50 points! A polynomial has been factored below, but some constants are missing. 2x^3 - 8x^2 - 24x = ax (x+b)(x+c) What are the missing values of a, b, and c?

The system of equations -3x + 3y = 9 and 2x - 7y = -14 belongs to the branch of math called Algebra. You can solve the system using methods like substitution or elimination. The solution for the system is x = -2, y = 1.6.

The given equations are part of the math branch known as Algebra, specifically a system of linear equations. The system consists of the following equations:

-3x + 3y = 9 and 2x - 7y = -14

To solve for x and y, you use the method of substitution or elimination. Let's use the method of elimination:

Multiply the first equation by 2 and the second equation by 3:

-6x + 6y = 18 and 6x - 21y = -42

Then, sum both equations (this will cancel the x variable, leading to a single equation with y):

-15y = -24

Finally, divide by -15 to solve for y, which gives y = 24/15 or 1.6. Substituting y into the first equation gives x = -2.

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Answer:

see explanation

Step-by-step explanation:

Given

8x - 6 > 12 + 2x ( subtract 2x from both sides )

6x - 6 > 12 ( add 6 to both sides )

6x > 18 ( divide both sides by 6 )

x > 3

Any value of x greater than 3 will be in the solution set

Answer:

7960

Step-by-step explanation:

4000+99*40

4000+3960

7960

I believe 50% of 284 =142

Answer:

284/50*100 = 586 or simply double 284

Step-by-step explanation:

Answer:

8,16,24,32,48

Step-by-step explanation:

When dividing a number by 7, only 7 different remainders are possible.

The remainders when dividing by 7 can not exceed 6, so the numbers in which we are interested can be represented as 7k+k or just 8k, where k=1, 2, ... , 6.

Answer:

8, 16, 24, 32, 40, 48

Step-by-step explanation:

Answer:A

Step-by-step explanation:The answer is A because if you divide the numbers equally, then you will get 1

The number of 1/8-acre plots in a 3/4-acre garden is 6.

The question is about dividing the total area of a garden into smaller plots and finding out how many plots there will be. Here, the total size of the garden is given as 3/4 acre and each plot is 1/8 acre in size. To find out how many 1/8-acre plots make 3/4 of an acre, we perform a division: 3/4 divided by 1/8. This is the same as multiplying 3/4 by the reciprocal (the 'flipped' fraction) of 1/8, which is 8/1. So, the calculation is 3/4 * 8/1 = 24/4 = 6. Therefore, there are 6 1/8-acre plots in a 3/4-acre garden.

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The inequality is:

[tex]5x+4y \leq 124[/tex]

Give one solution to the inequality:

Let x = 5 and y = 10

[tex]65\leq 124\,\,\,true[/tex]

Step-by-step explanation:

Cost of Gift cards= $5

Cost of Teddy bear = $4

Total money to spend on party = $124

The required inequality is:

Let no of gift cards= x

and no of teddy bears = y

The inequality is:

[tex]5x+4y \leq 124[/tex]

Give one solution to the inequality:

Let x = 5 and y = 10

then, the solution will be:

[tex]5x+4y \leq 124\\5(5)+4(10)\leq 124\\25+40\leq 124\\65\leq 124\,\,\,true[/tex]

Keywords: Solving inequalities

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Answer:

The inequality is 5x + 4y < and the line under the sign 124

(10,9)

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

A negative number divided by a positive number will be negative.

20/4 is 5.

(5x4=20)

Therefore (-20)/4 = (-5)

Answer:

-6(2b-c-3)

Step-by-step explanation:

Collect like terms

-12b+6c+12+6

Add the 2 numbers on right

-12b+6c+18

Factor -6 out of expression

-6(2b-c-3)

Answer:

2.03

Step-by-step explanation:

Answer: y = 4.88 + 0.525x

The equation of the line of best fit for the data shown in the picture is y=0.894x+0.535

A straight line is a combination of endless points joined on both sides of the point.

