The domain for f(x) and g(x) is all real numbers.


Let f(x) = x2 + 1 and g(x) = x4 − 1.


Find f · g.


A.
x6 + x4 − x2 − 1


B.
x4 + x2 − 1


C.
x8 + x4 − x2 + 1


D.
x6 − x2 − 1The domain for f(x) and g(x) is all real numbers.

Answer:

15

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +8^2=(x+2)^2[/tex]

we can simplify 8 squared to 64, and we can use FOIL to expand x plus 2 squared.

[tex](x+2)(x+2)=x^2+4x+4[/tex]

We have

[tex]x^2+64=x^2+4x+4[/tex]

We can subtract x squared plus four from both sides to get

[tex]60=4x[/tex]

Dividing by 4, we get [tex]x=15[/tex]

Answer:x=15

Step-by-step explanation:

remember the Pythagorean Theraum(sorry about spelling)

a^2 +b^2=c^2

the shortest is a^2 , b^2 is the second shortest, and c^2 is the hypotenuse, or the longest.

currently the hypotenuse (c^2)is x+2, (b^2) is x, and a^2 is 8

8x8=64

64+x^2=(x+2)^2

try solving it now.

64+15^2=(15+2)^2

289=289

So, x=15

Answer:

C. [tex]-x-6>-3.5[/tex]

Step-by-step explanation:

One is asked to find which inequality has ([tex]x=-3[/tex]) in its solution set. Remember that an inequality is another way to represent a set of solutions. In essence, it states that all numbers less than; less than or equal to; greater than; or greater than or equal to, are a part of the solution. One simplifies an inequality in a similar manner to how one simplifies an equation, by using inverse operations and simplification. Just note that when multiplying or dividing the inequality by a negative number, one has to flip the inequality sign to ensure the expression remains true.

Simplify each of the inequalities, then evaluate to see which one has ([tex]x=-3[/tex]) as a part of its solution set.

A. [tex]-x -6<-3.5[/tex]

[tex]-x<2.5[/tex]

[tex]x>-2.5[/tex]

B. [tex]-x-6>3.5[/tex]

[tex]-x>9.5[/tex]

[tex]x<-9.5[/tex]

C. [tex]-x-6>-3.5[/tex]

[tex]-x>2.5[/tex]

[tex]x<-2.5[/tex]

D. [tex]x-6>-3.5[/tex]

[tex]x>2.5[/tex]

As can be seen, option (C [tex]-x-6>-3.5[/tex]) is the only one that fits this requirement. Since option (C) simplifies down to ([tex]x<-2.5[/tex]) or in words, (x) is less than (-2.5). This option is the only one that fits the solution since (-3) is less than (-2.5).

Answer:

This is trapezium.

Area of this figure =1/2h(d1-d2)

1/2×5(14-8)

=30/2

=15cm^2

Answer:

are you look for finaincl loan

Step-by-step explanation:

9514 1404 393

Answer:

  9.23%

Step-by-step explanation:

The account balance for simple interest is given by ...

  A = P(1 +rt) . . . . . principal P invested for t years at rate r

  554 = 379(1 +r·5)

  554 = 379 + 1895r . . . . eliminate parentheses

  175 = 1895r . . . . . . . . . subtract 379

  r = 175/1895 ≈ 0.092348 ≈ 9.23%

Jennifer's account had an interest rate of about 9.23%.

Answer: x = 52

Step-by-step explanation:

You'd first deal with the 4 outside the parentheses, multiplying 10x-20 by 4. This would result in 40x - 80 = 200.

You'd then further isolate x, adding 80 on both sides, resulting in 40x = 2080. Divide by 40 on both sides and You'd get your answer of x = 52.

Answer:

Top right option

Step-by-step explanation:

multiplying the digits, you get the volume, which is 3/4

Answered by GAUTHMATH

The uppercase letters are the angles, while the lowercase letters are the sides. We have side 'a' opposite angle A, side b opposite angle B, side c opposite angle C.

We have this given info:

Let's use the law of sines to find angle B

sin(B)/b = sin(A)/a

sin(B)/25.5 = sin(25)/13.2

sin(B) = 25.5*sin(25)/13.2

sin(B) = 0.81642164

B = arcsin(0.81642164) or B = 180 - arcsin(0.81642164)

B = 54.72817392 or B = 180 - 54.72817392

B = 54.72817392 or B = 125.27182608

When rounded to the nearest whole degree, we get B = 55 or B = 125.

However, I'll use the slightly more accurate values of B for the next two sections.

