6 less than the quotient of y and 5.

Answer:

(x + 5)² - 25

Step-by-step explanation:

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

Explanation:

I'll use the variable x in place of 'a'

The expression we need to factor is [tex]21x^2-57x+30[/tex] which is in the form [tex]ax^2+bx+c[/tex]

So,

We'll plug those three values into the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-57)\pm\sqrt{(-57)^2-4(21)(30)}}{2(21)}\\\\x = \frac{57\pm\sqrt{729}}{42}\\\\x = \frac{57\pm27}{42}\\\\x = \frac{57+27}{42} \ \text{ or } \ x = \frac{57-27}{42}\\\\x = \frac{84}{42} \ \text{ or } \ x = \frac{30}{42}\\\\x = 2 \ \text{ or } \ x = \frac{5}{7}\\\\[/tex]

The two roots of [tex]21x^2-57x+30 =0[/tex] are [tex]x = 2 \text{ and } x = \frac{5}{7}[/tex]

The root x = 2 leads to the factor (x-2) after subtracting 2 from both sides.

The root [tex]x = \frac{5}{7}[/tex] leads to the factor (7x-5) after first multiplying both sides by 7, and then subtract 5 from both sides.

So we have this set of steps:

[tex]x = \frac{5}{7}\\\\7x = 5\\\\7x-5=0\\\\[/tex]

The two factors are (x-2) and (7x-5).

This leads to (x-2)(7x-5)

The last step is to replace x with 'a' so that the variables match up.

We arrive at  (a-2)(7a-5)

However, as the next section shows, we have a bit of a problem. Don't worry, it can be easily fixed.

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

Let's expand out that factored expression we found earlier.

[tex](a-2)(7a-5)\\\\b(7a-5)\ \text{ ..... let b = a-2}\\\\7ab - 5b\\\\7a(b) - 5(b)\\\\7a(a-2) - 5(a-2)\ \text{ ..... plug in b = a-2}\\\\7a^2-14a - 5a+10\\\\7a^2-19a+10\\\\[/tex]

That's not good. We should have arrived at the original expression [tex]21a^2-57a+30[/tex]. To fix this discrepancy, we can stick a 3 out front and then notice that:

[tex]3(a-2)(7a-5) = 3(7a^2-19a+10) = 21a^2-57a+30[/tex]

The error has been fixed.

We have the full factorization of 3(a-2)(7a-5)

The order of the factors doesn't matter, so we could have written the answer as 3(7a-5)(a-2). Usually the factor without any variables will be listed first.

Based on the screenshot you posted, if that '7' is locked in place, then the only possible answer is 3(7a-5)(a-2) since you'll have 3 in the first slot, then a ( in the next slot. The other slots are filled out in a similar manner. There are no spaces between any symbol or letter.

Step-by-step explanation:

Area of this plot =(84×84) m

2

=7056 m

2

length of rectangular plot =144 m.

We know that the area of the square plot is same as the area of the rectangular plot

Let breadth of rectangular plot be x.

then, 144x=7056 [∵ Area of a rectangle =l×b ]

⟹x=

144

7056

=49 m

∴ The width of rectangular plot is 49 m.

Answer:

If you have a party and your pizza was split up into 16 pieces, 8 people should be able to have 2 pieces.

Step-by-step explanation:

Answer: y= (1/4)x

Step-by-step explanation: Best guess given screenshot, matched with desmos.

The measure of the fifth interior angle is 102 degrees.

A polygon is an object with five sides. It is made up of five straight edges and 5 interior angles. The sum of interior angles is 540 degrees.

In order to determine the fifth interior angle, the sum of the four interior angles would be subtracted from  sum of interior angles in a polygon.

Fifth interior angle = 540 - (88 + 132 + 100 + 118)

= 540 - 438

= 102 degrees

Please find attached an image of a pentagon. A similar question was answered here: https://brainly.com/question/2906515

Answer:

1) C

2) B

3) D

4) A

5) B

Step-by-step explanation:

Hope this helps

MAy I get braineist pls???????????

Answer:

MARK ME AS BRAINLIEST!!!

Step-by-step explanation:

1. A

2. B

3. D

4. A

5. B

HAVE A NICE DAY!!!

:)

Answer:

AB = 105

Step-by-step explanation:

Since ∠ A and ∠ B  are equal then Δ ABC is isosceles with 2 congruent legs.

AC = BC , substitute values

6x - 7 = 5x + 7 ( subtract 5x from both sides )

x - 7 = 7 ( add 7 to both sides )

x = 14

Then

AB = 7x + 7 = 7(14) + 7 = 98 + 7 = 105

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\large\text{Gu\textbf{id}\textsf{e}}\bf\downarrow[/tex]

[tex]\large\textbf{2 negatives = positive}\\\large\textbf{2 positives = positive}\\\large\textbf{1 negative \& 1 positive = negative}\\\large\textbf{1 positive \& 1 negative = negative}\\\\\large\text{Negatives are BELOW 0}\\\large\text{Positives are ABOVE 0}\\\\\large\textsf{Negatives are on the LEFT side of zero.}\\\large\textsf{Positives are on the RIGHT side of zero.}[/tex]

[tex]\huge\textsf{-2(5n) \boxed{\rightarrow} \bf -10n}\\\\\\\\\huge\boxed{\rightarrow\text{-2n + (-2n) + (-2n) + (-2n) + (-2n)}}\\\huge\boxed{\rightarrow \text{\bf -2n - 2n - 2n - 2n - 2n}}\\\huge\boxed{\rightarrow{\text{-4n - 2n - 2n - 2n}}}\\\huge\boxed{\rightarrow \text{-6n - 2n - 2n}}\\\huge\boxed{\rightarrow \text{\bf -8n - 2n}}\\\huge\boxed{\rightarrow \boxed{\text{ -10n}}}[/tex]

[tex]\huge\text{\bf -5(2n)}\\\huge\boxed{\rightarrow \text{-10n}}[/tex]

[tex]\huge\boxed{\text{\bf Therefore, your answers \underline{\underline{could}} be: }}\\\huge\boxed{\bullet \textsf{ -2n - 2n - 2n - 2n -2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -8n - 2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -5(2n)}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

holi , cómo estás espero que bien bueno déjame te digo que está facil soy de México pero voy a clases de inglés y ya me la hicieron esa pregunta y es la D hojala te ayude mucho

Answer:

In no b 7 people has represented □

In no c 2 people referred giraffe than dogs

Answer:

(b)Total 8 complete square in given pictogram represented 64 people.

(c) 6 more people preferred giraffes than dogs.

Answer:

3 (x - 4)

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

You're counting by 4's. Which are the following 4,8,12,16,20 and so on. Hope this helps :D

Step-by-step explanation:

Start by multiplying both sides by cosα:

1 + sinα + (cos²α)/(1+sinα) = 2

sinα + (cos²α)/(1+sinα) = 1

Now multiply both sides by 1+sinα:

sinα + sin²α + cos²α = 1 + sinα

sin²α + cos²α = 1 Q.E.D.

Thats the answer and method i used

No.

To find the rate for how many miles Greg drove for 5 hours, we need to divide 300 by 5:

300 / 5 = 60.

60 miles represents the speed for 1 hour.

60<70.

The inequality indicates that his rate (60 miles per hour) is less than the speed limit.

Answer:

C 132 square units

Step-by-step explanation:

. Happy Friday

Answer:

7,3

Step-by-step explanation:

for every 5 it goes right it goes 4 up. 2,1+5,4=7,3

[tex]\\ \sf\longmapsto 2m^2=-200[/tex]

[tex]\\ \sf\longmapsto m^2=-100[/tex]

[tex]\\ \sf\longmapsto m=√-100[/tex]

[tex]\\ \sf\longmapsto m=√100i[/tex]

[tex]\\ \sf\longmapsto m=10i[/tex]

[tex]\huge \bf༆ Answer ༄[/tex]

The Correct choice is ~ D

The given triangles are not congruent, because they they just have all their corresponding angles equal to one another, so we need more information ~

Answer:

  100.9 yards

Step-by-step explanation:

One circuit of the track is a distance of ...

  C = 2πr = 2π(60 yd) = 120π yd.

At Alex's running rate, the distance covered in 20 minutes is ...

  (4 yd/s)(20 min)(60 s/min) = 4800 yd

The number of circuits will be ...

  (4800 yd)/(120π yd/circuit) = 40/π circuits ≈ 12.7324 circuits

The last of Alex's laps is more than half-completed, so the shortest distance to his starting point is 13 -12.7324 = 0.2676 circuits,

That distance is (0.2676 circuits)×(120π yd/circuit) ≈ 100.88 yd

The shortest distance along the track to Alex's starting point is about 100.9 yards.

_____

Additional comment

The exact distance is 120(13π-40) yards. The distance will vary according to your approximation for pi. If you use 3.14, this is about 98.4 yards.

A.3n+4+3n+4+4n

=3n+3n+4n+4+4

=10n+8

B.11n+4+n-12

=11n+n+4-12

=12n-8

C.6(6n-2)

=36n-12

D.4(3n-2)

=12n-8

E.4n+22-12+8n

=4n+8n+22-12

=12n+10

so,B and D are the expressions that are equivalent to 12n-8.

Answer:

29.32 feet

Step-by-step explanation:

area of a trapezoid = height/2 * (first base + second base)

125.4 = 5.3 / 2 * (18 + second base)

125.4 = 2.65 * (18 + second base)

We want to solve for the second base. To do this, we can start by isolating the (18+second base) by dividing each side by 2.65

47.32 = 18 + second base

subtract 18 from both sides to solve for the second base

29.32 = second base

Answer:

Hence y = (5k -3)/ (1 - k)

.... shown

Answer: u < 6

Step-by-step explanation: 2 + u < 8

u < (8-2)

u < 6

Answer:

B)  $7.50

Step-by-step explanation:

Interest (I) = Principal (P) x Interest Rate (r) x Time (t, in years)

I = 125(.03)(2)

I = 7.5

Answer:

12.5t + 8h = 259.5

t + h = 24

Step-by-step explanation:

Write one equation to deal with the costs and one equation to deal with the numbers of shirts and hats.

12.5t + 8h = 259.5

t + h = 24

Answer:

1270

Step-by-step explanation:

420+300+550

$420+300=720+550=1270

Answer:

C. Either positive or negative