3 12. DIG DEEPER There are 4 cups of iced tea. Is it possible for you and your friend to share the tea equally? If so, how much do you each get? If not, explain why not. 5 MTR Use Another Concept How can equivalent fractions help you solve? C​

The equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex] and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex]

A mathematical equation, such as 6 x 4 Equals 12 x 2, states that two quantities or units are similar. A noun that ranks. When two or more components must be taken into account together in to fully understand or describe the whole scenario, this is known as an equation.

a) To find the equation of the straight line shown, we need to determine its slope (or gradient) and [tex]y-[/tex]intercept. We can do this by choosing two points on the line and using the point-slope formula:

slope [tex]=[/tex] (change in y) / (change in x)

Let's choose the points [tex](1, 3)[/tex] and [tex](4, 7)[/tex] from the line.

slope [tex]= (7 - 3) / (4 - 1) = 4 / 3[/tex]

Now we can use the point-slope formula with one of the points to find the equation:

[tex]y - y1 = m(x - x1)[/tex]

where m is the slope and (x1, y1) is one of the points on the line.

Let's use the point (1, 3):

[tex]y - 3 = (4/3)(x - 1)[/tex]

Simplifying:

[tex]y = (4/3)x + 1[/tex]

So, the equation of the straight line shown is [tex]y = (4/3)x + 1[/tex].

b) To complete the statement "[tex]y = 3x + 5[/tex] passes through [tex](0, -5)[/tex]", we need to substitute [tex]x = 0[/tex] and [tex]y = -5[/tex] into the equation and verify that it is true:

[tex]y = 3x + 5[/tex]

[tex]-5 = 3(0) + 5[/tex]

[tex]-5 = 5 - 5[/tex]

[tex]-5 = -5[/tex]

Since the equation is true, we can say that the point [tex](0, -5)[/tex] is on the line [tex]y = 3x + 5[/tex].

c) We know that the gradient of the line we want to find is the same as [tex]y = 3x + 5[/tex], which is [tex]3[/tex]. We also know that it passes through the point [tex](0, 12)[/tex].

Using the point-slope formula with [tex]m = 3[/tex] and [tex](x1, y1) = (0, 12)[/tex]:

[tex]y - 12 = 3(x - 0)[/tex]

Simplifying:

[tex]y = 3x + 12[/tex]

So, the equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex]and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex].

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For no solution 7x+10

For one solution8x+0

For infinite solution 7x+5

An infinite solution is a solution to a system of equations that has an infinite number of possible solutions. In other words, any value for the variables in the system will satisfy all the equations.

2x+5+2x+3x

On adding the values with variables, x=7

On adding constant values=5

2x+5+2x+3x=7x+5

For no solution

7x+5=7x+10

For one solution

7x+5=8x

x=5

For infinite solution

7x+5=7x+5

Hence, For no solution 7x+10

For one solution 8x+0

For infinite solution 7x+5.

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The surface area οf the cοntainer is 314 ft².

A rectangle is a geοmetric shape that has fοur sides and fοur right angles (90 degrees) with οppοsite sides being parallel and equal in length. It is a type οf quadrilateral, a pοlygοn with fοur sides.

Tο find the surface area οf a rectangular prism, we need tο add the areas οf all six faces. The fοrmula fοr the surface area οf a rectangular prism is:

Surface area = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height οf the rectangular prism.

Substituting the given values, we get:

Surface area = 2(5)(9) + 2(5)(8) + 2(9)(8)

Surface area = 90 + 80 + 144

Surface area = 314 square feet

Therefοre, the surface area οf the cοntainer is 314 ft².

Answer: 314 ft².

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If Bill starts work at 8:15, works until 4:45, and has 90 minutes of breaks. Bill works for 36.25 hours in 5 days.

Work per day typically refers to the amount of time or effort expended by an individual during a typical working day.

First, let's find out how many hours Bill works in one day.

        8 hours and 45 minutes - 90 minutes of breaks

           = 7 hours and 15 minutes

           = 7.25 hours of work per day.

       7.25 hours per day x 5 days = 36.25 hours.

Therefore, Bill works for 36.25 hours in 5 days.

