Using arithmetic operations, rewrite this polynomial in standard, simplest form. (3x2 + 9x + 6) − (8x2 + 3x − 10) + (2x + 4)(3x − 7)

Answer: 145

3.7 x 60 = 222 (how far north she drove)

1.4 x 55 = 77 (how far south she drove)

222 - 77 = 145 (how far from home)

Answer:

A) (1/9)^8

Step-by-step explanation:

9^-5 × 9^-3 =

Rule: a^m * a^n = a^(m + n)

= 9^-8

Rule: (a^m)^n = a^(mn)

= (9^-1)^8

Rule: a^-m = 1/a^m

= (1/9)^8

Answer: A) (1/9)^8

Answer: 2.50

Step-by-step explanation: your answer is 2.50

Answer:-11

Step-by-step explanation:

use -6 to represent losing 6 yards

use -5 to represent losing 5 yards

add these together

(-6) + (-5) = -11

when adding two negative values, make sure your sum is negative

Answer:

it is 9

Step-by-step explanation:

6 plus 3 is 9

I had this for homework so I know

Answer:

Ricky = 1201

Pedro = 1476

Step-by-step explanation:

Assign variables

let p be the number of Pedro's base hits

let r be the number of Ricky's base hits

Create a system of equations

p + r = 2677            <= Pedro and Ricky got 2677 base hits

p = r + 275              <= Pedro had 275 more hits than Ricky

Solve using the substitution method (replace a variable with an expression)

p + r = 2677

Substitute "p" with "r + 275"

r + 275 + r = 2677

Combine like terms to simplify

2r + 275 = 2677

Isolate "r" by moving everything else to the right side.

2r = 2677 - 275                  Subtract 275 from both sides

2r = 2402

2r/2 = 2402/2                     Divide both sides by 2

r = 1201                              Ricky's base hits

To find Pedro's hits, substitute "r" into any equation.

p = r + 275

p = 1201 + 275                    Substitute r = 1201, then add

p = 1476                             Pedro's base hits

∴ Ricky had 1201 base hits and Pedro had 1476 base hits.

Final answer:

By setting up an equation where R represents Ricky's hits, and calculating R + 275 for Pedro's hits, we can solve for R and then find the number of hits for each player. Ricky had 1201 hits, while Pedro had 1476 hits.

Explanation:

To solve the problem of determining how many base hits Pedro and Ricky each had last season, we can use algebra. Let's let the variable R represent the number of hits Ricky had. Since Pedro had 275 more hits than Ricky, we can express Pedro's number of hits as R + 275. According to the question, the sum of their hits is 2677, so the equation will be R + (R + 275) = 2677.

Now, let's solve the equation:

R + R + 275 = 2677

2R + 275 = 2677

2R = 2677 - 275

2R = 2402

R = 2402 / 2

R = 1201

So, Ricky had 1201 hits. To find Pedro's hits, we substitute R into the expression R + 275:

Pedro's hits = R + 275 = 1201 + 275 = 1476

Therefore, Ricky had 1201 hits and Pedro had 1476 hits.

Answer:

9R30  

Step-by-step explanation:

         9

36)354

    324

      30

Answer:

x - [tex]\sqrt{7}[/tex]

Step-by-step explanation:

A polynomial has the form

first term is the term of highest degree followed by term of second etc.

note that x = [tex]x^{1}[/tex] ← degree 1

x - [tex]\sqrt{7}[/tex]

fits this description and is a polynomial of degree 1

Answer:   The answer is C

Step-by-step explanation:  15 - 2 = 13     13+5=18

Hope this helps :)

Answer:

7 buses are needed.

Step-by-step explanation:

There are 325 students and adults.

Each bus holds 48 people.

The number of buses needed = [tex]\frac{325}{48}[/tex] = 6.770833333

Since we cant have 0.770833333 buses, we accept that only 7 buses are needed here and that;

325 - (48 × 6) = 37 people will not fill the last bus.

