A wooden board 27 ft long is cut into two pieces so that the longer piece is 8
times as long as the shorter piece. Find the lengths of the two pieces.

[tex]\displaystyle\ y^4 +5y^2+9=(y^2+3)^2-y^2=(y^2-y+3)(y^2+y+3)[/tex]

Answer:

Solution given;

[tex] y^{4}+5y²+9[/tex]

keeping [tex]y^{4} and 9 together [/tex]

[tex]y^{4}+9+5y²[/tex]

[tex](y²)²+3²+5y²[/tex].....[I]

we have

a²+b²=(a+b)²-2ab

or

a²+b²=(a-b)²+2ab

same like that

[tex](y²)²+3²=(y²+3)²-6y² or (y²-3)²+6y²[/tex]

remember that while adding or subtracting the left term 5y² either adding 6y²or subtracting 6y²

should make the term perfect square

while subtracting it makes perfect square

so

we take

(y²)²+3²=(y²+3)²-6y²

again

substituting value of

(y²)²+3² in equation 1 and it becomes

(y²+3)²-6y²+5y²

solve like terms

(y²+3)²-y²

again

we have

a²-b²=(a+b)(a-b)

by using this.

(y²+3+y)(y²+3-y)

rearrange it

(y²+y+3)(y²-y+3) is a required factorisation form.

Answer:

It's an identity

Step-by-step explanation:

The answer is an identity

I identity are composed by sin^2 and cos^2

Tan^2 can be simplified into those two sin n cos

Answer:

V=1/3(pi)*r^2*h

Step-by-step explanation:

Think about a cylinder. If you combine 3 cones, you get a cylinder. Find the volume of a cylinder

Answer:

Step-by-step explanation:

V = 1/3 r^2 * π * h

3V = r^2 *π * h

3V/π = r^2 * h

h = 3V/(r^2 * π)

Answer:

Simplify the expression.

36a to the power of 7 then - 156a to the power of 4 then -15a to the power of3

Answer:

IK≅WY

Step-by-step explanation:

Answer:

93.2°

Step-by-step explanation:

[tex]\frac{sin(38)}{9} = \frac{sin(c)}{11}[/tex]  ... c =48.8

a =180-(38+48.8) = 93.2

Answer : I think it is 10899

Answer:

$843.67

Step-by-step explanation:

We can use a proportion to solve this problem:

12 : 100 = x : 896

x =(896 * 12)/100 = $107,52

896 - 107.52 = $788,48 (price of the computer after the discount)

7 : 100 = x : 788,48

x = (788,48 * 7)/100 = $55,1936

788.48 + 55,1936 = 843,6736 = $843.67 (final price)

The equation will be:

25 + d = t

where t is total money

Answer:

[tex]67.20\%[/tex]

Step-by-step explanation:

Given

[tex]n =2430[/tex] --- sample

[tex]r = 16.72\%[/tex] --- degeneration rate

From the findings, we have:

[tex]p = 377[/tex] --- tested positive

[tex]t =561[/tex] --- total test

Required

The positive predicted value (PPV)

This is calculated using:

[tex]PPV=\frac{Positive}{Total}[/tex]

i.e.

[tex]PPV = \frac{377}{561}[/tex]

[tex]PPV = 0.6720[/tex]

Express as percentage

[tex]PPV = 0.6720 * 100\%[/tex]

[tex]PPV = 67.20[/tex]

Answer:

We know that the expression that models the situation is:

45 - n

Where n is the amount that she lost.

We know that she lost $3 for each hour closed.

And the shop was 8 hours closed, so the total loss is:

8*$3 = $24

The profit is the difference between the revenue (we know that it is $45) and the loss (we know that it is $24)

Then the profit is:

$45 - $24 = $21

Answer: D

Step-by-step explanation:

360° - 90° - 90° - 108° = 72°

(Sum of angles in a quadrilateral = 360°)

Answer:

EXPLAINED ON THE ATTACHED

Answer:

20 minutes on the stationary bike

10 minutes on the treadmill

Step-by-step explanation:

x = minutes on bike

y = minutes on treadmill

x + y = 30

12x + 15y = 390

x = 30-y

12(30-y) + 15y = 390

360 - 12y + 15y = 390

3y = 30

y = 10

x + 10 = 30

x = 20

Answer:

a. 42

b. -12x-5

c. -60

d. -75

e. 66

f. -90

g. 144

h. -135

it's a 90 degree counterclockwise rotation around the origin (0,0).

see the screenshot for illustration

Answer:

B.

Step-by-step explanation:

⟶ 2³ × 3² is the prime factorization for which one of these choices?

