Which polynomial is in standard form

Answer:

16.6

Step-by-step explanation:

The rectangle has an area of 105. It's width is 7.

1: Find the length

     [tex]\frac{area}{width}[/tex]=length

     [tex]\frac{105}{7}[/tex]= 15

      Length=15

2: Pythagorean theorem

      [tex]a^{2} +b^2=c^2[/tex]

       [tex]7^{2}[/tex]+[tex]15^2=c^2[/tex]

       49+225=[tex]c^2[/tex]

        275=[tex]c^2[/tex]

         [tex]\sqrt{275}[/tex] = [tex]\sqrt{c^2\\}[/tex]

          16.55≈c

           Rounded to nearest tenth

              16.6

Answer:

B. 82.8

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The quadratic formula can be applied to any quadratic equation in the form [tex]ax^2+bx+c=0[/tex] (standard form).

The quadratic formula: [tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

I hope this helps!

Answer:

its true

Step-by-step explanation:

Answer:

a: 42 =  2*3*7

b: 31 = 31*1

c: 36 = 2*2*3*3

d: 45 = 3*3*5

Cada descomposición es unica.

Step-by-step explanation:

Sabemos que todo número entero puede ser reescrito como un producto de números primos.

Esta descomposición es única, dado que una vez tenemos un número escrito como producto de primos, esos números primos no pueden descomponerse en otra cosa, por lo que se concluye que una descomposición en primos es única.

a: 42

Para obtener la descomposición, podemos comenzar dividiendo por primos, comenzando por los más bajos.

En este caso, podemos comenzar por 2:

42/2 = 21

asi, podemos reescribir:

42 = 2*21

Ahora ya tenemos un factor que es primo, el 2, y un factor que no lo es, el 21.

Asi que debemos reescribir el 21 como producto de primos.

Y sabemos que 3*7 = 21, donde ambos 3 y 7 son primos, entonces:

42 = 2*21 = 2*3*7

42 = 2*3*7

así hemos reescrito 42 como un producto entre números primos.

b. 31

31 es un número primo, por lo que su descomposición es:

31 = 31*1

c. 36

Comenzamos dividiendo por 2.

36/2 = 18

36 = 2*18

Volvemos a dividir por 2 el 18.

18/2 = 9

18 = 2*9

reemplazando eso en nuestra descomposición obtenemos:

36 = 2*18 = 2*2*9

9 es impar así que no podemos dividir por 2, pasamos al próximo número primo, el 3.

9/3 = 3

9 = 3*3

Reemplazando eso, obtenemos:

36 = 2*2*3*3

d. 45

no podemos dividir por 2, puesto que es un número impar, así que pasamos al próximo primo, el 3.

45/3 = 15

45 = 3*15

Ahora descompongamos el 15.

15/3 = 5

15 = 3*5  (notar que 3 y 5 son primos)

Reemplazando eso, obtenemos:

45 = 3*15 = 3*3*5

45 = 3*3*5

Answer:

Step-by-step explanation:

Join OB.

∠A=∠A  (common)

[tex]\frac{AP}{AO} =\frac{\frac{1}{2} AO}{AO} =\frac{1}{2} \\\frac{AQ}{AB} =\frac{\frac{1}{2} AB}{AB} =\frac{1}{2} \\\frac{AP}{AO} =\frac{AQ}{AB}[/tex]

∴ ΔAPO and ΔAOB are similar.

[tex]\frac{PQ}{OB} =\frac{1}{2} \\[/tex]

∠P=∠O

∠Q=∠B

So PQ║OB

Similarly RS║OB

∴PQ║RS

Answer:

Step-by-step explanation:

In  [tex]\frac{rs}{a}=k[/tex] begin by multiplying both sides by a to get

rs = ak  and divide away the s to get

[tex]r=\frac{ak}{s}[/tex]

Answer:

8

Step-by-step explanation:

Using the chord chord theorem

10(4) = 5x

Solve for x

Simplify multiplication

40 = 5x

Divide both sides by 5

40/5 = 8

5x/5 = x

We're left with x = 8

Note:

Chord chord theorem states that if two chords intersect then the product of the measures of each part of one chord is equal to the product of the measures of the parts of the other chord.

Because the chords shown intersect the product of the parts of each chord should be equal to each other ( 4 * 10 = 5x )

Source: https://www.dummies.com/education/math/geometry/how-to-use-the-chord-chord-power-theorem

Answer:  13.46 km/h

Step-by-step explanation:

7 1/2 hr= 450 min

6057/450= 13.46

Answer:

The larger number is -6, the smaller number is -15

Step-by-step explanation:

We have two numbers, a and b.