We have a data in the table:

Let's suppose the equation for the line is:

y = mx + c

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

The value of m is given by:

[tex]\rm m = \frac{S_{xy}}{S_{xx}} }[/tex]    and

[tex]\rm S_{xy} = \sum_{i=1}^{n}x_iy_i-\frac{(\sum_{i=1}^{n}x_i)(\sum_{i=1}^{n}y_i)}{n}[/tex]

[tex]\rm S_{xx} = \sum_{i=1}^{n}x_i^2-\frac{(\sum_{i=1}^{n}x_i)^2}{n}[/tex]

From the table(data is not mentioned we have assumed the data) the values of  [tex]\rm \sum_{i=1}^{n}x_iy_i= 415[/tex], [tex]\rm {\sum_{i=1}^{n}x_i= 44[/tex], [tex]\rm {\sum_{i=1}^{n}y_i= 42[/tex],

[tex]\rm {\sum_{i=1}^{n}x_i^2= 438[/tex], and n = 5.

[tex]\rm S_{xy}= 415-\frac{44\times42}{5} \Rightarrow 45.4\\\\\rm S_{xx}= 438- \frac{44^2}{5} \Rightarrow 50.8[/tex]

[tex]\rm m = \frac{45.4}{50.8} } \Rightarrow 0.8937 \approx0.894[/tex]

For c we have to calculate the means of x and y for this:

[tex]\rm \bar{x} = \frac{\sum x}{n} \Rightarrow \frac{44}{5} \Rightarrow8.8[/tex]

[tex]\rm \bar{y} = \frac{\sum y}{n} \Rightarrow \frac{42}{5} \Rightarrow8.4[/tex]

Now, put the above values in the equation of a line to find the value of c

8.4 = (0.894)(8.8)+c

c = 0.5328 ≈ 0.535

Now the line is y = 0.894x+0.535

Thus, the line of best fit for the data shown in the picture is y=0.894x+0.535

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Answer: 24/55

Step-by-step explanation:

multiply both numerators and denominators

6/11 × 4/5 = 24/55

If there is a strong positive correlation between "x" and "y" then when "x" increases, "y" tends to increase

If variables x and y have strong negative correlation then as "x" increases in value, "y" will decrease; similarly, if "x" decreases in value, "y" will increase

1) If the variables x and y have a strong positive correlation, what generally happens to y as x increases?

Let us first understand about strong positive correlation

Given that "x" and "y" has strong positive correlation

Correlation coefficients are used to measure the strength of the relationship between two variables.

Positive correlation:

Positive correlation is a relationship between two variables in which both variables move in tandem—that is, in the same direction.  A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.

When one variable moves higher or lower, the other variable moves in the same direction with the same magnitude.

Therefore if there is a strong positive correlation between "x" and "y" then when "x" increases, "y" tends to increase

2) What if x and y have a strong negative correlation?

Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa.

Negative correlation is a relationship between two variables whereby they move in opposite directions.

If variables x and y have strong negative correlation then as "x" increases in value, "y" will decrease; similarly, if "x" decreases in value, "y" will increase

For this case we must find an expression equivalent to:

[tex]36y-18x-108y + 54[/tex]

We add similar terms:

[tex]36y-108y-18x + 54 =[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]-72y-18x + 54[/tex]

Thus, an equivalent expression is:

[tex]-72y-18x + 54\\-18x-72y + 54[/tex]

Answer:

[tex]-18x-72y + 54[/tex]

Final answer:

To find equivalent expressions, we combine like terms in the given expression 36y - 18x - 108y + 54.

Explanation:

To find expressions equivalent to 36y - 18x - 108y + 54, we can combine like terms.

First, combine the y terms: 36y - 108y = -72y.

Next, combine the x terms: -18x.

Combining the constants, we have: 54.

Putting it all together, the equivalent expression is: -18x - 72y + 54.

Answer:

40 minutes

Step-by-step explanation:

60 pages / (1 1/2 pages/ minute)

= 60 / 3/2 minutes

= 40 minutes

Answer:

330 minutes

Step-by-step explanation:

11/2 times 60/1

so basically just do 60 times 11 equals

660 then divided by 2 equals 330

so she will read 60 pages in 330 minutes, I hope I did it right

I think I'm wrong

Answer:

Explanation:

To find a relationship modeled by the given function it is recommendable to factor it.

The function is:

The first step to factor it is to extract common factor 4x:

The second step is to factor the quadratic trinomial.

That is made by writting it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is:

Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.

Thus, the volume of the prism is the product of the three factors:

Answer:

72 degrees

Step-by-step explanation:

Congruent supplements Theorem.

The symbol m∠LNM denotes the measure of the angle formed by points L, N, M. The 'm' stands for measure, '∠' denotes an angle, and LNM are the points forming the angle. In this context, m∠LNM is 72 degrees.

The term m∠LNM refers to the measure of angle LNM. In mathematical notation, the symbol '∠' is often used to denote an angle, and LNM refers to the points forming the angle. For instance, if you have a triangle or any other polygon, and points L, N, and M are three vertices (corners) of the shape, then ∠LNM would be the angle at vertex N, formed by the intersection of line segments LN and NM. Given that m∠LNM is said to be 72°, this indicates that the measure of angle LNM is 72 degrees.

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Answer:

x=5, y=5. (5, 5).

Step-by-step explanation:

x=3y-10

x=2y-5

--------------

3y-10=2y-5

3y-2y-10=-5

y-10=-5

y=-5+10

y=5

x=2(5)-5=10-5=5

Answer:

375 adult tickets and 302 student tickets

Step-by-step explanation:

s+a=677

a=s+73

s+s+73=677

2s+73=677

2s=604

s=302

a= 375

Final answer:

Explanation on finding the number of adult tickets sold for a school play when the total number of tickets sold and the relationship between adult and student tickets are known.

Explanation:

The total number of tickets sold for the school play was 677.

Let x be the number of adult tickets sold.

It is given that there were 73 fewer student tickets than adult tickets, so the number of student tickets sold would be x - 73.

Therefore, x + (x - 73) = 677.

Solving this equation, we find that 2x - 73 = 677, 2x = 750, x = 375.

So, 375 adult tickets were sold.

Answer:

Step-by-step explanation:

[tex]9(2x+1)-4(x-6)=6(2x+1)+5(x-6)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(9)(2x)+(9)(1)+(-4)(x)+(-4)(-6)=(6)(2x)+(6)(1)+(5)(x)+(5)(-6)\\\\18x+9-4x+24=12x+6+5x-30\\\\\text{combine like terms}\\\\(18x-4x)+(9+24)=(12x+5x)+(6-30)\\\\14x+33=17x-24\qquad\text{subtract 33 from both sides}\\\\14x+33-33=17x-24-33\\\\14x=17x-57\qquad\text{subtract}\ 17x\ \text{from both sides}\\\\14x-17x=17x-17x-57\\\\-3x=-57\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{-57}{-3}\\\\x=19[/tex]

Algebra tiles are a useful tool to simplify expressions. Depending on their shape and decoration, they represent different parts of the expression. Review your tiles and match them to the four given expressions carefully.

The question pertains to Algebra and specifically, matching a simplified algebraic expression to a set of tiles. The exact matching algebraic expression cannot be determined as the set of tiles isn't provided in the question but here's how you would approach this kind of problem:

If you're using algebra tiles, squares typically represent x², rectangles portray x, and small squares depict constants like 2. The color or decoration of a tile may indicate a positive or negative value. For example, a square with '- ' could mean '-x²'.

So if you've got a square with '- ', a rectangle without a decoration, and two small plain squares, your expression should be '-x² - x + 2'. If the rectangle had a '-', your expression would be '-x² + x + 2' instead.

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The set of tiles shown represents the expression x² - x + 2.

The set of tiles shown represents the expression x² - x + 2.

To match the tiles to the simplified expression, look at the coefficient and exponent of x on each tile. The first tile has an exponent of 2 and a coefficient of 1. The second tile has an exponent of 1 and a coefficient of -1. The third tile has an exponent of 0 and a coefficient of 2. Therefore, the simplified expression that matches the set of tiles is x² - x + 2.

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Answer:

4.  B

5.  C

Step-by-step explanation:

4.

We can say the 5 angles of the Pentagon PQRST equals 540 degrees.

We see that Angle P and Angle T are 90 degrees each.

R is given as 100

Q and S are same, let it be "x"

Now we can write an equation:

P + Q + R + S + T = 540

90 + x + 100 + x + 90 = 540

Solving for x, we get:

2x + 280 = 540

2x = 540 - 280

2x = 260

x = 260/2

x = 130

Angle Q is equal to x, so that is 130

Correct answer is B

5.

When 2 parallel lines are cut by transversal, the corresponding angles are equal.

The 60 degree angle given and the angle adjacent (beside) to angle x are same. So we can say that is equal to 60 degrees as well.

