Factor the trinomial completely.

a^4 -2a^2 - 35

CLASS 8 SPOT TEST

1. WHAT IS THE PROBABILITY THAT AN INTEGER CHOSEN AT RANDOM BETWEEN 1 TO 10 INCLUSIVE IS EVEN?

2. A BAG CONTAINS 5 WHITE, 4 BLACK AND 1 BLUE BALLS. ONE BALL IS CHOSEN AT RANDOM. WHAT IS THE PROBABILITY THAT IT IS BLACK?

3. FIND THE PROBABILITY OF GETTING AN ODD NUMBER IN A SINGLE TOSS OF A FAIR DIE?

4. A FAIR DIE IS THROWN 900 TIMES. FIND THE NUMBER OF TIMES YOU WOULD EXPECT TO GET A 6.

5. THE PROBABILITY THAT IT WILL BE CLOUDY TOMORROW IS 0.45. WHAT IS THE PROBABILITY THAT IT WILL NOT BE CLOUDY TOMORROW?

Step-by-step explanation:

1. Of the following 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Only these 5 are even: 2, 4, 6, 8, 10.

The probability on an even number is 5 / 10 = 0.5 = 50%

2. The total number of balls is 10.

5 WHITE, 4 BLACK AND 1 BLUE

The probability on a black ball is 4 / 10 = 0.4 = 40%

3. A fair die can show the following 6 numbers 1, 2, 3, 4, 5, 6.

Only these 3 are odd: 1, 3, 5.

The probability on an odd number is 3 / 6 = 0.5 = 50%

4. The probability of a six is 1 / 6. If the die is cast for 900 times you can expect it to be 900 * 1 / 6= 900/6 = 150. The number of times you would expect a 6 would be 150.

5. If the probability on a cloudy tomorrow is 0.45, then in mathematics, that defines the propability for an non cloudy tomorrow as 1 - 0.45 = 0.55, which is 55%.

(The total should always add up to 100%).

Answer:

144 inches.

Step-by-step explanation:

One foot = 12 inches

One square foot = 144 inches.

Answer:

144

Step-by-step explanation:

Foot=12 inch

Square foot= foot times foot

Square foot= 12 inch times 12 inch

Square foot= 144 square inch.

Answer:

Step-by-step explanation:

3 tickets to attend an Off-Broadway show cost $81,

4 tickets cost $108; and

5 tickets cost $135.

Let the price of a ticket=k

Therefore:

Solving any of the equation above gives: x=27

We therefore have:

[tex]\left|\begin{array}{c|c|c|c|c|c}$Tickets&1&2&3&4&5\\$Total Cost(\$)&27&54&81&108&135\end{array}\right|[/tex]

Let y be the total cost of x tickets

An equation for the relationship is therefore:

y=27x (where x is the number of tickets and y is the total costs (in $)).

Answer:

47.12388

Step-by-step explanation:

Wheel Diameter = Wheel 2 x Radius; 50 cm / 2 = 25 cm.

For one rotation of the wheel, the distance travelled = circumference of the wheel.

Circumference = 2 x pi x radius = 2 x 3.1415926858 x 25 cm = 157.07 cm approx.

Distance travelled with 30 turns of the wheel = 30 x 157.07 = 4712.39cm approx.

Distance in meters = 4712.39cm / 100 = 47.12388 meters approximate (1 cm = 1/100th of a meter).

hope it helps you

The requried bicycle wheel makes approximately 1910 complete rotations over a distance of 3 km.

The circumference of the bicycle wheel is equal to its diameter multiplied by π (pi).

Here

Circumference = diameter x π = 50 cm x 3.14 ≈ 157 cm

To find the number of rotations, we need to divide the distance traveled by the circumference of one rotation:

Number of rotations = Distance ÷ Circumference

Number of rotations = 300000cm ÷ 157 cm = (3000 m ÷ 157 cm) ÷ (100 cm ÷ 1 m) = 1910.82

Therefore, the bicycle wheel makes approximately 1910 complete rotations over a distance of 3 km.

Learn more about circumference here:

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Answer: 21.21 meters

Step-by-step explanation:

Hi, to answer this, first we have to calculate the circumference (C) of the wheel:

C = π x diameter

Replacing with the values given:

C = π x 45 = 141.37 cm

Then we multiply it by the number of revolutions:

141.37 x 15 = 2,120.6 cm

Since  

1 cm = 0.01 m

2,120.6 x 0.01 = 21.21 meters

Feel free to ask for more if needed or if you did not understand something.

Answer:

76.3 cm²

Step-by-step explanation:

step 1

step 2

step 3

step 4

Answer:

3 / 5x^6y^6

Step-by-step explanation:

= -9x^-1y^-9/-15x^5y^-3

= -9y-9 / -15x^6y^-3

= -9 / -15x^6y^6

= 3 / 5x^6y^6

Answer:

b on edge

Step-by-step explanation:

Answer:

  0.4762

Step-by-step explanation:

There are 9C5 = 126 ways to choose 5 candidates to give speeches. There are (5C3)(4C2) = 60 ways that 3 of those candidates can be biology majors (and the other two can be non-biology majors). The probability of interest is ...

