Factor by grouping: x^3 + 3x^2 - 25x -75 Which of the following is one of the factors?

ANSWER

[tex]c. \ln( \frac{2 {x}^{3} }{3y}) [/tex]

EXPLANATION

We want to write

[tex] ln(2x) + 2 ln(x) - ln(3y) [/tex]

as a single logarithm.

Use the power rule to rewrite the middle term:

[tex]n \: ln(a) = ln( {a}^{n} ) [/tex]

[tex]ln(2x) + ln( {x}^{2} ) - ln(3y) [/tex]

Use the product rule to obtain:

[tex]ln(a) + ln(b) = ln(ab) [/tex]

[tex]ln(2x \times {x}^{2} )- ln(3y) [/tex]

[tex]ln(2{x}^{3} )- ln(3y)[/tex]

Apply the quotient rule:

[tex] ln(a) - ln(b) = ln( \frac{a}{b})[/tex]

[tex]ln(2{x}^{3} )- ln(3y) =\ln(\frac{2 {x}^{3} }{3y})[/tex]

Answer:

3  5  30  32

Step-by-step explanation:

The question in English is

The age of 4 members of a family adds up to 70. Mom is 6 times bigger than her son and 10 times bigger than her daughter. Dad is 2 years older than Mom. How old are each of the family members? Write the result in ascending order and separated by spaces

Let

x----> Mon's age

y----> Son's age

z----> Daughter's age

w---> Dad's age

we know that

x+y+z+w=70 -----> equation A

x=6y ----> y=x/6 -----> equation B

x=10z ----> z=x/10 -----> equation C

w=2+x -----> equation D

substitute equation B, C and D in equation A and solve for x

x+(x/6)+(x/10)+(2+x)=70

Multiply by 60 both sides

60x+10x+6x+120+60x=4,200

136x=4,200-120

x=4,080/136

x=30 years

Find the value of y

y=x/6 -----> y=30/6=5 years

Find the value of z

z=x/10 ----> z=30/10=3 years

Find the value of w

w=2+x ----> w=2+30=32 years

Write the result in ascending order and separated by spaces

3  5  30  32

so

Daughter  Son  Mon  Dad

Answer:

D

Step-by-step explanation:

Given that AB and CD are parallel lines, then

∠c and ∠e are same side interior angles and are supplementary

Answer:

D. Supplementary

Step-by-step explanation:

Consecutive Interior Angles Theorem:

If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary.

Supplementary means the sum of the angles is 180 degrees.

Another name for consecutive interior angles is same side interior angles. The angles are on the same side of the transversal (in this case to the left) and they are in between the parallel lines which is the interior.

Answer:

4

Step-by-step explanation:

Answer:

first q is 2.75

second q is 1.5

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

Final answer:

The problem is a linear system where we find the cost of sugar cookie dough (x) at $12 per package and chocolate chip cookie dough (y) at $16 per package by forming and solving two linear equations.

Explanation:

The problem presented is one of linear systems, where we are asked to find the cost of one package of sugar cookie dough (x) and one package of chocolate chip cookie dough (y). To solve for x and y, we need to create two equations based on the information given:

13x + 6y = $252 (Lisa's sales)

8x + 12y = $288 (Julia's sales)

By solving this system of equations, we can determine the cost of each type of cookie dough. Using either substitution or elimination method will lead us to the solution. For this example, I'll use the elimination method:

Multiply each side of the first equation by 2, and the second equation by -1, and then add them together to eliminate y:
26x + 12y = $504
-8x - 12y = -$288
18x = $216
x = $216 / 18
x = $12

Substitute x back into any one of the original equations to find y:

13($12) + 6y = $252
$156 + 6y = $252
6y = $252 - $156
6y = $96
y = $96 / 6
y = $16

So the cost per package is $12 for sugar cookie dough and $16 for chocolate chip cookie dough.

B. y=2.25x+4.00 (eg. 2020)

Answer:

Step-by-step explanation:

The slanting line has a slope of approximately 1, so the angle this line makes with the horiz. axis is approx. 45 degrees.

Answer:

B

Step-by-step explanation:

It's not going to be a right angle. The two lines of a right angle are perpendicular. A is incorrect.

C is incorrect. 85o is pretty close to 90 degrees. That angle is nowhere's near that large.

D is incorrect. 160 degrees is nearly a straight line. The angle shown isn't.

That leaves B.

B looks to be 45 degrees and since the others are incorrect, B must be your answer.

