Factor this trinomial with a leading coefficient of 1. The trinomial being 2x^2y-34xy+144y

Answer:

The three zeros are 5 , -2 and [tex]\frac{1}{4}[/tex]. The second option is correct.

Step-by-step explanation:

The given polynomial is,

[tex]f(x)=4x^3-13x^2-37x+10[/tex]

Use hit and trial method, Put x=-2

[tex]f(x)=4(-2)^3-13(-2)^2-37(-2)+10=0[/tex]

Since the value of function is 0 at x=-2 therefore (x+2) is a factor of the given polynomial.

Divide the given polynomial by using synthetic division or long division.

[tex]f(x)=(x+2)(4x^2-21x+5)[/tex]

Use grouping method to find the factors,

[tex]f(x)=(x+2)(4x^2-20x-1x+5)[/tex]

[tex]f(x)=(x+2)(4x(x-5)-(x-5))[/tex]

[tex]f(x)=(x+2)(x-5)(4x-1)[/tex]

Equate each factor equal to 0.

[tex]x=-2,5,\frac{1}{4}[/tex]

Therefore, the  three zeros are 5 , -2 and [tex]\frac{1}{4}[/tex]. The second option is correct.

a) To find k for parallel lines, equate slopes to get k = -10/3. b) For perpendicular lines, use negative reciprocal slopes to find k = 3/10.

To determine the conditions for parallelism and perpendicularity, we need the slope of each line. The slope-intercept form of a line is y = mx + b where m is the slope.

To find the slope of the first line, we rearrange 3x-5y=9 to the form of y = mx + b, resulting in y = (3/5)x - (9/5). Therefore, the slope is 3/5. For the second line, rearranging 2x+ky=11 gives us y = (-2/k)x + (11/k). The slope of the second line is -2/k.

For the lines to be parallel, their slopes must be equal, so 3/5 = -2/k. Solving for k, we get k = -10/3. For the lines to be perpendicular, the product of their slopes must be -1 (since perpendicular lines have negative reciprocal slopes). This gives us (3/5)(-2/k) = -1, and solving for k yields k = 3/10.

right triangle us pythagorean theorem

a^2 + b^2 = c^2

75^2 + 100^2 = C^2

5625 +10000 = c^2

15625 =c^2

c=Sqrt(15625) = 125

hypotenuse = 125

 answer is C

Final answer:

The slope for a line passing through two points can be found using the formula m = (y2 - y1) / (x2 - x1). By substituting the given points into the formula, the slope for the line passing through (1, 0.1) and (7, 26.8) is found to be 4.5.

Explanation:

The formula for the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

m = (y2 - y1) / (x2 - x1)

To find the slope for the given points (1, 0.1) and (7, 26.8), we can substitute the values into the formula:

m = (26.8 - 0.1) / (7 - 1) = 4.5

Therefore, the slope for the line passing through the given points is 4.5.

a. The equation for the line in point-slope form is [tex]\( y + 1 = \frac{5}{6}(x - 2) \).[/tex]

b. The equation in standard form is ( 5x - 6y = 16 ).

a. To find the equation of the line in point-slope form, we use the formula [tex]\(y - y_1 = m(x - x_1)\)[/tex], where (m) is the slope and [tex]\((x_1, y_1)\)[/tex] is a point on the line. Given the points (2, -1) and (8, 4), we can calculate the slope (m) as [tex]\(\frac{{y_2 - y_1}}{{x_2 - x_1}}\)[/tex]. Substituting the values, we get:

[tex]\[ m = \frac{{4 - (-1)}}{{8 - 2}} = \frac{5}{6} \][/tex]

Now, using the point-slope form, we substitute the values for (m) and [tex]\((x_1, y_1)\)[/tex]:

[tex]\[ y + 1 = \frac{5}{6}(x - 2) \][/tex]

b. To convert the equation to standard form, we want to eliminate fractions and express it as (Ax + By = C), where (A), (B), and (C) are integers. Multiply both sides of the equation by 6 to clear the fraction:

6(y + 1) = 5(x - 2)

Distribute the terms:

(6y + 6 = 5x - 10)

Bring all terms to one side:

[ 5x - 6y = 16 ]

So, the equation in standard form is (5x - 6y = 16). This form is preferred for certain applications, making it easier to identify coefficients and intercepts.