  60/126 ≈ 0.4762

__

nCk = n!/(k!(n-k)!)

Answer:

5

Step-by-step explanation:

To evaluate (g ￮ h)(9), evaluate h(9) , then use this value to evaluate g(x)

h(9) = [tex]\sqrt{9}[/tex] = 3, then

g(3) = 2(3) - 1 = 6 - 1 = 5

Answer:B

Step-by-step explanation:

-36 – 8=-44

36+8=44

-36 + (-8)=-44

8 – 36=-28

-8+36=28

As you can see only B equals -44 just like the expression given,

Hope my explanation helps

Answer:

14

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 3x² + 1 - (1 - x)

= 3x² + 1 - 1 + x

= 3x² + x , thus

(f - g)(2)

= 3(2)² + 2 = 3(4) + 2 = 12 + 2 = 14

if i understand correctly what you mean by this question the answer could be

14/24

28/48

you can just keep multiplying the top and the bottom by the same number to get an equivalent fraction

im sorry if i understood the question wrong, i hope this helped a little bit

Disclaimer: The options are missing. The options to the question are:

A.7x1/12; B.7/7x12/12; C.1/7x7/12; D.12x1/7

The expression equivalent to 7/12 is 7x1/12. So, option A. is the right choice.

Two fractions are said to be equivalent fractions when they both give the same value in their reduced or simplest form.

We are asked to find the expression equivalent to 7/12 from the given options.

To solve the question, we reduce all the options to their simplest form. The option = 7/12 will be our answer.

As we can see only option A. 7 * 1/12 = 7/12 in its simplest form, so it is the right option.

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Answer:

2+i or 2-i (D)

Step-by-step explanation:

First you use the quadratic formula.  X= (-b +/- [tex]\sqrt{b^{2}-4ac }[/tex])/2a

a=1

b=-4

c=5

X= (4 +/- [tex]\sqrt{16-20}[/tex])/2

X=(4 +/- [tex]\sqrt{-4}[/tex])/2

The square root of -4 is 2i.  i=√-1.  Therefore 2i= 2√-1 .If you simplify that, it becomes  √-4i.  

X= (4+/- 2i)/2

X= 2+/-i

X= 2+i or 2-i

Answer:

3+7i

Step-by-step explanation:

Answer:

Associative

Step-by-step explanation:

I got it on edge hope ur not as far behind as me boys

Answer: B on ed, i just took my test

Step-by-step explanation:

Answer:

on edge 2021

Step-by-step explanation:

just took the test :)

Answer:

A

Step-by-step explanation:

[tex]\dfrac{21a^3-14a}{-7}= \\\\\\\dfrac{-7(-3a^3+2a)}{-7}= \\\\\\-3a^3+2a[/tex]

Hope this helps!

Answer: [tex]8(4x^3-y^2)[/tex]

Step-by-step explanation:

[tex]32x^3-8y^2[/tex]

[tex]8(4x^3-y^2)[/tex]

Answer: 0.6 liters per kilometer

Step-by-step explanation:

(A) 475L - 50km

(B) 375L - 200km

Subtract liters.

475-375=100L

Subtract km

200-50=150km

Divide liters per km

100/150=0.6L/km

Answer:

13.50=0.75(x+10)

Step-by-step explanation:

From the options given, it seems the price of either of Sandals or sneakers is given as 10 and the other is x

If Price of Sandals or sneakers=x

And the price of the other one is 10

Total price=(x+10)

25% discount is given

So she will pay 75% of the total cost

75%=0.75

Total cost =$13.50

She would pay 75% of (x+10)

Which is

0.75(x+10)=13.50

13.50=0.75(x+10)

Answer:

The answer is $13.50 = 0.75(x + 10)

Step-by-step explanation:

I am doing the assignment right now

Your Welcome :)

The given equation is in the form ax^2 + bx + c = 0, where

a = 2

b = -12

c = 18

Those a,b,c values are plugged into the discriminant formula below

d = b^2 - 4ac

d = (-12)^2 - 4(2)(18)

d = 144 - 144

d = 0

The discriminant is zero, so there is only one real root. This root is specifically a rational number.

[tex]the \: answer \: is \: of \: option \: a \\ \\ for \: example \\ \\ if \: a = b \: and \: b = c \\ then \: we \: can \: say \: a = c \\ hope \: it \: helps[/tex]

Answer:

A is the answer

Step-by-step explanation:

The transitive property is if ABC=DEF and DEF=GHI, then ABC=GHI. The concept is the same here, just with different letters.

Answer:

125.66

Step-by-step explanation:

Answer:

The expression to find Carey's hourly rate is: [tex]c = 2*a - 2[/tex]. Carey's hourly rate is $10.

Step-by-step explanation:

Anderson receives 1 more than half of carey's hourly rate. If we call Anderson's rate by "a" and Carey's by "c", we can express this phrase in the following equation:

[tex]a = \frac{c}{2} + 1[/tex]

We want to find the Carey's rate, therefore we need to isolate the "c" variable.

