What polynomial must be added to x^2-2x+6 so that the sun is 3x^2+7x?

Answer:

8 to 10

Step-by-step explanation:

The solution to the system of equations 2x + 3y = 10 and 3x - 4y = -2 is x = 2 and y = 2.

Given the system of equations in the question:

2x + 3y = 10

3x - 4y = -2

To determine the solution to the system of equations, we can use the elimination method:

2x + 3y = 10

3x - 4y = -2

Multiply the first equation by 4 and the second equation by 3:

We have:

8x + 12y = 40

9x - 12y = -6

Now, we add the two equations.

We have:

17x + 0 = 34

x = 34/17

x = 2

Now, plug x = 2 into the first equation and solve for y:

2x + 3y = 10

2(2) + 3y = 10

4 + 3y = 10

3y = 10 - 4

3y = 6

y = 6/3

y = 2

Therefore, the value of x is 2 and the value of y is 2.

Calculating the number of subway riders who took between 30 and 43 trips involves finding z-scores for these trip numbers, looking up the corresponding probabilities in the normal distribution table, and multiplying the difference by the total population of riders.

The question relates to normal distribution and requires calculating the number of individuals in a given population that fall within a specific range of values. The population in question is 800,000 subway riders whose number of trips are normally distributed with a mean (μ) of 56 and a standard deviation (σ) of 13. The task is to find out how many riders took between 30 and 43 trips last January.

To solve this, we first find the z-scores for the values 30 and 43. The z-score is calculated by subtracting the mean from the value and dividing the result by the standard deviation. This will give:

Next, we look up these z-scores in a standard normal distribution table to find the probabilities corresponding to these z-scores. The difference between these probabilities will give us the proportion of riders who took between 30 and 43 trips. Finally, we multiply this proportion by the total population of riders (800,000) to get the number of riders. Assume that the probabilities from the z-table are 0.0228 for z = -2 and 0.1587 for z = -1.

The calculation would be approximately:

Number of riders = 800,000 * (0.1587 - 0.0228) = 800,000 * 0.1359 = 108,720 riders

Answer: [tex]64.36^{\circ}[/tex]

Step-by-step explanation:

According to the question,

PQ ║ RS

And, PQ and RS are cut by the same transversal CD.

Then, By the alternative interior angle theorem,

The alternative interior angles made by the transversal CD on parallel lines PQ and RS must be congruent.

Thus, [tex]\angle PXY\cong \angle XYS[/tex]

⇒ [tex]m\angle PXY = m\angle XYS[/tex]  ( by the property of congruent angles )

Here  [tex]m\angle PXY = 64.36^{\circ}[/tex]  

⇒ [tex]m\angle XYS = 64.36^{\circ}[/tex]

The expression for log_{b} (ad) is log_{b} a + log_{b} d. Option (C) is the correct answer.

"Logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation".

For the given situation,

The positive numbers are a,b and d.

By product rule of the logarithm,

[tex]log_{b} (ad) = log_{b} a + log_{b} d[/tex]

Hence we can conclude that option (C) is the correct answer.

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Final answer:

Equations are derived from verbal statements by identifying mathematical operations and their relationships to quantities. The resulting equations represent these statements algebraically, where 'n' is the variable representing the unknown number.

Explanation:

Translating sentences into equations is a fundamental skill in algebra, vital for solving problems and understanding mathematical relationships.

Three more than four times a number is equal to twelve: 4n + 3 = 12.

The sum of a number and two is twice the number: n + 2 = 2n.

The quotient of a number and twelve is the sum of eight and the number: n / 12 = n + 8.

Five more than three times a number is equal to eight: 3n + 5 = 8.

The sum of a number and six is seven times the number: n + 6 = 7n.

The quotient of a number and six is equal to nine: n / 6 = 9.

Seven less than a number is two: n - 7 = 2.

Twenty-seven is the product of three and a number: 3n = 27.

Twelve less than six times a number is equal to three times the number: 6n - 12 = 3n.

Remember to define the variable 'n' as the number mentioned in the sentences and solve the equations to find the value of 'n'.

Answer: option A only

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Final answer:

improper fraction 56/9.

Explanation:

To write the mixed number 6 2/9 as an improper fraction, you should first multiply the whole number by the denominator of the fraction, then add the numerator of the fraction.

Answer:

[tex]10 ft^2[/tex]

Step-by-step explanation:

We are given that

Length of soccer field=336 feet

Width of soccer field=210 ft

Width of soccer table=2.5 feet

We have to find the area of soccer table which is similar to soccer field in size.

Let x be the length of soccer table.

We know that when two figures are similar then ratio of their corresponding sides are equal.