Let's check,

1) 6 = 3 × 2 [So, obviously not this choice]

2) 25 = 5 × 5 = 5² [Not this either]

3) 36 = 3 × 2 × 2 × 3 = 3² × 2² [Doesn't match with 2³ × 3²]

4) 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3² [Matches]

⟶ The answer is, choice 72.

[tex]\underbrace{ \overbrace{ \mathfrak{Carry \: On \: Learning}}}[/tex]

Answer:

x = 42.5

Step-by-step explanation:

A triangle inscribed inside of a circle using the diameter of the circle as it's hypotenuse is a right triangle ( a 90 degree triangle ) where the angle opposite of the hypotenuse is the 90 degree angle ( angle C )

Hence angle C = 90

If angle C = 2x + 5

Then 2x + 5 = 90

Notice that we just created an equation that we can use to solve for x

We now solve for x algebraically

2x + 5 = 90

Step 1 subtract 5 from both sides

2x + 5 - 5 = 90 - 5

Outcome: 2x = 85

Step 2 divide both sides by 2

2x/2 = 85/2

Outcome: x = 42.5

Answer:

Answer:

Step-by-step explanation:

each die has numbers 1-6 thus there are 36 (6*6) possible outcomes

a) 18 of the 36 are even = 1/2 = .5 = 50%

b) (1,2) and (2,1) are the only 3's 2/36 = 1/18 = .055

c) there are 10 combos that are LESS THAN 6 (2,3,4,5)

   10/36 = .277 = 27.7%

2 3 4 5 6 7

3 4 5 6 7 8

4 5 6 7 8 9

5 6 7 8 9 10

6 7 8 9 10 11

7 8 9 10 11 12

Answer:

x=12

Step-by-step explanation:

Line that's perpendicular to y=49 should be a vertical line of the form x=a

Now the line passes through (12,35) so the equation of the line is,

x=12

Answered by GAUTHMATH

[tex]\displaystyle\Large \boldsymbol -2 \cdot \frac{3}{12} \cdot \frac{5}{10} \cdot \frac{7}{15} =-2 \cdot \frac{3 \!\!\!\!\diagup \cdot1}{3 \!\!\!\!\diagup\cdot 4} \cdot \frac{5 \!\!\!\!\diagup\cdot 1}{5 \!\!\!\!\diagup\cdot 2} \cdot \frac{7}{15} =\\\\\\-\frac{2 \!\!\!\!\diagup\cdot 7 }{2 \!\!\!\!\diagup\cdot 4 \cdot 15} =\boxed{-\frac{7}{60}}[/tex]

Answer:

475 students, 125 adults

Step-by-step explanation:

x + y= 600......equation 1

5x +9y= 3500.......equation 2

From equation 1

x +y = 600

x= 600-y

Substitute 600-y for x in equation 2

5(600-y) +9y= 3500

3000-5y+9y= 3500

3000+4y= 3500

4y= 3500-3000

4y= 500

y= 500/4

y= 125

Substitute 125 for y in equation 1

x + y= 600

x + 125= 600

x = 600-125

x= 475

Hence there are 475 students and 125 adults

Answer:

45 x 56=

2520 and

5 x 7=35*8=280*9=2520

2520=2520

Hope This Helps!!!

Answer:

x=0.5 or 1/2

Step-by-step explanation:

Given:

A line passes through the points (-1, -1) and (5,8).

To find:

Which points lie on the same line?

Solution:

If a line passes through two points, then the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:

[tex]y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))[/tex]

[tex]y+1=\dfrac{8+1}{5+1}(x+1)[/tex]

[tex]y+1=\dfrac{9}{6}(x+1)[/tex]

[tex]y+1=\dfrac{3}{2}(x+1)[/tex]

Multiply both sides by 2.

[tex]2(y+1)=3(x+1)[/tex]

[tex]2y+2=3x+3[/tex]

[tex]2y=3x+3-2[/tex]

[tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex]

So, the equation of the line is [tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex].

Now, check each point for this equation.

Putting [tex]x=-3[/tex], we get

[tex]y=\dfrac{3}{2}(-3)+\dfrac{1}{2}[/tex]

[tex]y=\dfrac{-9+1}{2}[/tex]

[tex]y=\dfrac{-8}{2}[/tex]

[tex]y=-4[/tex]

Similarly,

For [tex]x=9,y=15[/tex].

For [tex]x=1,y=2[/tex].

For [tex]x=4,y=6.5[/tex].

For [tex]x=3,y=5[/tex].

For [tex]x=-2,y=-2.5[/tex].

Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.