High school
math/ geometry

Answer:

Step-by-step explanation:

1. y = 2x

       y = 2*4 = 8  Checks, therefore

y = 20  for x = 10

2. y = 3x

       y = 3*(0.3) = 0.9  Checks, therefore:

y =  3*(1.5) = 4.5  

       y = 3*

3. y = 5/x

       y = 5/(1/2) = 10  Checks, therefore:

       3 = 5/x

x = 5/3

4 v = wu

7*3 = 21  Checks, therefore:

v =  (3/4)*(6) = (18/4) = (9/2)

v = (2/3)wu

v = (2/3)*7*3 = 14 Checks

5 m = Kn/p  [Add the K as a constant that will make m = Knp true at some value of K]

9 = K*2/(1/3)

27 = (K*2)

27 = 2K

K = (3/2)

       m = (3/2) (n/p)

       m = (3/2)*((1/2)/(1/3))

        m = (3/2)*(3/2)

        m = 1

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

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.

Answer:

That is an improper fraction

Step-by-step explanation:

When the numerator (the top) is greater than the denominator (The bottom) then the fraction is improper

Hope this helps!

Answer:

Improper fraction

Step-by-step explanation:

Answer:

There are 35 boys in the class.

Step-by-step explanation:

Girls to Boys ratio = 3:7

Total number of students in class = 50

Let total number of girls be '3x' and total number of boys be '7x'

Total number of girls + Total number of boys = Total number of students

3x + 7x = 50

10x = 50

x = 50/10

x = 5

[tex] \therefore [/tex]

Total number of girls = 3 × 5 = 15

Total number of boys = 7 × 5 = 35

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:

7,3

Step-by-step explanation:

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

[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 ~

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

a) Point O

b) [tex]\overline{OB}[/tex]

c) [tex]\overline{AB}[/tex]

4) arc DE (m)

5) [tex]\overline{DE}[/tex]

6) Semicircle AEB

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.

Answer: y= (1/4)x

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

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:

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

.... shown

Answer:

1270

Step-by-step explanation:

420+300+550

$420+300=720+550=1270

Explanation:

(i)Total number of copies are at Pradnya = 5 dozen

We know that 1 dozen = 12

⇛5×12 = 60

Given copies to Anushka = half of 60

⇛60/2 = 30 copies

Given copies to Prajwala = 1/5 the copies

⇛ (1/5)×60

⇛60/5

⇛12 copies

Total number of given copies = 30+12 = 42

Remaining copies = 60-42 = 18

Answer: Remaining copies = 18

(ii)Let the number of Rs. 10 notes be X

So given that

all are equal in number

So, Number of Rs 20 notes = Number of Rs. 50 notes = Number of Rs. 100 = X

Total number of notes

= X+X+X+X = 4X

Value of Rs. 10 = 10X

Value of Rs. 20 = 20X

Value of Rs. 50 = 50X

Value of Rs. 100 = 100X

Total amount = Rs. 900

⇛10X +20X +50X+100X = 900

⇛180X = 900

⇛X = 900/180

⇛X = 5

Number of Rs. 10 notes = Number of Rs. 20 notes = Answer: number of Rs. 50 notes = Number of Rs. 100 = 5

(iii) Let the number of rows be X

Number of saplings per each row = 47

Total number of saplings of X rows = 47X

According to the given problem,

Total number of saplings purchased by Mangalakaku = 6016

⇛47X = 6016

⇛X = 6016/47

⇛X = 128

Answer: Total number of rows = 128

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:

(x + 5)² - 25

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

12 / 24 = 1/2

Answer:

12/24

Step-by-step explanation:

use the stander rise over run since the rise is 12 it goes over the run which is 24

[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]

Answer: u < 6

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

u < (8-2)

u < 6

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

Answer:

3 (x - 4)

Step-by-step explanation:

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

Answer:

see explanation

Step-by-step explanation:

The perimeter P is the sum of the 4 sides of the rectangle.

The opposite sides of the rectangle are congruent , then

P = 2x + 1 + 2x + 1 + x + x ← collect like terms

P = 6x + 2

Answer:

B  (the second number line)

Step-by-step explanation:

[tex]\sqrt{49}[/tex] = 7, so [tex]\sqrt{47}[/tex] would be close to 7

Answer:

272×620=168,640

Step-by-step explanation:

If koala airlines carries 272 in average then the answer is 168,640

Answer:

  g(x) = 24(2^(x-1)) +16

Step-by-step explanation:

A function is stretched vertically by a factor of 'a' by multiplying by 'a'.

  g(x) = 4·f(x) = 4(6(2^(x-1) +4)

  g(x) = 24(2^(x-1)) +16

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: