as: x* (1/48)ax

So, if a measurement on the model is x, the corresponding measurement on the actual locomotive would be (1/48)ax.

By taking the quotient between the volume of the sink and the volume for each cone, we will see that both of your answers are correct.

How many coops does Carissa need to scoop out in each case?

First, we know that the sink has a volume V = (2000/3)*pi in^3

A) First she uses a cone of a diameter of 4 in and a height of 8 in.

Remember that the volume of a cone of diameter D and height H is:

V = pi*(D/2)^2*H/3

Then this cone has a volume of:

V' = (pi/3)*(4in/2)^2*8in = (pi/3) 32 in^3

The number of scoops needed to completely remove the water out of the sink is given by the quotient between the two volumes, it is:

Rounding it, we get 63, so she needs to scoop 63 times.

B) This time the diameter is 8 in and the height 8 in, so the volume of the cone is:

V'' = (pi/3)*(8in/2)^2*8in = (pi/3)*128 in^3

This time, she needs to scoop:

Rounding to the next number we get 16, she needs to scoop 16 times.

So yes, both of your answers are correct.

l be beneficial both in school and in other parts of your life.[1]

Answer:

Step-by-step explanation:

To determine how many conical cups of water Carissa must scoop out of the half-sphere sink to empty it, divide the volume of the sink by the volume of each cup.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

To determine the volume of conical cup 1 (in terms of π) given it has a diameter of 6 in and a height of 14 in, substitute r = 3 and h = 14 into the volume of a cone formula:

[tex]\begin{aligned}\implies V_{\sf cup\:1}&=\dfrac{1}{3} \pi (3)^2(14)\\\\&=\dfrac{1}{3} \pi (9)(14)\\\\&=\dfrac{126}{3} \pi\\\\&=42 \pi\;\sf in^3\end{aligned}[/tex]

Divide the given volume of the sink by the volume of conical cup 1 to calculate the number of cups of water Carissa must scoop out of the sink to empty it.

[tex]\begin{aligned}\implies \dfrac{4500}{3}\pi \div 42 \pi &=\dfrac{4500}{3}\pi \times \dfrac{1}{42 \pi}\\\\ &=\dfrac{4500 \pi}{126 \pi}\\\\&=\dfrac{4500}{126}\\\\&=35.7142867...\\\\&=36\;\sf(nearest\;whole\;number)\end{aligned}[/tex]

Therefore, Carissa must scoop out 36 cups of water to empty the sink.

To determine the volume of conical cup 2 (in terms of π) given it has a diameter of 10 in and a height of 12 in, substitute r = 5 and h = 12 into the volume of a cone formula:

[tex]\begin{aligned}\implies V_{\sf cup\:2}&=\dfrac{1}{3} \pi (5)^2(12)\\\\&=\dfrac{1}{3} \pi (25)(12)\\\\&=\dfrac{300}{3} \pi\\\\&=100\pi\;\sf in^3\end{aligned}[/tex]

Divide the given volume of the sink by the volume of conical cup 2 to calculate the number of cups of water Carissa must scoop out of the sink to empty it.

[tex]\begin{aligned}\implies \dfrac{4500}{3}\pi \div 100 \pi &=\dfrac{4500}{3}\pi \times \dfrac{1}{100 \pi}\\\\ &=\dfrac{4500 \pi}{300\pi}\\\\&=\dfrac{4500}{300}\\\\&=15\end{aligned}[/tex]

Therefore, Carissa must scoop out 15 cups of water to empty the sink.

Answer: x> -28/13

Step-by-step explanation:

1.

Simplify the expression

2. Combine multiplied terms into a single fraction

3. Distribute

4. Rearrange terms

5. Combine multiplied terms into a single fraction

6. Multiply by 1

7. Multiply all terms by the same value to eliminate fraction denominators

8. Cancel multiplied terms that are in the denominator

9. Distribute

10. Distribute

negative five-sevenths ( 21 x plus 35 ) < 1/3 ( 9-6 x )

negative 315 x minus 525 is less than negative 42 x plus 63

2

Add

525

to both sides

3

Simplify the expression

4

Add

42 x

to both sides

5

Simplify the expression x> -28/13

The height of the right rectangular prism aquarium is 7 inches

We can use the formula for the volume of a right rectangular prism to find the height of the aquarium.

The formula is V = l x w x h,

Where V is the volume, l is the length, w is the width, and h is the height.

In this case, we know that the volume of the aquarium is 1120 cubic inches, the length is 20 inches, and the width is 8 inches.