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

Let's consider the case that B = 54.72817392

This would have to mean

A+B+C = 180

C = 180-A-B

C = 180-25-54.72817392

C = 100.27182608  which rounds to C = 100

Through the law of sines we can say

c/sin(C) = a/sin(A)

c = sin(C)*a/sin(A)

c = sin(100.2718 2608)*13.2/sin(25)

c = 30.73327084 which rounds to c = 30.7

One solution is

A = 25, B = 55, C = 100

a = 13.2, b = 25.5, c = 30.7

As you can probably guess, the phrasing "solve the triangle" means find all sides and angle measures.

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

Now we'll consider the case that B = 125.27182608

We follow the same steps as the previous section

A+B+C = 180

C = 180-A-B

C = 180-25-125.27182608

C = 29.72817392 which rounds to C = 30

and

c/sin(C) = a/sin(A)

c = sin(C)*a/sin(A)

c = sin(29.72817392)*13.2/sin(25)

c = 15.48842618 which rounds to c = 15.5

The other solution is

A = 25, B = 125, C = 30

a = 13.2, b = 25.5, c = 15.5

Check out the diagrams below.

Answer: 135

Step-by-step explanation: Write 150% as 150/100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have 150/100 of 90= 150/100 X 90

Therefore, the answer is 135

If you are using a calculator, enter 150÷100×90 which will give you 135 as the answer.

150 percentage of 90 is 135 which we obtained by multiplying 1.5 with 90.

"Percent" means "per hundred," so when we say "150%," it means 150 per hundred or 150 out of 100.

To find 150% of 90, we can use the following formula:

150% of 90 = (150/100) × 90

Convert 150% to a decimal.

To do this, divide 150 by 100:

150/100 = 1.5

Multiply the decimal value by 90:

1.5 × 90

= 135

So, 150% of 90 is 135 which means that 135 is 150% of 90, which is equivalent to saying that 135 is 1.5 times larger than 90.

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Answer:

Step-by-step explanation: Hope this helps

Answer:

15x^9

Step-by-step explanation:

A=l x w

5x^4 times 3x^5 is basically 3*5*x^4*x^5

when you multiply exponents with the same base, you add the exponents, so it becomes 15x^9

Answer:

50.24

Step-by-step explanation:

A = Area

Radius = 4 (The radius is half of the diameter

Diameter = 8

Pie = 3.14

A = (pie)r^2

A = (3.14)4^2

A = (3.14)16

A = 50.24

Answer:

2*sqrt6 = 2*apprx2 = 4

5*sqrt10 = 5*3.1 = 15.5

4*sqrt2 = 4*1.4 = 6.4

3*sqrt3  = 3*1.7 = 5.1

4, 5.1, 6.4, 15.5 or... 2sqrt6, 3sqrt3, 4sqrt2, 5sqrt10

​

Answer:

4/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step 1

Find the height:

Step 2

Find the area:

We can expect to roll a prime number 48 times.

Theoretically, when you roll a number cube all the possible numbers have the same probability, 1/6.

We know that the numbers in a number cube are {1, 2, 3, 4, 5, 6}

Of these, the primes are: 2, 3, and 5.

So half of the outcomes of a number cube are primes.

This means that, in every single roll, the probability of getting a prime number is 1/2.   (1/6 + 1/6 + 1/6 = 3/6 = 1/2)

Then for 96 rolls, we should expect to see in half of these a prime number as an outcome.

This means that we should expect to roll a prime number 96/2 = 48 times.

If you want to learn more about probability, you can read:

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You should expect to roll a prime number 64 times.

To determine, if you roll a number cube 96 times, how many times would you expect to roll a prime number, the following calculation must be performed, knowing that the prime numbers are those that can only be divided by 1 or by themselves:  

A cube has 6 sides. Therefore, the numbers in the cube will be 1, 2, 3, 4, 5 and 6. Of these numbers, only 4 and 6 are not prime, since 4 is divisible by 2 and 6 is divisible by 2 and 3.

Therefore, 4/6 numbers are prime, that is, 66.66% of the numbers in the cube.

Therefore, if you roll a number cube 96 times, since 96 x 4/6 equals 64, you should expect to roll a prime number 64 times.

Learn more in https://brainly.com/question/23715861.

Answer:

all diagram can be folded into triangular pyramid.

Answer:

8

Step-by-step explanation:

(3+5)^2/8=(8)^2/8=64/8=8

Answer: 8

Step-by-step explanation:

(3+5)^2/8=

(8)^2/8=

64/8=

8

Answer: 5 and 7

Step-by-step explanation:

Given

Sum of the integers is 12

Product of the integers is 35

Suppose the integers are [tex]x[/tex] and [tex]y[/tex]

[tex]\Rightarrow x+y=12\\\\\Rightarrow y=12-x\\\Rightarrow xy=35\\\text{Substitute y}\\\Rightarrow x(12-x)=35\\\Rightarrow 12x-x^2=35\\\Rightarrow x^2-12x+35=0\\\Rightarrow x^2-7x-5x+35=0\\\Rightarrow (x-7)(x-5)=0\\\Rightarrow x=5\ or\ 7[/tex]

[tex]\therefore \text{y can be }7\ or\ 5[/tex]

Hence, the numbers are 5 and 7.