[tex]\frac{c}{2} + 1 = a\\\frac{c}{2} = a - 1\\c = 2*a - 2[/tex]

Since Anderson earns $6, then we can find Carey's rate:

[tex]c = 2*6 - 2 = 12 - 2 = 10[/tex]

Answer:

A)

6 = c/2 + 1

Answer:

(g*h)(5) is g(h)=x

Step-by-step explanation:

because if h(x)=x-7 and g(x)=x^2.

Answer:

4

Step-by-step explanation:

[tex]h(x)=x-7 \\\\g(x)=x^2 \\\\(g\circ h)(5)= (5-7)^2=(-2)^2=4[/tex]

Hope this helps!

Using composite functions, it is found that the equivalent expression at x = 5 is given by:

[tex](g \circ h)(5) = 4[/tex]

A composite function is when a function is used as an input to another function, hence, that is:

[tex](g \circ h)(x) = g(h(x))[/tex].

In this problem, we have that the functions are given as follows:

Then, the composite function is given by:

[tex](g \circ h)(x) = g(h(x)) = g(x - 7) = (x - 7)^2[/tex].

We want to find the value of the composite function at x = 5,  hence we have that:

(5 - 7)² = 4.

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Answer: 41

Step-by-step explanation:

Answer:

c:16

Step-by-step explanation:

Answer:

So first we have 10x = 0. We divide by 10 on both sides, so then we get x = 0. We still have 0 because 0/10 = 0.

So that means that the answer is

Answer:

? = 10

Step-by-step explanation:

2(5x+4)=8 - DISTRIBUTE

= 10x + 8 = 8

10x + 8 = 8

- 8

10x = 0

10x/10 = 0/10

x = 0

Answer:

(a)Cat

(b)8 animals

(c)6 people

Step-by-step explanation:

From the attached diagram:

Let the [tex]\square[/tex] be x.

Half of [tex]\square[/tex] =x/2

From the pictogram, we then have:

[tex]Cat = x+\frac{x}{4} \\Dog=x+\frac{3x}{4}\\Giraffe=2x+\frac{x}{2}\\Monkey =x+\frac{x}{2}\\Dolphin=3x[/tex]

Therefore:

[tex]x+\frac{x}{4} +x+\frac{3x}{4}+2x+\frac{x}{2}+x+\frac{x}{2}+3x=80\\8x+\frac{x}{4}+\frac{3x}{4}+\frac{x}{2}+\frac{x}{2}=80\\10x=80\\x=8[/tex]

So we have the following numbers

[tex]Cat = x+\frac{x}{4} =8+\frac{8}{4}=10\\Dog=x+\frac{3x}{4}=8+\frac{3*8}{4}=14\\Giraffe=2x+\frac{x}{2}=2*8+\frac{8}{2}=20\\Monkey =x+\frac{x}{2}=8+\frac{8}{2}=12\\Dolphin=3x=3*8=24[/tex]

(a)Cat was the least popular

(b) [tex]\square[/tex] represents 8 animals

(c)

Number of People who preferred giraffe=20

Number of People who preferred dogs=14

Difference=20-14=6

Therefore, 6 more people preferred  giraffes than dogs.

A pictogram is a simple drawing that represents something

(a). Cat is least popular animal

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

(c) 6 more people preferred giraffes than dogs.

Let us consider that a large complete square represented by variable y .

Since, peoples whose favourite animal is cat is represented by a complete square and one fourth of square.

It means, Peoples who like cat = [tex]y+\frac{y}{4}[/tex]

Similarly,

People who like dog = [tex]y+\frac{3}{4}y[/tex]

Peoples who like Giraffe = [tex]2y+\frac{y}{2}[/tex]

Peoples who like monkey = [tex]y+\frac{y}{2}[/tex]

Peoples who like Dolphin = [tex]3y[/tex]

Since, total people = 80

Therefore,

       [tex]y+\frac{y}{4}+y+\frac{3}{4}y+2y+\frac{y}{2}+y+\frac{y}{2} +3y=80\\\\10y=80\\\\y=\frac{80}{10}=8[/tex]

So, a complete large square is equivalent to 8 peoples.

Peoples who like giraffes = [tex]2y+\frac{y}{2}=2(8)+\frac{8}{2}=20[/tex]

Peoples who like dog = [tex]y+\frac{3}{4}y=8+(\frac{3}{4} ) 8=14[/tex]

So, 20 - 14 =6 more people preferred giraffes than dogs.

Thus,

(a) Cat is least popular animal

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

(c) 6 more people preferred giraffes than dogs.

Learn more:

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Answer:

2/7

Step-by-step explanation:

7/8 ÷ 3 1/16

Change to an improper fraction

3 /16 = (16*3+1)/ 16 =49/16

7/8 ÷49/16

Copy dot flip

7/8 * 16/49

Rewrite

7/49 * 16/8

Simplify

1/7 * 2/1

2/7

Answer:

Step-by-step explanation:

4p(p−7q)

=(4p)(p+−7q)

=(4p)(p)+(4p)(−7q)

=4p squared −28pq