Therefore, we can write:

1120 = 20 x 8 x h

Simplifying the right side of the equation, we get:

1120 = 160h

Dividing both sides by 160, we obtain:

h = 1120/160 = 7

Therefore, the height of the aquarium is 7 inches.

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Answer:7

Step-by-step explanation:

16 oranges can be purchased in linear equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                                      Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

cost of 12 oranges = 45

Thus, number if oranges we will get for ₹1 = 12/45 oranges.

Thus, the number of oranges that we can buy fro ₹60 = (12/45) × 60 = 16.

Thus, 16 oranges can be purchased.

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The tοtal amοunt earned, including cοmmissiοn and base pay, is $63.50, rοunded tο the nearest hundredth.

Tο answer this questiοn, we need tο knοw the cοmmissiοn rate fοr the lοbster raviοli and k salads. Let's assume the cοmmissiοn rate is 10% fοr bοth items.

If the lοbster raviοli cοst $15 each and the steak salads cοst $12 each, then the tοtal cοmmissiοn earned wοuld be:

3 x $15 x 0.10 + 5 x $12 x 0.10 = $13.50

Therefοre, the cοmmissiοn earned is $13.50.

Tο find the tοtal amοunt earned, including cοmmissiοn and base pay, we simply add the cοmmissiοn earned tο the base pay:

$50 + $13.50 = $63.50

Therefοre, the tοtal amοunt earned, including cοmmissiοn and base pay, is $63.50, rοunded tο the nearest hundredth.

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Answer:

Step-by-step explanation:

I'm unable to solve this, The photo is unclear and to small.

The answer for x - 10y = 14/3.

To solve for x and y, we can use the first equation to solve for y in terms of x:

-3y = 1

y = -1/3

Now we can substitute this value of y into the second equation and solve for x:

11y - x = -5

11(-1/3) - x = -5

-x = -5 + 11/3

-x = -4/3

x = 4/3

Now that we have found the values of x and y, we can substitute them into the expression x - 10y:

x - 10y = (4/3) - 10(-1/3)

x - 10y = 4/3 + 10/3

x - 10y = 14/3

Therefore, x - 10y = 14/3.

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The set containing the roots of the graphed quadratic function is given as follows:

{-3, 1}

The roots of a function can be obtained from the graph of the function, as they also represent the x-intercepts of the function.

The x-intercepts of a function are given by the values of x at which the graph of the function crosses the x-axis, which is the horizontal axis.

The values of x for which the graphed function crosses the x-axis are given as follows:

Hence the set containing the roots of the graphed quadratic function is given as follows:

{-3, 1}

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D. x ≤ 14

Hope this helped :)

The heaviest fish caught weighed more than 12 pounds.

What is mean in statistics?

In statistics, the mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the values in the data set and dividing the sum by the number of values. The mean is also called the arithmetic mean or the average. It is commonly used to describe the typical value of a group of numbers.

To determine which statement is supported by the data, we need to analyze the weights of the fish that Terri and her father caught. Here are some possible statements that could be supported by the data:

A. The average weight of the fish caught was less than 7 pounds.

B. The heaviest fish caught weighed more than 12 pounds.

C. The total weight of the fish caught was more than 60 pounds.

D. The range of weights of the fish caught was between 4 and 12 pounds.

To determine which statement is supported, we can calculate some basic statistics:

Mean (average) weight: (5.6 + 11.0 + 4.0 + 12.2 + 7.0 + 10.0 + 4.2) / 7 = 7.8 pounds

Maximum weight: 12.2 pounds

Minimum weight: 4.0 pounds

Range of weights: 12.2 - 4.0 = 8.2 pounds

Total weight: 5.6 + 11.0 + 4.0 + 12.2 + 7.0 + 10.0 + 4.2 = 54 pounds

Based on this analysis, we can see that statement C ("The total weight of the fish caught was more than 60 pounds") is not supported by the data, as the total weight was only 54 pounds.

Statement A ("The average weight of the fish caught was less than 7 pounds") is also not supported, as the average weight was 7.8 pounds.

Statement B ("The heaviest fish caught weighed more than 12 pounds") is supported, as the heaviest fish weighed 12.2 pounds.

Finally, statement D ("The range of weights of the fish caught was between 4 and 12 pounds") is also supported, as the weights ranged from 4.0 to 12.2 pounds.

Therefore, the correct answer is either B or D, depending on the context of the question.

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The number of touchdowns scored by the defense of the professional football team in the season was C. 10 touchdowns.

The team scored a total of 242 points, and the defense scored about 24% of those points, which is:

0.24 x 242 = 58.08

This means that the defense scored approximately 58 points during the season. If a touchdown is worth 6 points, we can find the number of touchdowns scored by the defense by dividing the total number of points scored by 6:

58 / 6 = 9.67

So the defense scored approximately 9.67 touchdowns during the season. Since we can't have a fraction of a touchdown, the closest whole number answer would be 10 touchdowns.

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Answer:

A business person will use algebra to determine whether a piece of equipment does not lose its worth if it is in stock.

Step-by-step explanation:

The speed of both car A and car B are the same which is 0.7 miles per minute

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

Let x represent the distance travelled by car A and y represent the distance travelled by car B

Speed of car A = x /20

Car B reaches in 50 minutes, hence:

Speed of car B = y/50

Since both speed are same;

x/20 = y/50

20y = 50x    (1)

Car B is 21 miles farther, then:

y - x = 21     (2)

x = 14, miles y = 35 miles

Speed of car A = speed of Car B = 14/20 = 35/50 = 0.7 miles per minute

The speed is 0.7 miles per minute

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The image reflected by the line of the triangle is attached below.

What is an image?

A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

The coordinates of the vertices of the triangle are (1, -2), (8,1), (4,-9).

The rule of reflection across the y = x line is (x,y) → (y,x).

The reflection of (1, -2) across the y = x line is (-2,1).

The reflection of (8,1) across the y = x line is (1,8).

The reflection of (4,-9) across the y = x line is (-9,4).

The coordinates of the vertices of the reflected triangle are (-2,1), (1,8), and (-9,4).

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The student's percentile will be 28.

Calculating percentiles is a common practise. The majority of the time, we can define percentile as a score below which a predetermined percentage of other scores fall. We might be able to tell when someone received a test score of 65 out of 90. But without knowing what percentile he belongs to, this number is meaningless. When a score is in the 90th percentile, it signifies that it is higher than the scores of 90% of test-takers.

Given : Student's rank = 144 out of 200

So, there are 56 (200-144) students whose rank is below that student.

We know that, percentile

= no. of ranks below that rank / total no. of ranks * 100

So, his percentile = 56/200 * 100

                             = 28 percentile.

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Overall, the W-2 form is an important document for employees to receive and keep for tax purposes, but it is not comprehensive in terms of all the financial details of their employment.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

A W-2 form is an Internal Revenue Service (IRS) tax form that employers are required to provide to their employees every year. It reports the employee's annual wages and the amount of taxes withheld from their paychecks. While a W-2 form contains a lot of important information about an employee's earnings and tax withholding, it does not include every detail about their employment or financial situation. Some examples of information that are not included on a W-2 form include:

Information about non-wage income, such as interest or dividends

Information about benefits received, such as health insurance or retirement plan contributions

Information about deductions or credits, such as charitable contributions or education expenses

Information about stock options or other forms of equity compensation

Information about expenses related to employment, such as travel or equipment costs.

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Answer:

Step-by-step explanation:

The 8 is in the hundreds place.

Answer:

The 8 is in the hundreds place.

Step-by-step explanation:

2,000 (Thousands Place)

800 (Hundreds Place)

90 (Tens Place)

4 (Ones Place)

0.0 (Tenths Place)

2,894.0

Answer:

Refer to pic..........

Using displacement, His unit rate every mile per hour will be 4 miles/hours.

When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.

Mario walked at a rate of 2/3 mile every 10 minutes.

We have,

Distance = 2/3 miles

Time = 10 minutes

On substituting these values in the above formula, we get

speed = 2/10.3

We have to find the unit rate in mile per hour, so we need to multiply it by 60, 1/15 × 60 = 4 miles/hours

Hence, his unit rate every mile per hour will be 4 miles/hours.

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The restaurant location problem as a nonlinear optimization model is given below.

The restaurant location problem can be formulated as a goal programming model with the following components:

Decision variables:

x1: the x-coordinate of the restaurant location

x2: the y-coordinate of the restaurant location

Goals:

Minimize the total distance from the restaurant to the three suburbs, calculated as follows:

Distance from suburb 1: |x1 - 1| + |x2 - 2|

Distance from suburb 2: |x1 - 6| + |x2 - 18|

Distance from suburb 3: |x1 - 12| + |x2 - 8|

Maximize the accessibility of the restaurant to the three suburbs, measured as the sum of the reciprocals of the distances from the restaurant to each suburb:

Accessibility = 1 / (|x1 - 1| + |x2 - 2|) + 1 / (|x1 - 6| + |x2 - 18|) + 1 / (|x1 - 12| + |x2 - 8|)

Constraints: None

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