Answer:

B

Step-by-step explanation:

-10 + 3x - x - 7x + 5x + 7 + 2x

combine like terms

-10 + 3x - x - 7x + 5x + 7 + 2x

-3 + 3x - x - 7x + 5x + 2x

the -7x and the 5x + 2x cancel out to 0, so for the x terms we are left with 3x -x to get 2x

= 2x - 3

Answer:

Yes, by SSS Similarity Theorem

Step-by-step explanation:

the triangles are similar because the sides are proportional, the common ratio is 1.5.

if you look at the corresponding sides of the triangle and multiply 1.5 to the smaller triangle measurements, you get the bigger triangle's corresponding measurements:

3 * 1.5 = 4

4 * 1.5 = 6

6 * 1.5 = 9

Yes the triangle are similar by SSS Similarity Theorem.

Triangles' similarity can be characterized based on their attributes.

If two triangles are similar,

(I) their respective angles are equal, and

(ii) their corresponding sides have the same proportion (or proportion

We have two triangles.

From the triangle we can write

AB / ED = 4/ 6 = 2/3

and, AC / FD = 6 / 9 = 2/3

and, BC / EF = 3 / 4.5 = 30 /45 = 2/3

Thus, AB / ED = AC / FD = BC / EF = 2/3

By SSS Similarity Criteria triangles are similar.

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Step-by-step explanation:

the answer of the following is in the figure

Answer:

Solution given:

Sin[tex]\theta_{1}=\frac{1}{4}[/tex]

[tex]\frac{opposite}{hypotenuse}=\frac{1}{4}[/tex]

equating corresponding value

opposite=1

hypotenuse=4

adjacent=x

By using Pythagoras law

hypotenuse²=opposite²+adjacent²

4²=1²+x²

16=1+x²

x²=16-1

x=[tex]\sqrt{15}[/tex]

In II quadrant

Cos angle is negative

Cos[tex]\theta_{1}=\frac{-adjacent}{hypotenuse}[/tex]

Answer:

[tex]\displaystyle \cos ( \theta _{1} ) = - \frac{ \sqrt{15}}{ 4 }[/tex]

Step-by-step explanation:

on a unit circle there're 4 Quadrant. on Q:I sin and cos both are positive,on Q:II cos is negative and sin positive, on Q:III both sin and cos are negative and on Q:IV cos is positive and sin negative.

actually a unit circle is a coordinate plane but

it'll be required later

well to solve the problem we can consider Pythagorean theorem which states that the square of sin and cos is equal to 1. therefore,

[tex] \displaystyle \sin ^{2} ( \theta) + \cos ^{2} ( \theta) = 1[/tex]

[tex] \rm \displaystyle \implies \boxed{\cos ^{} ( \theta) = \sqrt{1 - \sin ^{2} ( \theta) }}[/tex]

in this case,

Thus substitute:

[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \left( \frac{1}{4} \right) ^{2} }[/tex]

simplify square:

[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \frac{1}{16} }[/tex]

simplify substraction:

[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{16 - 1}{16} }[/tex]

simplify numerator:

[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{15}{16} }[/tex]

recall redical rule:

[tex]\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ \sqrt {16} }[/tex]

simplify square root:

[tex]\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ 4 }[/tex]

since cos is negative on Q:II hence,

[tex]\displaystyle \cos ( \theta _{1} ) = \boxed{- \frac{ \sqrt{15}}{ 4 }}[/tex]

and we're done!

Answer:

i hope it will help

Step-by-step explanation:

I did not get the equation so I solve it with two methods

Answer:

Step-by-step explanation:

Given equation of the quadratic function is,

y = x² + 5x - 7

Convert this equation into vertex form,

y = x² + 2(2.5x) - 7

  = x² + 2(2.5x) + (2.5)² - (2.5)² - 7

  = (x + 2.5)²- 6.25 - 7

  = (x + 2.5)² - 13.25

Therefore, vertex of the function is → (-2.5, -13.25)

For the solutions,

y = 0

(x + 2.5)² - 13.25 = 0

x = (±√13.25) - 2.5

x = (±3.64) - 2.5

x = 1.14, -6.14

Solutions → (-6.14, 0) and (1.14, 0)

Answer:

[tex]3y = 6,=> y=2[/tex]

Step-by-step explanai

on:

Answer:

The given polynomial is,

2x³+5x²-8x-10=0

all possible roots of a polynomial,

ax³+b²+c x +d=0 ← all possible factors of ration (d/a)

Therefore, eq (1), all possible factors are the factors of ratio (-10/2)

which are, B) { ± 1, 1/2, ± 2, ± 5/2, ±5, ± 10}

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