We know that one number is larger than another by 9.

Then we can write:

a = b + 9

then a is larger than b by 9 units.

If the greater number is increased by 10 (a + 10) and the lesser number is tripled (3*b), the sum of the two would be -41:

(a + 10) + 3*b = -41

So we got two equations:

a = b + 9

(a + 10) + 3*b = -41

This is a system of equations.

One way to solve this is first isolate one variable in one of the two equations:

But we can see that the variable "a" is already isolated in the first equation, so we have:

a = b + 9

now we can replace that in the other equation:

(a + 10) + 3*b = -41

(b + 9) + 10 + 3*b = -41

now we can solve this for b.

9 + b + 10 + 3b = -41

(9 + 10) + (3b + b) = -41

19 + 4b = -41

4b = -41 -19 = -60

b = -60/4 = -15

b = -15

then:

a = b + 9

a = -15 + 9 = -6

a = -6

Answer:

a)

b)

Answer:

a.) 12 + 5√2 - 2√6

b.) 24

Step-by-step explanation:

a) √25 + √50 - √24 + √49

Calculate the square root .

Simplify the radical expression.

Combine like terms.

b.) √2 ( 2√8 - 3√32 + 4√50 )

Simplify the radical expression.

Evaluate the power.

Calculate the products.

Combine like terms.

Multiply.

Answer:

The 65,000 salary

Step-by-step explanation:

Because the 30,000 salary after 5 years would be 31,500.

30,000+300=30,300

30,300+300=30,600

30,600+300=30,900

30,900+300=31,200

31,200+300=31,500

The 65,000 paying company

65,000x1.05=68,250

68,250x1.05=71.662.5

71,662.5x1.05=75,245.625

75,245.625x1.05=79,007.90625

79,007.90625x1.05=82,958.3015625

her salary after 5 years would be 82,958.3015625

Answer:

[tex]v(t) = 2t - 5[/tex]

Step-by-step explanation:

Given

[tex]s(t) = t^2 - 5t + 1[/tex]

Required

The speed of the particle

To do this, we simply differentiate the position function

i.e.

[tex]v(t) = s'(t)[/tex]

So, we have:

[tex]s(t) = t^2 - 5t + 1[/tex]

Differentiate

[tex]s'(t) = 2t - 5 + 0[/tex]

[tex]s'(t) = 2t - 5[/tex]

So, the speed function is:

[tex]v(t) = 2t - 5[/tex]

Answer:

12,6,4,3

Step-by-step explanation:

factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

if you take 12,6,4,3 and add them together they equal 25 which is greater than 21 but less than 30

Answer:

3, 4, 9, and 12

3, 6, 6, and 12

Step-by-step explanation:

First, list out the factors of 36.

1, 2, 3, 4, 6, 9, 12, 18, and 36

The combinations of 4 numbers could be:

9 and 4, and 12 and 3  =  28

6 and 6, and 12 and 3  =  27

Answer:

p^3 - 7p^2q^2 + 2pq

Step-by-step explanation:

3pq +5p^2q^2 + p^3 = p^3 + 5p^2q^2 + 3pq

Let the number be x.

x + p^3 + 5p^2q^2 + 3pq + p^3 - pq

= 3p^3 - 2p^2q^2 + 4pq

x + p^3 + p^3 + 5p^2q^2 + 3pq - pq

= 3p^3 - 2p^2q^2 + 4pq

x + 2p^3 + 5p^2a^2 + 2pq

= 3p^3 - 2p^2q^2 + 4pq

x

= 3p^3 - 2p^2q^2 + 4pq - (2p^3 + 5p^2q^2 + 2pq)

= 3p^3 - 2p^2q^2 + 4pq - 2p^3 - 5p^2q^2 - 2pq

= 3p^3 - 2p^3 - 2p^2q^2 - 5p^2q^2 + 4pq - 2pq

= p^3 - 7p^2q^2 + 2pq

Therefore,

p^3 - 7p^2q^2 + 2pq should be added.

Answer:

A: Only (2,3)

Step-by-step explanation:

1. 3-3 = 5(2-2) WORKS! (2,3)

2. 2-3 = 5(3-2) Does not work :(

Answer:

Only A

Step-by-step explanation:

If you plug in x or y into the equation, only (2, 3) works

Answer:

Each week = $ 1311.41

Each fortnight = $ 2622.84

Each month =  $ 5702.5

Step-by-step explanation:

Given that,

Annual salary of Kelly = $ 68,430

As we know,

There are 52.18 weeks in a year.