Answer:

[tex]\large\boxed{x=8\sqrt2}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}\\\\\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=8,\ leg=8,\ hypotenuse=x.\\\text{Substitute:}\\\\x^2=8^2+8^2\\\\x^2=2(8^2)\to x=\sqrt{2(8^2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=\sqrt2\cdot\sqrt{8^2}\qquad\text{use}\ \sqrt{a^2}=a\\\\x=8\sqrt2[/tex]

[tex]\bold{METHOD\ 2}\\(look\ at\ the\ picture)\\\\\text{We have}\ a=8.\ \text{Therefore}\ a\sqrt2=8\sqrt2[/tex]

Answer:

6 feet from the edge of the wall

Step-by-step explanation:

The cost increase is:

(4 - 3) / 3 × 100%

33%

The answer is none of these.

Answer:

Option E. None of these.

Step-by-step explanation:

A merchant paid $3 each for golfing hats and sold for $4 each. He earned a gross profit of $1 per hat.

We have to calculate the percent of increase in cost price Or percentage profit.

Percentage profit = [tex]\frac{\text{(Selling price - Cost price)}}{\text{cost price}}(100)[/tex]

= [tex]\frac{(4-3)}{3}.(100)[/tex]

= [tex]\frac{100}{3}=33.33[/tex]%

Which not in any option.

Therefore, Option E. None of these is the answer.

Answer:

Each burrito platter costs $_31_ and each taco platter costs $_23__ .

Step-by-step explanation:

Let's first express both orders into equations.  Let's simply use b for the burritos platters and t for the tacos platters:

4b + 5t = 239

3b + 5t = 208

We can use the subtraction method easily on this one:

4b + 5t = 239

-

3b + 5t = 208

==============

1b + 0t = 31

b = 31

So, the burrito platters ost $31 each.

Now, let's find how much are the tacos ones.  Just take the first equation:

4(31) + 5t = 239

124 + 5t = 239

5t = 115

t = 23

Taco platters cost $23.

Let's test that with the second equation:

3b + 5t = 208

3(31) + 5(23) = 208

93 + 115 = 208

208 = 208

Verified!

Answer:

9

Step-by-step explanation:

if every container needs 1/3 of one cup and you have 3 cups then multiply 3 by 3 and you have your answer

Miss Diego will be able to fill 9 containers.

We must divide the quantity of sugar by the quantity of sugar each container can hold to find the total number of containers.

It is given that Miss Diego has three cups of sugar.

It is also given that the containers can hold 1/3 of a cup.

We are asked to find the total number of containers she can fill.

This can be done as shown below:

Total number of cups = Total cups of sugar/quantity of sugar each container can hold

= 3 / (1/3)

= 3 * 3

= 9

The number of containers that can be filled is found. The total number of containers that can be filled is equal to 9 containers.

Therefore, we have found that Miss Diego will be able to fill 9 containers.

Learn more about division here: https://brainly.com/question/1622425

#SPJ2

Answer:

2110 dollars / month

Step-by-step explanation:

Formula

New Salary = Old Salary * (1 + 5.5/100)

Solution

New Salary = 2000 * (1 + 0.055)

New Salary = 2000 * 1.055

New Salary = 2110 dollars / month

Answer:

Last Choice: 6 * 3 * 3 square inches

Step-by-step explanation:

The net is made up of 6 squares. Each square measures 3 inches by 3 inches. The area of one square is 3 * 3 square inches. The total surface is 6 times the area of one square.

Answer: 6 * 3 * 3 square inches

Answer:

C. [tex]y=3\cdot 5^x[/tex]

Step-by-step explanation:

First two options show linear function and last two options show exponentioal functions. From the table you can see that

[tex]\dfrac{3}{5}=5\cdot \dfrac{3}{25}\\ \\3=5\cdot \dfrac{3}{5}\\ \\15=5\cdot 3\\ \\75=5\cdot 15[/tex]

This gives you that the function is exponential. Let the expression for the function be [tex]y=ab^x.[/tex] Substitute two values:

at x=0:

[tex]y=a\cdot b^0\\ \\3=a\cdot b^0\\ \\3=a\cdot 1\\ \\a=3[/tex]

at x=1:

[tex]y=a\cdot b^1\\ \\15=a\cdot b\\ \\15=3\cdot b\\ \\b=\dfrac{15}{3}\\ \\b=5[/tex]

Hence

[tex]y=3\cdot 5^x[/tex]

Answer:

$930

Step-by-step explanation:

The amount payable at maturity of the loan is simply the sum of the loan amount and the fee charged on the loan.

The loan amount is 890 while the fee charged on the loan is 40. The amount repayable at maturity is thus;

890 + 40 = 930.

Therefore, he has to pay $930 by the time the loan reaches maturity.

Answer:

$930

Step-by-step explanation:

Daryl took out a single payment loan for $890.

That charged a $40 fee.

He takes loan of $890 that charged a $40 fee for a single time, so his maturity amount = loan amount + fees of $40

He have to pay by the time the loan reaches maturity = 890 + 40

                                                                                         = $930

He have to pay $930 by the time of maturity.