[tex]\frac{336}{x}=\frac{210}{2.5}[/tex]

[tex]x=\frac{336\times 2.5}{210}=4[/tex]

Length of soccer table=4 ft

Area of soccer table=[tex]length\times breadth[/tex]

Area of soccer table=[tex]4\times 2.5=10 ft^2[/tex]

Hence , the area of soccer table=[tex]10 ft^2[/tex]

Answer:

84

Step-by-step explanation:

When an orange ball is picked, you toss 3 coins and there are 2^3 = 8 permutations for tossing 3 coins. Now since we have 7 orange balls there will be 7 * 8 = 56 sample spaces with orange balls.

In the experiment, if the ball drawn is orange, three coins are tossed. Otherwise, two coins are tossed. The sample space will have 12 elements with an orange ball.

To determine the number of elements in the sample space that have an orange ball, we need to consider two cases: when the ball drawn is orange and when the ball drawn is not orange (red).

If the ball drawn is orange, three coins are tossed. The sample space in this case will have 23 = 8 elements, representing all possible outcomes of the coin tosses.

If the ball drawn is not orange (red), two coins are tossed. The sample space in this case will have 22 = 4 elements, representing all possible outcomes of the coin tosses.

Therefore, the total number of elements in the sample space that have an orange ball is 8 (when the ball is orange) + 4 (when the ball is not orange) = 12.

Final answer:

An even function has the property f(x) = f(-x), exemplified by the quadratic function f(x) = x². To prove it's even, substituting -x for x results in f(-x) = (-x)², which simplifies to f(-x) = x² equaling the original function, confirming its evenness and y-axis symmetry.

Explanation:

An example of an even function is the quadratic function f(x) = x². An even function is defined by the property that f(x) = f(-x). Here's a step-by-step explanation to show that f(x) = x² is even:

This even property shows symmetry about the y-axis since the function's graph appears the same on either side of the y-axis. Understanding this helps in various mathematical applications, such as simplifying expectation-value calculations in quantum mechanics or solving geometry problems using the Pythagorean theorem.

Answer:

Bianca need to pay $13.43 monthly to avoid interest capitalization.

Step-by-step explanation:

Principal value = $2600

Time = 10 years = 120 months

Interest rate = 6.2% = 0.062

Now, Find amount of payment by using the formula :

[tex]Payment = \frac{Rate\times Principal}{1-(1+rate)^{-time}}\\\\\implies Payment = \frac{0.062\times 2600}{1-(1+0.062)^{-120}}\\\\\implies Payment = \$ 161.32 [/tex]

Total payment is to be paid in 1 year :

[tex]\text{So, Monthly payment = }\frac{161.32}{12}=\$13.43[/tex]

Hence, Bianca need to pay $13.43 monthly to avoid interest capitalization.

Answer:

The sequence is arithmetic

Step-by-step explanation:

we know that

In an arithmetic sequence, the difference between consecutive terms is always the same and is called common difference

In this problem we have

[tex]3,9,15,21,...[/tex]

Let

[tex]a1=3, a2=9,a3=15,a4=21[/tex]

[tex]a4-a3=21-15=6[/tex]

[tex]a3-a2=15-9=6[/tex]

[tex]a2-a1=9-3=6[/tex]

The sequence is arithmetic

The common difference is equal to [tex]6[/tex]

The slope of the curve x²y-xy²=4 is defined everywhere except for points where x = 2y. This conclusion is reached by using implicit differentiation and the product rule to find the derivative (slope), and then determining where the slope is undefined.

To find where the slope of the curve is defined for the equation x²y-xy²=4, we first need to find the derivative of the equation. The derivative will give us the slope of the tangent line at a specific point. This process involves using the Product Rule of differentiation. The Product Rule states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.

For the given equation, we first need to rewrite it in the form: y = f(x). However, as y cannot be easily expressed solely as a function of x in this case, we will need to use implicit differentiation. Implicit differentiation assumes that y is a function of x, even if it's not explicitly stated. By using the product rule, we get 2xy + x² × (dy/dx) - y² - 2xy × (dy/dx) = 0; simplifying this, we get (x² - 2xy) × (dy/dx) = y² - 2xy. So dy/dx = (y² - 2xy) / (x² - 2xy).

Thus, the slope of the curve is defined wherever the denominator, x² - 2xy, does not equal zero, since division by zero is undefined. Hence, we need to solve x² - 2xy ≠ 0. Solving this inequality, we find that the slope of the curve is defined for all (x,y) except where x = 2y.

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Let

x-------> the number of dinner

y-------> the number of lunch

we know that

[tex]8x+5y \leq 42[/tex] -------> equation A

[tex]x=y[/tex] ------> equation B

Substitute equation B in equation A

[tex]8[y]+5y \leq 42[/tex]

[tex]13y \leq 42[/tex]

[tex]y \leq 42/13[/tex]

[tex]y \leq 3.23[/tex]

so

the greatest number of lunch is [tex]y=3[/tex]

[tex]x=y[/tex]

Hence

the greatest number of dinner is [tex]x=3[/tex]

therefore

the greatest number of meals is

[tex]x+y=3+3=6[/tex]

the answer is

[tex]6[/tex]