Answer:

slope = 2.5 and the y intercept is 3

Step-by-step explanation:

To find the slope we can use the formula

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

I will use the point (2,8) (6,18)  We can pick any 2 point we want.

 = (18-8)/(6-2)

  = (10/4)

  = 2.5

To find the y intercept we need to find the equation of the line.

We will use the point slope form

y-y1= m(x-x1)

y-8 = 2.5(x-2)

Distribute the 2.5

y-8 = 2.5x-5

Add 8 to each side

y-8+8 = 2.5x-5+8

y = 2.5x+3

This equation is in slope intercept form  y = mx+b

where the slope is 2.5 and the y intercept is 3

Hi There!

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

Find The Slope:

[tex]m = \frac{13 - 8}{4 - 2} = \frac{5}{2} or 2.5[/tex]

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

Find The Y-Intercept:

Substitute using x = 2 and y = 8

Use y = mx + b

Substitute: 8 = 2.5(2) + b

Simplify: 8 = 5 + b

Subtract 5 too both sides: 8 - 5 = 5 + b - 5

Simplify: 3 = b

Y-Intercept = 3

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

Point Slope Form: y - 8 = 2.5(x - 2)

Slope Intercept Form: y = 2.5x + 3

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

Hope This Helps :)

Answer:

4617 yd

Step-by-step explanation:

30.5 ft make 1 roll of tape

Length of tape = 454 × 30.5/1

Length of tape = 13 847 ft

1 ft = 3 yd

Length of tape = 13 847 × 1/3

Length of tape = 4617 yd

The coefficient of q in the sum of (23q - 34) and (-16q - r) is 7.

In mathematics, a coefficient is a numerical factor or constant that multiplies a variable or term in an algebraic expression. It determines the scale or magnitude of the term and is often used in equations, polynomials, and linear expressions.

The sum of the two expressions is (23q - 34) + (-16q - r).

To find the coefficient of q in this sum, we need to combine the like terms.

Combining the q terms, we have 23q - 16q = 7q.

Therefore, the coefficient of q in the sum of the two expressions is 7.

Answer:

[tex]\frac{2}{81}[/tex]

Step-by-step explanation:

Step 1

List the experimental probabilities of each color using the first letter of that color. The spinner is spun 18 times The probabilities are listed below. P(blue)=3/18, P(red=4/18), P(white) =3/18, P(yellow)=2/18, P(black)=5/18, P(purple)=1/18

Step 2

The second step is to calculate the required probability given the information in step 1. The probability that George will spin a red and then a yellow is obtained by multiplying the probability that he spins a red and the probability that he spins a yellow. This calculation is shown below,

[tex]P=P(red)\times P(yellow)=\frac{4}{18} \times \frac{2}{18} =\frac{8}{324} =\frac{2}{81}.[/tex]

The correct answer is  [tex]\frac{2}{81}[/tex]

Answer:

Step-by-step explanation:

You just add and subtract

To find the quadratic equation with roots 6 and -5 and a leading coefficient of 3, we use the format 3(x - 6)(x + 5) and expand it to get the equation 3x² - 3x - 90 = 0.

The quadratic equation with roots 6 and -5 and a leading coefficient of 3 can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants. Since the roots are 6 and -5, and the leading coefficient (a) is 3, we can use the fact that a quadratic equation with roots r and s can be written as a(x - r)(x - s). Thus, our equation becomes 3(x - 6)(x + 5). 

Expanding this, we have:

The quadratic equation with the given roots and leading coefficient is 3x² - 3x - 90 = 0.