Compare prices, consider discounts, and watch for additional costs like shipping. Choose the option with the lowest total expense for buying the $100 item.

To determine the most cost-effective choice for buying the $100 item, you should consider any available discounts, promotions, or deals offered by different sellers or platforms. Here are a few strategies you could consider:

1. **Comparison Shopping**: Check multiple retailers or online platforms to see if the item is available at a lower price elsewhere. Websites and apps dedicated to comparison shopping can help streamline this process.

2. **Discounts and Coupons**: Look for any available discounts or coupons that you can apply to your purchase. Many retailers offer promotional codes or special deals that can help reduce the cost of the item.

3. **Cashback and Rewards**: Some credit cards or loyalty programs offer cashback or rewards points for purchases. If you have a card or program like this, see if you can earn rewards or cashback by buying the item through a specific retailer.

4. **Timing**: Consider timing your purchase to coincide with sales events or promotions, such as Black Friday, Cyber Monday, or seasonal sales. Buying during these periods can often result in significant savings.

5. **Shipping and Handling Costs**: Be mindful of any additional costs associated with shipping and handling. Sometimes, even if the base price of the item seems lower from one seller, the shipping costs may make the overall purchase more expensive.

By comparing prices, looking for discounts, and considering additional costs, you can find the most cost-effective option for purchasing the $100 item.

Complete Question:

Which of these is the most cost effective choice for buying the item using a paid membership card to buy it at a 10 percent discount buying it on line at a 10 percent discount without sales tax?

Answer:

The correct option is B) $680.

Step-by-step explanation:

Consider the provided information.

Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest.

Let she invested x amount with 8% interest rate.

Total amount she invested was $1,500, thus the amount she invested with 6% interest rate was 1500-x.

Total interest she earn was $106.40

Write this information into mathematical form.

[tex]x\times \frac{8}{100}+\frac{6}{100}(1500-x)=106.40[/tex]

[tex]x\times 0.08+0.06(1500-x)=106.40[/tex]

[tex]0.08x+90-0.06x=106.40[/tex]

[tex]0.08x-0.06x=106.40-90[/tex]

[tex]0.02x=16.4[/tex]

[tex]x=820[/tex]

Hence, she invested $820 with 8% interest rate.

The amount she invested with 6% interest rate was 1500-x.

Substitute the value of x in above.

1500-820=680

Hence, she invested $680 with 6% interest rate.

The correct option is B) $680.

In a place value relationships. The relationship between 2 the same digit place next to each other is the value of the number to left is 10 times bigger than to the value to the left and from the decimal point to the right is 10 times smaller of value than the digit in their right.

Let say for example:
1111
1 thousands, 1 hundreds, 1 tens, and 1 ones.
Let’s start from 1 = 1 x 10 = 10
That would be 10 X 10 = 100
then 100 X 10 = 1000

Notice that their value increase base on its place value if we multiply the given number by 10. 

Another one is

912.98 in where 9 is hundreds, 1 is tens, 2 is ones and after the decimal points, in where  9 is tenths and 8 is hundredths.

Notice each place value next to each other. Each value is ten times in difference.

Answer:

c 4.47

Step-by-step explanation:

got it right on my test

The distance from (−3, 1) to (−1, 5) is 4.47

Slope of line is defined as the angle of line.  

The distance between two points is found by

[tex]d = \sqrt{( (x_2-x_1)^2 + (y_2-y_1)^2)}[/tex]

[tex]d = \sqrt{ ( (-1--3)^2 + (5-1)^2)}[/tex]

[tex]d=\sqrt{( (2)^2 + (4)^2)}[/tex]

[tex]d=\sqrt{(4+16)}[/tex]

[tex]d=\sqrt{(20)}[/tex]

d = 4.472135955

Rounding to the nearest hundredth

d = 4.47

Hence,  the distance from (−3, 1) to (−1, 5) is 4.47

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Final answer:

The company must sell either 2,000 or 5,000 items to break even, as determined by setting the profit function to zero and factoring the resulting quadratic equation.