So,

Weekly income = Annual salary ÷ no. of weeks in the year

= $ 68,430 ÷ 52.18

= $ 1311.42

Fortnight income = 2 * weekly income

= 2 * $ 1311.42

= $ 2622.84

Each month's income = Annual income ÷ 12(no. of months)

= $ 68,430 ÷ 12

= $ 5702.5

Answer:

3

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

The a value is from the center to the maximum

We want from minimum to max so we need 2 times the amplitude

a = 7

2 *7 = 14

Answer:

99cm²

Step-by-step explanation:

area for a triangle = 1/2 x b x h

area = 1/2 x 11 x 18

area = 99cm²

Answer:

[tex]\tan x=21/20[/tex]

Step-by-step explanation:

In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. (o/a)

For angle [tex]x[/tex], its opposite side is 21 feet and its adjacent side is 20 feet. Therefore, we have:

[tex]\boxed{\tan x=21/20}[/tex]

Answer:

9 sides

Step-by-step explanation:

Sum of the measures of the interior angle of a polygon with n sides:

(n - 2)180

Measure of 1 interior angle of a regular polygon of n sides:

(n - 2)180/n

Sum of the measures of the exterior angles of a polygon, one per vertex:

360

Measure of 1 exterior angle of a regular polygon of n sides:

360/n

(n - 2)180/n = 360/n + 100

Multiply both sides by n.

(n - 2)180 = 360 + 100n

Distribute on left side.

180n - 360 = 360 + 100n

Subtract 100n from both sides.

80n - 360 = 360

Add 360 to both sides.

80n = 720

Divide both sides by 80.

n = 9

Answer: 9 sides

Answer:

9 to 3

Step-by-step explanation:

Those who don't enjoy reading: 8+1=9

Those who don't enjoy playing video games: 1+2=3

Ratio is 9 to 3.

Answer:

C) 840

C) 87

D) 3000-150n

Step-by-step explanation:

Answer:

c

c

d

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

85.9 > 85.31 > 85 > 84.52

Dallas, Fort Worth, San Antonio, Austin

Answer:

B is the Answer.

Step-by-step explanation:

A transformation of a function can be represented by

[tex]a(bx - h) + k[/tex]

where a is the vertical stretch or compression, b is the horizontal stretch or compression. H is the shift horizontally and k is the shift vertically.

The new function has a 2 instead of 1 on the orginally function. The function will stretch since 2 is greater than 1.

B is the answer.

Answer:

a +73°=90°

a= 90°-73°

a =17°

d+18°=90°

d=90°-18°

d =72 °

The first circle has equation

(x - 2)² + (y + 1)² = 4²

and the second has equation

(x - 2)² + (y - 5)² = (√10)²

Solve for (x - 2)² :

(x - 2)² + (y + 1)² = 4²   ==>   (x - 2)² = 16 - (y + 1)²

(x - 2)² + (y - 5)² = (√10)²   ==>   (x - 2)² = 10 - (y - 5)²

Then

16 - (y + 1)² = 10 - (y - 5)²

16 - (y ² + 2y + 1) = 10 - (y ² - 10y + 25)

15 - 2y - y ² = -15 + 10y - y ²

30 - 12y = 0

12y = 30

y = 30/12 = 5/2

(this is the y coordinate of A and B)

Then solve for x :

(x - 2)² = 16 - (5/2 + 1)²

(x - 2)² = 15/4

x - 2 = ± √(15/4) = ±√15/2

x = 2 ± √15/2

(these are the x coordinates for either A or B)

The intersections are the points A = (2 - √15/2, 5/2) and B = (2 + √15/2, 5/2). We want to find the squared distance between them:

(AB)² = [(2 - √15/2) - (2 + √15/2)]² + (5/2 - 5/2)²

(AB)² = (-√15)² + 0²

(AB)² = 15

Answer:

30 min

Step-by-step explanation:

60 divided by 20= 30min

By definition of conditional probability,

P(B | A) = P(A ∩ B) / P(A)

==>   P(A) = P(A ∩ B) / P(B | A) = 0.15/0.75 = 0.2

By definition of complement,

P(B') = 1 - P(B)

==>   P(B) = 1 - P(B') = 1 - 0.7 = 0.3

Now by the inclusion/exlcusion principle, we have

P(A U B) = P(A) + P(B) - P(A ∩ B)

==>   P(A U B) = 0.2 + 0.3 - 0.15 = 0.35