Answer:

width = 4.16 meter

length = 6.49 meter

Step-by-step explanation:

Area of the rectangle =27 m²

Let the width of the rectangle be x meter

So, Length = 3 * width - 6

                  = 3*x - 6

                  = 3x-6 meter

Area of the rectangle = length * width

27 = (3x-6)*x

Flipping the sides of the equation, we have

(3x-6)*x =27

Distributing the left side, we get

(3x)*(x) - (6)*(x) = 27

=> 3x² - 6x = 27

Subtract 27 from both sides,

3x² - 6x -27 = 27 - 27

=> 3x² - 6x -27 = 0

Factoring out 3 from all the terms on the left side, we have

3(x² - 2x -9) = 0

Dividing both sides by 3, we have

[tex]\frac{3(x^{2}-2x-9) }{3}[/tex] = [tex]\frac{0}{3}[/tex]

Cancelling out the 3's on the left, we get

x² - 2x -9 = 0

We'll use the quadratic formula to solve for the x,

x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]

Comparing the quadratic equation x² - 2x -9 = 0 with ax² + bx + c = 0, we get

a = 1 (as x² has no coefficient)

b = -2

c = -9

Plugging in the values of a, b, and c into the quadratic formula, we get

x = [tex]\frac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(-9) } }{2(1)}[/tex]

=> x = [tex]\frac{2\pm\sqrt{4+36 } }{2}[/tex]

=> x = [tex]\frac{2\pm\sqrt{40}}{2}[/tex]

=> x = [tex]\frac{2\pm2\sqrt{10}}{2}[/tex]

Factoring out 2 from the top, we get

x = [tex]\frac{2(1\pm\sqrt{10})}{2}[/tex]

Canceling out the 2's from the top and bottom, we have

x = [tex]1\pm\sqrt{10}[/tex]

Either x = [tex]1+\sqrt10[/tex] or x= [tex]1-\sqrt10[/tex]

=> x = 1 + 3.162 or x = 1 - 3.162

=> x = 4.162 (possible) or x = -2.162 (not possible as width can't be negative)

So, width = 4.16 meter (rounded off to the nearest hundredth)

Now,

Area of the rectangle = length * width

27 = length * 4.16

Flipping the sides of the equation,

length * 4.16 = 27

Dividing both sides by 4.16, we get

[tex]\frac{length * 4.16}{4.16} = \frac{27}{4.16}[/tex]

Cancelling out 4.16 from the top and bottom of the left side, we get

length = 6.490

=> length = 6.49 meter (rounded off to the nearest hundredth)

Answer:

$.43 per pen

Step-by-step explanation:

To find the unit rate, we take the price of the pens and divide by the number of pens

$1.29/3

$.43 per pen

Answer: $0.43

Step-by-step explanation:

Unit rate is how much each pen costs.

If the total amount is $1.29 for all three pens, then the price for one pen should be calculated by 1.29/3, therefore, the answer is $0.43

Answer:

The domain is {3,4,5,6}

Step-by-step explanation:

Because all your x - values is ur domain and ur y - values is ur range

Answer:

AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent

In triangle RAS and triangle QAT

[tex]\angle R =\angle Q[/tex]   [Angle]

[tex]AS =AT[/tex]    [Side]                                       [Given]

By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.

⇒ [tex]\angle 5= \angle 6[/tex]      [By base ∠'s of isosceles triangle are equal]

By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.

[tex]\angle 4[/tex], [tex]\angle 5[/tex] are supplementary and [tex]\angle 6[/tex], [tex]\angle 7[/tex] are supplementary.

⇒[tex]\angle 4+ \angle 5 =180^{\circ}[/tex] and

[tex]\angle 6+ \angle 7 =180^{\circ}[/tex]  

Two [tex]\angle 's[/tex] supplementary to equal [tex]\angle 's[/tex]

[tex]\angle 4+ \angle 5 =\angle 6+ \angle 7[/tex]

Since,  [tex]\angle 5 =\angle 6[/tex]  

then, we get;

[tex]\angle 4 =\angle 7[/tex]  [Angle]

then, by AAS postulates,

[tex]\triangle RAS \cong \triangle QAT[/tex]

By CPCT[Corresponding Part of Congruent Triangles are equal]

[tex]RS = QT[/tex]              Hence Proved!

Answer:

1+5*2 or simplified, 1+10= 11

Answer:

The system of linear equations are

y = 15 + 2x  

y = 3x

Step-by-step explanation:

Let us assume that the number of new release movies be x.

Let us assume that the total cost  be y.

As given

Members of a movie rental club pays a minimum of $15 annual membership fee and $2 for new release movies.

Than the equation becomes

y = 15 + 2x

As given

Nonmembers pay $3 for new release movies.

y = 3x

Therefore the system of linear equations are

y = 15 + 2x  

y = 3x

Answer:

-3

Step-by-step explanation:

6-4 (x+3)

2(x+3)

2x+6=0

2x=-6

2x/2= -6/2

x=-3

Answer:

The answer Is D

Step-by-step explanation: I looked it up on Google, next time just type it into Google because it will solve it on a calculator for you.

Answer: It is choice D

Step-by-step explanation: To figure out 25% of 1,200, multiply 1,200 by 0.25. 1,200 x 0.25 = 300

Answer:

4 heads

Step-by-step explanation:

Assuming the coins are properly weighted such that each side is equally likely, this means that getting heads is the same probability as getting tails. We're told that getting 2 heads and 4 tails is a 23.4% chance. If we somehow fool our brains into thinking heads and tails swap, then it would be 4 heads and 2 tails. The swap is simply changing the labels for each coin. It really doesn't matter. This symmetry is useful to help simplify larger problems.

If the coins were altered so that the chances of getting heads on any single coin toss was something like 60%, then swapping the labels wouldn't work because the two sides would be different.

Answer:

for pluto answer is 451

Step-by-step explanation:

Answer:

(x - 3)² + (y - 2)² = 8

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre to a point on the circle

To find r use the distance formula

r = √(x₂ - x₁)² + (y₂ - y₁)²

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, 4)

r = [tex]\sqrt{(5-3)^2+(4-2)^2}[/tex] = [tex]\sqrt{4+4}[/tex] = [tex]\sqrt{8}[/tex]

(x - 3)² + (y - 2)² = ([tex]\sqrt{8}[/tex])²

(x - 3)² + (y - 2)² = 8 ← equation of circle

Answer:

First one is wrong. x should be 16.

Second one is not completely visible, so cannot say.

Step-by-step explanation:

In the last step, the divison by 4 yields:

x/16 = 1, so x = 16

Answer:

C. 31

Step-by-step explanation:

3000 there are 3-4 errors

If we first divide 24,000 by 3,000, will get 8

then since there a error for each 3,000 books, we do 8 x 4 = 32 and 8 x 3 = 24

32 (8 x 4)  the max amount of printing errors

24 (8 x 3) the minimum amount of printing errors

So we should expect 24-32 printing errors

Only answer between the numbers is c. 31

Final answer:

The exact number of books that could have a printing error out of 24,000, given the rate of 3 to 4 errors per 3,000 books, can be calculated to be within a range, making 31 the only viable option provided.

Explanation:

The question is about determining the exact number of books that will have a printing error out of 24,000, given that there are between 3 and 4 printing errors per every 3,000 books. To find the possible number of errors, we multiply the number of books (24,000) by the rate of errors (3 to 4 per 3,000). This gives us a range of possible errors, from (24,000 / 3,000) * 3 = 24 to (24,000 / 3,000) * 4 = 32. Therefore, the only option within this range is 31.

Answer:

y = 3(x + 3)² - 31

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h. k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

take out a common factor of 3 from the first 2 terms

y = 3(x² + 6x) - 4

add/subtract ( half the coefficient of the x-term)² to x² + 6x

y = 3(x² + 2(3)x + 9 - 9 ) - 4

y = 3(x + 3)² - 27 - 4

y = 3(x + 3)² - 31 ← in vertex form