This 60 degree angle and x form a straight line. The degree measure of a straight line (or a straight angle) is 180 degrees. Thus we can write:

60 + x = 180

Now, we solve for x:

60 + x = 180

x = 180 - 60

x = 120

The correct answer is C

Answer:

280

Step-by-step explanation:

Answer:280

Step-by-step explanation:

From 240 to 260 you add 20 each time so 260 plus 20 will give us the answer (280)

Answer:

515

Step-by-step explanation:

If it's a multiple of five and not ten, that would be the units digit must be 5. Hundreds=units. 11-10=1. So the answer is 515

The number is a multiple of 5 but not 10, with the units and hundreds digits being the same and their sum being 11. Therefore, the number is 505.

This question can be solved by analyzing the given clues. The number is a multiple of 5 but not 10, so it cannot end in 0. The units and hundreds digits are the same, meaning they both have to be a single digit number. Additionally, the sum of the three digits is 11.

Since the units and hundreds digits are the same, and their sum is 11, they both must be equal to 5. Thus, the number is 505.

A(-2,-4), B(-4,-2), C(-6,-4)

Translating by (2,3) adds 2 to the x and 3 to the y so gives

A'(0,-1), B'(-2,1), C'(-4, -1)

Reflecting in x=0 (the y axis) keeps the ys the same but negates the xs

A''(0,-1), B''(2,1), C''(4,-1)

I'll leave the drawing to you.

Answer:

[tex]\large\boxed{5x-6y=16}[/tex]

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

We have the equation in the point-slope form. Convert:

[tex]y+1=\dfrac{5}{6}(x-2)\qquad\text{multiply both sides by 6}\\\\6y+6=6\!\!\!\!\diagup^1\cdot\dfrac{5}{6\!\!\!\!\diagup_1}(x-2)\\\\6y+6=5(x-2)\qquad\text{use the distributive property}\\\\6y+6=(5)(x)+(5)(-2)\\\\6y+6=5x-10\qquad\text{subtract 6 from both sides}\\\\6y+6-6=5x-10-6\\\\6y=5x-16\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+6y=5x-5x-16\\\\-5x+6y=-16\qquad\text{change the signs}\\\\\boxed{5x-6y=16}[/tex]

Answer:

y= 1/2x-1

Step-by-step explanation:

The equation of a line is y= mx+c

m represents the slope of the line

c represents the y-intercept

So we plug in our information into the equation.

The slope is 1/2 so y= 1/2x + c

The line crosses at (0,-1) which makes -1 the y-intercept as the line crosses at this point on the y-axis.

Therefore, y= 1/2x-1

To write an equation for a line with a slope of 1/2 that crosses the y-axis at the point (0,-1), we can use the slope-intercept form of a linear equation, y = mx + b. Substitute the given values into the equation to get y = (1/2)x - 1.

To write an equation for a line with a slope of 1/2 that crosses the y-axis at the point (0,-1), we can use the slope-intercept form of a linear equation, which is y = mx + b.

Here, 'm' represents the slope and 'b' represents the y-intercept.

Since the slope is 1/2 and the y-intercept is at (0,-1), we can substitute these values into the equation to get y = (1/2)x + (-1) or y = (1/2)x - 1.

This equation represents a line with a slope of 1/2 and crosses the y-axis at the point (0,-1).

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Answer:

[tex]\large\boxed{0.00003400=3.4\cdot10^{-4}}[/tex]

Step-by-step explanation:

The scientific notation:

[tex]a\cdot 10^k[/tex]

where

[tex]1\leq a<10,\ k\in\mathbb{Z}[/tex]

[tex]0.0003400=0\underbrace{.0003}_{4\to}4=3.4\cdot10^{-4}\\\\0.00034=3.4:10000=3.4:10^4=3.4\cdot\dfrac{1}{10^4}=3.4\cdot10^{-4}\\\\\text{used}\ a^{-n}=\dfrac{1}{a^n}[/tex]

Answer:

31

Step-by-step explanation:

given f(x) = 2x + 25,  

f(3) =2(3) + 25

= 6 + 25

= 31

Answer:

Step-by-step explanation:

Answer:

11j + 4

Step-by-step explanation:

Disregard parentheses in this situation.

3j + 11 + 8j - 7

Add the j's

11j + 11 - 7

11j + 4

Answer:

A

Step-by-step explanation:

I just did it

Based on the above description, the areas of triangle ABC and DEF  is compared to The area of △ABC is equal to the area of △DEF.

Looking at the image show:

The area of  △ABC

= 4 x 3 x 1/2

=6

The  area of  △DEF

= 6 x 2 x 1/2

= 6

Therefore, from the above, the areas of triangle ABC and DEF  is compared to The area of △ABC is equal to the area of △DEF.

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