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Answer:

K

Step-by-step explanation:

[tex]c + d \: - 2(c + d) \\ = c + d - 2c - 2d \\ = - c - d \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

a)  A(5) = 10 * e^(-0.05*5)

b)  7.776

To solve the given problem, the initial amount of chlorine should be assumed as 'P0' and the exponential function should be written in the form of y = P_0 * e^(kt) where P_0 is the initial amount of chlorine and k is the rate of change. Therefore, for the given problem, the exponential function can be given by: y = P_0 * e^(-0.05t) where P_0 is the initial amount of chlorine and t is the number of hours. This equation will give the amount of chlorine remaining after t hours. The formula for exponential decay is given by:A(t) = A₀ * e^(-kt) Where A(t) is the amount after time t, A₀ is the initial amount, k is the rate of decay, and t is the time elapsed. To calculate the remaining amount of chlorine after a certain number of hours, we'll utilize the formula above .Let's start with the given information: An exponential function that gives the amount of chlorine remaining after t hours is to be found. P₀ = the initial amount of chlorine, which is 10.We can also figure out the rate of decay from the given information. The amount of chlorine is reduced by 5% per hour, which means the rate of decay is 0.05. We need to put a negative sign in front of the rate of decay to indicate that it is decreasing. Let's use the formula to find the amount of chlorine remaining after 5 hours. Then, substitute A₀ = 10, k = -0.05, and t = 5 into the equation above to obtain A(5) = 10 * e^(-0.05*5) = 7.776.So, the amount of chlorine remaining after 5 hours is 7.776.

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The side which clοses tο the acute angle will be the adjacent side tο the acute angle and the lοngest side is the Hypοtenuse.

What are Sides οf a right-angled triangle?  

In a right-angled triangle, there are three sides. One side is called the hypοtenuse and the οther twο sides are adjacent tο the right angle and are called the legs οf the triangle.

In a right triangle, the side οppοsite the right angle is always the lοngest side and is called the hypοtenuse. The twο οther sides are called the legs οf the triangle, and οne οf the legs is adjacent tο each οf the acute angles.

Tο determine which side is adjacent tο a specific acute angle, yοu need tο identify which οf the twο legs is clοsest tο that angle. The side clοsest tο the angle is the adjacent side.

Fοr example, if yοu have a right triangle with acute angles A and B, and leg AB is adjacent tο angle A, then leg BC is adjacent tο angle B.

Alternatively, yοu can use the trigοnοmetric functiοns sine, cοsine, and tangent tο determine the relatiοnship between the sides οf a right triangle and its angles.

The side which clοses tο the acute angle will be the adjacent side tο the acute angle and the lοngest side is the Hypοtenuse.

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The grouping of data  or sample points is a component of the machine learning process known as clustering.

The task of arranging a set of objects into an identical group in a way that makes them more similar to one another than those found in different groups is known as cluster analysis or clustering.

A scatter plot is an unique type of plot or mathematical diagram that displays data for usually 2 parameters for a collection of data. It uses Cartesian coordinates.

Coordinates, it is a set or group of values that show an exact or accurate position.

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Answer:

a) 7/9 * 2

Because 7*2/9 = 1.555556, which is less than 2.

All the other options' products are greater than 2.

Please mark as brainliest!

DONT FORGET!!

Answer:

a. When x > k, the cost of running the ad for a week can be expressed as:

C = p + e(x - k)

where C is the cost in dollars, p is the cost per k lines, e is the cost per extra line, and (x - k) is the number of extra lines over k.

b. When x ≤ k, the cost of running the ad for a week can be expressed as:

C = p

where C is the cost in dollars and p is the cost per k lines. Since the number of lines x is less than or equal to k, there are no extra lines and the cost is simply the base cost of p dollars for k lines.

Hope this helped! I'm sorry if it's wrong. If you need more help, ask me! :]

The factored forms of the equations and the intercepts would be:

g(x) = x² - 4x - 21:

h(x) = x² + 8x + 12:

For g(x) = x² - 4x - 21:

To find the factored form, we need to factor the quadratic expression:

g(x) = (x - 7)(x + 3)

To find the x-intercepts, we set g(x) = 0 and solve for x:

(x - 7)(x + 3) = 0

x = 7 or x = -3

To find the y-intercept, we set x = 0 and evaluate g(x):

g(0) = (0 - 7)(0 + 3) = -21

Therefore, the y-intercept of g(x) is (0,-21).

For h(x) = x² + 8x + 12:

h(x) = (x + 2)(x + 6)

To find the x-intercepts, we set h(x) = 0 and solve for x:

(x + 2)(x + 6) = 0

x = -2 or x = -6

To find the y-intercept, we set x = 0 and evaluate h(x):

h(0) = (0 + 2)(0 + 6) = 12

Therefore, the y-intercept of h(x) is (0,12).

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0.571

Given data: The accompanying table shows the numbers of male and female students in a certain region who received​ bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts​ (a) through​ (c) below.Table:Males FemalesTotalsFreshman 12 25 37Sophomore 14 18 32Junior 17 14 31Senior 9 12 21Totals 52 69 121a) A freshman is selected at random.b) A senior male is selected at random.c) A female is selected at random.a) For part a, we have to find the probability of selecting a freshman at random. The total number of students is 121. And the number of freshmen is 37. The probability of selecting a freshman at random is:37/121 = 0.306b) For part b, we have to find the probability of selecting a senior male at random. The total number of seniors is 21. And the number of senior males is 9. The probability of selecting a senior male at random is:9/121 = 0.074c) For part c, we have to find the probability of selecting a female at random. The total number of females is 69. And the total number of students is 121. The probability of selecting a female at random is:69/121 = 0.571Therefore, the probability of each event is:a) 0.306b) 0.074c) 0.571

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The missing value that completes the frequency table is 100

A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.

How to solve:

From the graph given,

The battery life(hours) from x = 15  to x= 20 has a frequency of 130

The battery life(hours) from x= 28 to x= 30 has a frequency of 100

It can be inferred that from the battery life of the different models, the missing value is 100 and when you crosscheck the data, you would find this is correct and accurate.

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The probability of randomly selecting a temperature between 70 and 75 is approximately 0.8291.

To find the probability that a randomly chosen temperature is between 70 and 75, we need to use the z-score formula as shown below:

z = (x - μ) / σ

Where:x = 70 and 75μ = 79σ = 4z1 = (70 - 79) / 4 = -2.25z2 = (75 - 79) / 4 = -1P(70 < x < 75) = P(-2.25 < z < -1)

To find the probability for the above inequality, we need to use a calculator. We know that the probability of the standard normal distribution is equal to 1.

Hence, P(-2.25 < z < -1) = Φ(-1) - Φ(-2.25) = 0.8413 - 0.0122 ≈ 0.8291. Therefore, the probability is about 0.8291.

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Value of Q3 is approximately 114.1 given mean and standard deviation.

We must identify the IQ score that separates the bottom 9% from the top 91% in order to determine P9. The normal distribution of IQ scores has a mean of 100 and a standard deviation of 15, as is well known. The z-score for the 9th percentile can be calculated using a calculator or a typical normal distribution table.

[tex]z = invNorm(0.09) = -1.34[/tex]

The formula for converting a z-score to an IQ score is as follows:

IQ equals z * standard deviation + mean, or -1.34 * 15 + 100, or 79.1.

P9 is therefore roughly 79.1.

We must identify the IQ score that distinguishes the top 25% from the rest in order to determine Q3. Assuming a normal distribution, IQ values have a mean of 105 and a standard deviation of 15. Since the top 25% and the 75th percentile are the same, we can use a calculator or a conventional normal distribution table to determine the z-score that represents the 75th percentile:

[tex]z = invNorm(0.75) = 0.67[/tex]

We can then use the formula for transforming a z-score to an IQ score:

IQ = z * standard deviation + mean = 0.67 * 15 + 105 = 114.05

Therefore, Q3 is approximately 114.1.

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The two values of b that make the system inconsistent are b = -4.79 (negative) and b = 4.79 (positive). This is found by setting the discriminant of the quadratic equation in x to be negative.

We can solve this problem by substituting y = 4x + b into the first equation:

x² + (4x + b)² = 25

Expanding the square and simplifying, we get:

x² + 16x² + 8bx + b² - 25 = 0

Combining like terms, we get a quadratic equation in x:

17x² + 8bx + (b² - 25) = 0

For the system to be inconsistent, this quadratic equation must have no real solutions (i.e., the discriminant must be negative). Therefore, we need:

(8b)² - 4(17)(b² - 25) < 0

Simplifying and solving for b, we get:

64b² - 4(17b² - 425) < 0

98b² < 1700

b² < 1700/98

b < ±sqrt(1700/98)

b < ±4.79

Therefore, the two values of b that make the system inconsistent are:

b = -4.79 (negative)

b = 4.79 (positive)

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From the graphs in the given coordinate plane, the functions that have complex roots are function b, function d and function f.

From the question, we are to determine the functions that have complex roots in the given coordinate plane.

In a quadratic graph, if the vertex of the quadratic function lies above the x-axis, and the parabola opens upward, there will be NO x-intercepts. The graph will have complex roots.

Also, if the vertex of the quadratic function lies below the x-axis, and the parabola opens downward , there will be NO x-intercepts.

The graph will have complex roots.

In the given coordinate plane, the functions that have complex roots are function b, function d and function f.

Hence, the functions b, d, and f have complex roots.

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The weight of the smaller dog is 5.6 pounds.

Let the weight of the smaller dog be x, then,

The weight of the larger dog = 1.4 pounds.