Explanation:

To determine how many items must be sold for the company to break even, we need to set the profit function p(x) equal to zero and solve for x. In this case, the profit function is given by p(x) = -4x^2 + 28x - 40. Setting this to zero, we have:

-4x^2 + 28x - 40 = 0

Now, we need to solve this quadratic equation for x. To do this, we can factor the equation, use the quadratic formula, or complete the square. Since the coefficients are manageable, we'll try to factor first:

-4(x^2 - 7x + 10) = 0

Let's look for two numbers that multiply to 10 and add up to 7, which are 5 and 2. We can now factor further:

-4(x - 5)(x - 2) = 0

From the factored form, we get two potential solutions for x when the profit is zero:

x = 5

x = 2

Since x represents the number of items sold in thousands, the company must sell either 2,000 or 5,000 items to break even.

Answer:

positive linear association

hope this helps

2/9 divided by 5/12 simplifies to 2/15

Here we have to divide,

2/9 divided by 5/12

To divide fractions,

We have to flip the second fraction and multiply it by the first fraction. This gives us,

⇒ (2/9) ÷ (5/12) = (2/9) x (12/5)

We can simplify this expression by canceling out any common factors between the numerators and denominators.

In this case,

2 and 12 have a common factor of 2, while 9 and 5 don't have any common factors. This gives us,

⇒ (2/9) x (12/5) = 24/45

To express this fraction in its simplest form,

we can divide both the numerator and denominator by their greatest common factor, which in this case is 3.

This gives us,

6/45 = (24 ÷ 3) / (45 ÷ 3)

        = 8/15

Therefore, 2/9 divided by 5/12 simplifies to 8/15.

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If three lines meet at a single point, we say that the lines are concurrent.

Note that median is a line joining one vertex of a triangle with the midpoint of its opposite side.

Draw two medians for the given isosceles triangle.

Now, join the point of intersection of these medians and the third vertex.

If we prove the midpoint of the opposite side lies on this line, then it will be proved that the medians of the given isosceles triangle meet at a point.

Hence, here is the correct statement with blanks filled.

The midpoint of a side lies on the line containing the opposite vertex and the point where the other two medians intersect.

The car's fuel mileage on the highway is 40.32 mpg, which is 12% more than the 36 mpg it gets in the city.

To determine the car's fuel mileage on the highway, given that it is 12% more than the fuel mileage in the city, we start with the given city mileage of 36 miles per gallon (mpg). We calculate the additional mileage gained on the highway by taking 12% of 36 mpg, which is 0.12 × 36 mpg = 4.32 mpg. Adding this to the city mileage gives the highway mileage:

36 mpg + 4.32 mpg = 40.32 mpg on the highway.

Using the formula for compound interest, if you deposit $2,000 at 10% each year, the future balance in your account after 10 years would be approximately $5,187.12. This is due to the effect of compounding where the interest is calculated on both the principal and the accumulated interest.

The subject of this question is compound interest which is a Mathematics topic typically covered in High School. The formula A=p(1+r)^t is used to calculate the future balance in your savings account considering compound interest. Here, 'A' represents the future balance, 'p' is the current principle or balance, 'r' is the rate of interest, and 't' is time in years.

To answer your specific question: If you deposit $2,000 at a 10% rate each year, how much money will be in your account in 10 years? Let's plug the numbers into the formula. In this case, p=$2000, r=0.10 (as 10% equals 0.10 in decimal), and t=10 years.

So, A = 2000*(1 + 0.10)^10. Solving this, the future balance in your account after 10 years would be approximately $5,187.12. This is significantly more than simple interest ($100 × 0.05 × 3 = $15 in your example) due to the effect of compounding, as the interest is calculated on the principal plus the accumulated interest.

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