Answer:

A right triangle

Step-by-step explanation:

Suppose a, b, c are the sides of a triangle,

If a² = b² + c² or b² = a² + c² or c² = a² + b²

Then the triangle is called a right angled triangle,

If a² + b² > c², a² + c² > b², b² + c² > a²

Then the triangle is called an acute triangle,

If a = b = c

Then the triangle is called an equilateral triangle,

If a² + b² < c², where c is the largest side of the triangle,

Then the triangle is called an obtuse triangle,

Now, In triangle RST,

By the distance formula,

[tex]RS=\sqrt{(3-1)^2+(-1-(-3))^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}\text{ unit }[/tex]

Similarly,

ST = √40 unit,

TR = √32 units,

Since, ST² = RS² + TR²

Hence, by the above explanation it is clear that,

Triangle RST is a right angled triangle,

First option is correct.

Answer:

this isa right triangle!!!

Step-by-step explanation:

this isa right triangle!!!

Answer:

(3, -7) are the coordinates

Answer:

1 inch : 5 yards.

Step-by-step explanation:

Paco's first scale was 2 : 5 which is 1 : 2.5.

Now as the length of the pool on the drawing was reduced from 10 in to 5 ins,  that means the scale was doubled so the answer is:

1 : 2*2.5 = 1 : 5 .

Answer:

[tex]c=\frac{99}{32}[/tex]

Step-by-step explanation:

The given quadratic equation is [tex]2x^2-5x+c=0[/tex].

Comparing this equation to:  [tex]ax^2+bx+c=0[/tex], we have a=2,b=-5.

Where: [tex]x_1+x_2=\frac{5}{2}[/tex] and [tex]x_1x_2=\frac{c}{2}[/tex]

The difference in roots is given by:

[tex]x_2-x_1=\sqrt{(x_1+x_2)^2-4x_1x_2}[/tex]

[tex]\implies 0.25=\sqrt{(2.5)^2-4(\frac{c}{2})}[/tex]

[tex]\implies 0.25^2=6.25-2c[/tex]

[tex]\implies 0.0625-6.25=-2c[/tex]

[tex]\implies -6.1875=-2c[/tex]

Divide both sides by -2

[tex]c=\frac{99}{32}[/tex]

Answer:

The value of c is 3.09375.

Step-by-step explanation:

Given : The difference between the roots of the equation [tex]2x^2-5x+c=0[/tex] is 0.25.

To find : The value of c?

Solution :

The general quadratic equation is [tex]ax^2+bx+c=0[/tex] with roots [tex]\alpha,\beta[/tex]

The sum of roots is [tex]\alpha+\beta=-\frac{b}{a}[/tex]

The product of roots is [tex]\alpha\beta=\frac{c}{a}[/tex]

On comparing with given equation, a=2, b=-5 and c=c

Substitute the values,

The sum of roots is [tex]\alpha+\beta=-\frac{-5}{2}[/tex]

[tex]\alpha+\beta=\frac{5}{2}[/tex] .....(1)

The product of roots is [tex]\alpha\beta=\frac{c}{2}[/tex] ....(2)

The difference between roots are [tex]\alpha-\beta=0.25[/tex] .....(3)

Using identity,

[tex]\alpha-\beta=\sqrt{(\alpha+\beta)^2-4\alpha\beta}[/tex]

Substitute the value in the identity,

[tex]0.25=\sqrt{(\frac{5}{2})^2-4(\frac{c}{2})}[/tex]

[tex]0.25=\sqrt{\frac{25}{4}-2c}[/tex]

[tex]0.25=\sqrt{\frac{25-8c}{4}}[/tex]

[tex]0.25\times 2=\sqrt{25-8c}[/tex]

[tex]0.5=\sqrt{25-8c}[/tex]

Squaring both side,

[tex]0.5^2=25-8c[/tex]

[tex]0.25=25-8c[/tex]

[tex]8c=25-0.25[/tex]

[tex]8c=24.75[/tex]

[tex]c=\frac{24.75}{8}[/tex]

[tex]c=3.09375[/tex]

Therefore, the value of c is 3.09375.

Answer:

Car B

Step-by-step explanation:

Car B's price changes by the greatest amount (£40) when rounded to the nearest £100 among the three cars.

To determine which price changes by the greatest amount when rounded to the nearest £100, let's first calculate the rounded prices for each car:

Car A: £12380 rounds to £12400

Car B: £16760 rounds to £16800

Car C: £14580 rounds to £14600

Now, let's compare the differences between the original prices and the rounded prices:

- For Car A: £12400 - £12380 = £20

- For Car B: £16800 - £16760 = £40

- For Car C: £14600 - £14580 = £20

The greatest difference is £40, which occurs for Car B. Therefore, the price of Car B changes by the greatest amount when rounded to the nearest £100.

recall that to find the x-intercept we set y = 0 and solve for "x".

and to find the y-intercept, we set x = 0 and solve for "y", so let's do so

x = 0, so then the equation turns into

y = 3x² + 5x - 2

y = 3(0)² + 5(0) - 2

y = -2

when x = 0, y = -2, ( 0 , -2 ).

Answer:

Kwan's work

Step-by-step explanation:

The given equation is:

[tex]\frac{w}{13.5}=9.7[/tex]

We multiply both sides by 13.5 to obtain:

[tex]\frac{w}{13.5}\times 13.5=9.7\times 13.5[/tex]

We simplify to get;

[tex]w=9.7\times 13.5[/tex]

We multiply out the RHS to get:

[tex]w=130.95[/tex]

Answer:

kyan's work

Step-by-step explanation:

i did the test

Answer: [tex]a_{25} = 128[/tex]

Step-by-step explanation:

You need to use this formula:

[tex]a_n = a_1 + (n - 1)d[/tex]

Where [tex]a_n[/tex] is the nth] term,  [tex]a_1[/tex] is the first term,"n" is the term position and  "d" is the common diference.

You must find the value of "d". Substitute [tex]a_1=8[/tex], [tex]a_9=48[/tex] and [tex]n=9[/tex] into the formula and solve for "d":

[tex]48 = 8 + (9 - 1)d\\48=8+8d\\48-8=8d\\40=8d\\d=5[/tex]

Now, you can calculate the 25th term substituting into the formula these values:

[tex]a_1=8[/tex]

[tex]d=5[/tex] and [tex]n=25[/tex]

Then you get:

[tex]a_{25} = 8 + (25 - 1)5[/tex]

[tex]a_{25} = 8 + 120[/tex]

[tex]a_{25} = 128[/tex]

Answer:

no solutions

Step-by-step explanation:

Answer:

Exactly one solution.

Step-by-step explanation:

We have been given a system of equations. We are asked to find the number of solutions for our given system.

[tex]y=x+2...(1)[/tex]

[tex]6x-4y=-10...(2)[/tex]

We can see that equation (1) in slope-intercept form of equation.

We will convert equation (2) in slope-intercept form of equation as shown below:

[tex]6x-6x-4y=-10-6x[/tex]

[tex]-4y=-6x-10[/tex]

Divide both sides by [tex]-4[/tex].

[tex]\frac{-4y}{-4}=\frac{-6x}{-4}+\frac{-10}{-4}[/tex]

[tex]y=\frac{3}{2}x+\frac{5}{2}[/tex]

We can see that slopes of both lines are different, therefore, our given lines will intersect exactly at one point and our given system of equations has exactly one solution.

Answer:

see explanation

Step-by-step explanation:

Either both equations are equal or are multiples of each other

As an example consider the 2 equations

4x - y = 2 → (1)

- 12x + 3y = - 6 → (2)

Multiply (1) by - 3

- 12x + 3y = - 6 → (3)

Subtract (3) from (2) term by term

(- 12x - (- 12)x) + (3y - 3y) = (- 6 - (- 6)), that is

(- 12x + 12x) + 0 = - 6 + 6

0 = 0

This indicates the solution has infinite solutions

let x = k, k is a real number then from (1) y = 4x - 2 ⇒ y = 4k - 2

Thus (k, 4k - 2) will generate solutions to the system of equations

Answer:

108 cm²

Step-by-step explanation:

The lateral area of this pyramid is the addition of the six triangle areas formed on its lateral side.

The area of each triangle is:

Area = (1/2)*side*slant

Area = (1/2)*3*12 = 18 cm²

Then the lateral area is 6*18 = 108 cm²

Answer:

108cm2

Step-by-step explanation:

Answer:

the awnser would be a tangent of the plate     i hope this helps

Step-by-step explanation:

Answer:

c. Radius of the plate

Step-by-step explanation:

The radius of a circle is a segment that goes from the center of the circumference to any point of the perimeter of the circumference, as the plate is a circle, and you have a straight line going from the center of the circumference to a point in the perimeter it is a radius.

Answer:

210.6 cm

Step-by-step explanation:

Given that a piece of ribbon is cut into two shorter pieces in the ratio 2.8:1.25.

So that means length of the first smaller piece = 2.8x

and length of the second smaller piece = 1.25x

Then difference between their lengths = 2.8x-1.25x = 1.55x

Given that difference is equal to 80.6 centimeters then we get

1.55x=80.6

or x= 80.6/1.55

or x=52

then length of the original piece = 2.8x+1.25x

= 2.8*52+1.25*52

= 145.6+65

= 210.6 cm