The combined weight of the dogs =  12.6 pounds.

Therefore,

The sum of the weight of the larger dog and smaller dog = the combined weight of the dogs.

That is,

1.4 + x + x = 12.6

1.4 + 2x =  12.6

2x = 12.6 - 1.4

2x = 11.2

x = 11.2 ÷ 2

x = 5.6.

Hence, the weight of the smaller dog is 5.6 pounds.

?

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Your question is incomplete, and the complete question would be:

Karen has two dogs. the larger dog weighs 1.4 pounds more than the smaller dog. the combined weight of the two dogs is 12.6 pounds. what is the weight of the smaller dog?

(a) P(green or red) = 0.3946

(b) P(blue, red, or yellow) = 0.7606

(c) P(not brown) = 0.7807

(d) P(not green) = 0.6559

What is probability?

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.

The total number of M&M's is 2552.

(a) P(green or red) = P(green) + P(red)

= 364/2552 + 507/2552

= 0.2692

(b) P(blue, red, or yellow) = P(blue) + P(red) + P(yellow)

= 399/2552 + 507/2552 + 351/2552

= 0.4917

(c) P(not brown) = 1 - P(brown)

= 1 - 538/2552

= 0.7891

(d) P(not green) = 1 - P(green)

= 1 - 364/2552

= 0.8575

Hence,

(a) P(green or red) = 0.3946

(b) P(blue, red, or yellow) = 0.7606

(c) P(not brown) = 0.7807

(d) P(not green) = 0.6559

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Width of the mat is 0.75 m

Answer:Triangle problemGiven a right triangle, perimeter = 198 cm Hypotenuse = 85 cmLet the other sides of the triangle be a and b respectively.To find the value of a and bSolutionWe know that, in a right triangle with sides a and b, and hypotenuse c Pythagoras Theorem can be usedc² = a² + b²Formula for perimeter of a triangle is P = a + b + cFrom the given values, we can substitute the values for P and c.198 = a + b + 85 198 - 85 = a + b 113 = a + bTo get the values of a and b, we need one more equation We can use Pythagoras theorem since it is a right triangle85² = a² + b²7225 = a² + b²a² = 7225 - b²b² = 7225 - a²Substitute b² into the previous equation113 = a + b7225 = a² + (7225 - a²)7225 = 2a²a² = 7225 / 2a = √(7225 / 2) = √(36125 / 8) = 75.59 cmNow that we have found the value of a, we can find b using the Pythagoras Theorem85² = 75.59² + b²b² = 85² - 75.59²b = √(85² - 75.59²) = 49.79 cm Therefore, a = 75.59 cm, b = 49.79 cmWidth of rubber matA square swimming pool has an area of 289 m²The area of the pool can be expressed as (side)²Therefore, side = √289 = 17 mLet the width of the rubber mat be w. Since it is uniform, it will be the same on all sides. Area of the pool and mat = (side + 2w)² - side² = 289From the above equation, we can solve for w:4w(side) + 4w² = 0+ 4w² + 4w(side) - 289 = 04(w + side/2)² - 289 = 0(w + side/2)² = 289 / 4w + side/2 = ±17/2 w + side/2 = 8.5 or w + side/2 = -8.5side/2 can never be negative, therefore we can consider only w + side/2 = 8.5 w = 8.5 - side/2w = 8.5 - 17/2 = 0.75m Width of the mat is 0.75 m

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To find f(-6), we need to substitute -6 for x in the expression for f(x):

f(x) = 2x^2 + 5x - x/3

f(-6) = 2(-6)^2 + 5(-6) - (-6)/3

f(-6) = 2(36) - 30 + 2

f(-6) = 72 - 30 + 2

f(-6) = 44

Therefore, f(-6) = 44.

Answer:

3x+5x=8x

-3t+-t=-4t

3p+3p=6p

2n+n=3n

5g+-g=4g

7y+y=8y

4+12=16

Step-by-step explanation:

On solving the question we have that We can see that RS + ST = RT, equation  confirming that S is on segment RT: RT = RS + ST = 5 + 10 = 15

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

Because S is on the section RT, we know that RS + ST = RT. As a result, we may construct the following equation:

RS + ST = 3x + 1 + (x + 2) = 15

To simplify this equation, we can combine similar terms:

4x + 3 = 15

Subtraction of 3 from both sides yields:

4x = 12

When we divide both sides by 4, we get:

x = 3

RS = x + 2 = 5 and ST = 3x + 1 = 10 as a result.

We can see that RS + ST = RT, confirming that S is on segment RT:

RT = RS + ST = 5 + 10 = 15

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For given quadratic equation, the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.

What exactly are quadratic equations?

A quadratic equation is a second-degree polynomial equation of the form:

ax²+ bx + c = 0

where x is the variable and a, b, and c are constants, with a ≠ 0. The term "quadratic" comes from the Latin word "quadratus", which means "square". In other words, a quadratic equation is an equation that involves the square of the variable x.

Now,

We are given that the profit of the company (in millions of dollars) can be represented by the equation y = x² - 16x + 67, where x is the number of years since the company started.

We want to find when the company had a profit of 7 million dollars.

So, we can set y = 7 in the equation:

7 = x² - 16x + 67

Rearranging and simplifying:

x² - 16x + 60 = 0

Now, we can solve for x using the quadratic formula:

x = (-(-16) ± √((-16)^2 - 4(1)(60))) / 2(1)

x = (16 ± √(16)) / 2

x = 8 ± 2

Therefore, the solutions are x = 10 or x = 6.

This means that the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.

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Step-by-step explanation:

Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?

The value of q in the question is q>-12/15

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions

The given inequality is 5(p−3q)<12

Opening the bracket we have

5p - 15q < 12

The solution can only be gotten if we assume p = 0

the substitute p=0 in the inequality to have

-15q < 12

dividing both sides by -15 to have

-15q/-15 < 12/-15

therefore q > 12/-15

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a) The populations in 1980, 1990, 2000, and 2010 are 157,000, 218,000, 269,000, and 308,000 respectively.

b) the population will reach 390,000 in 270 years

c) No, as t increases, the population increases rapidly

(a) To find the population in 1980, 1990, 2000, and 2010, we substitute the corresponding values of t into the given model and round the answers to the nearest whole number.

Population in 1980: P = 75.9e^(0.0316*10) = 156,604

Population in 1990: P = 75.9e^(0.0316*20) = 217,643

Population in 2000: P = 75.9e^(0.0316*30) = 269,099

Population in 2010: P = 75.9e^(0.0316*40) = 308,227

(b) To find when the population of Horry County will reach 390,000, we need to solve the equation 390 000 = 75.9e^(0.0316t) for t.

Taking the natural logarithm of both sides, we get:

ln(390,000/75.9) = 0.0316t

Simplifying, we get:

t = ln(390,000/75.9)/0.0316 ≈ 270.395

Rounding down to the nearest whole year, we get that the population will reach 390,000 in 270 years

(c) The model assumes that the population growth rate will remain constant over time. However, in reality, population growth rates can be affected by a variety of factors, such as changes in birth and death rates, immigration, emigration, and natural disasters.

Therefore, it is unlikely that the model will be valid for long-term predictions of the population. The model can provide a good estimate of the population for the short-term, but it is not reliable for predictions far into the future.

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The sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]

What is sum?

In mathematics, the term "sum" refers to the result obtained by adding two or more numbers or quantities together. It also be used to refer to the total amount of something, such as the sum of money you have in your bank account, or the sum of the lengths of all the sides of a polygon.

To find the sum or difference of [tex]-2x^2+x+6 + (5x^2-4x-2)[/tex] we need to combine like terms.

[tex]-2x^2+x+6 + (5x^2-4x-2) &\\\\= (-2x^2 + 5x^2) + (x - 4x) + (6 - 2)[/tex]

[tex]&= 3x^2 - 3x + 4[/tex]

Therefore, the sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]

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For the equilateral triangles we have:

1) x = 5, y =  √50

2) a = 2, b = √8

3)y = 8, x = √128

4) a = b = 7/√2

We can see some triangles, remember that for a right triangle whose angles are 45°, we have an equilateral triangle.

So the two legs have the same measure.

1) Here we can see that x = 5, and the hypotenuse is given by:

y^2 = 5^2 + 5^2

y^2 = 50

y = √50

2) Here we have a = 2, then the hypotenuse is:

b^2 = 2^2 + 2^2

b^2 = 8

b = √8

3) Here we have y = 8, then the hypotenuse is:

x^2  = 8^2 + 8^2

x^2 = 128

x = √128

On the last triangle we can see that the hypotenuse is 7, and we know that a = b

then:

7^2 = a^2 + b^2

7^2 = a^2 + a^2

49 = 2*a^2

(49/2) = a^2

√(49/2) = a

7/√2 = a = b

Learn more about equilateral triangles at:

https://brainly.com/question/17264112

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Answer:

28

x 76

----

168 (units digit of 76 multiplied by 28)

1408 (tens digit of 76 multiplied by 28)

----

2128

Therefore, 28x76 is equal to 2128.

Step-by-step explanation: