How do I even start this? And how to i order the equation to solve

How Do I Even Start This? And How To I Order The Equation To Solve

Answers

Answer 1

[tex]f(g(h(x)))=f(g(\sqrt x))=f(\sqrt x-1)=\boxed{(\sqrt x-1)^4+4}[/tex]

This is because

[tex]h(x)=\sqrt x[/tex]

[tex]g(x)=x-1[/tex]

[tex]\implies g(h(x))=\sqrt x-1[/tex]

(that is, replace any instance of x in the definition of g with √x )

and

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

[tex]\implies f(\sqrt x-1)=(\sqrt x-1)^4+4[/tex]

(replace any x in f with √x - 1)

Also acceptable:

[tex](\sqrt x-1)^4+4=((\sqrt x)^4-4(\sqrt x)^3+6(\sqrt x)^2-4\sqrt x+1)+4[/tex]

[tex]=\boxed{x^2-4x\sqrt x+6x-4\sqrt x+5}[/tex]

(assuming x is not negative)


Related Questions

determine whether or not the function r(x) =x^2-2 is one -to-one

Answers

Answer:

The function is not one-to-one

Step-by-step explanation:

This is a quadratic function.

[tex]f(x)=x^2-2[/tex]

A function is one-to-one

[tex]\text{if } f(x_1)=f(x_2) \Leftrightarrow x_1=x_2[/tex]

The function given is not one-to-one because there are values of the input [tex]x[/tex], which leads to the same output.

For example.

[tex]y=f(2)=2^2-2=\boxed{2}[/tex]

[tex]y=f(-2)=(-2)^2-2=\boxed{2}[/tex]

Solve for x: 3/5=x-1/8

Answers

Answer:

x = [tex]\frac{29}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{3}{5}[/tex] = [tex]\frac{x-1}{8}[/tex] ( cross- multiply )

5(x - 1) = 24 ← distribute parenthesis on left side

5x - 5 = 24 ( add 5 to both sides )

5x = 29 ( divide both sides by 5 )

x = [tex]\frac{29}{5}[/tex]

Which statement best explains why the sine of an acute angle is equal to the cosine of the angles complement

Answers

Answer:

Option (B)

Step-by-step explanation:

From the figure attached,

ΔABC is a right triangle.

Cosine and Sine ratios from the given triangle will be,

SinA = [tex]\frac{\text{Opposite side}}{Hypotenuse}[/tex]

        = [tex]\frac{a}{c}[/tex]

CosB = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

         = [tex]\frac{a}{c}[/tex]

Therefore, both the ratios (Sine and Cosine) will be equal as [tex]\frac{a}{c}[/tex]

Option (B) will be the correct option.

5 times the quantity 7 minus a number f in an algebraic expression.

Answers

Answer:

(5*7)-f

Step-by-step explanation:

Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]

Algebraic expression

Algebraic expression is the combination of terms that consists of numbers  and variables connected by arithmetic operators.

Given statement is 5 times the quantity 7 minus a number f in an algebraic expression.

We need to write it in an algebraic expression

5 times a quantity. for product we use multiplication sign

For addition we use + sign and for difference we use minus sign .

5 times the quantity 7 means 5 multiplied by 7

[tex]5 \cdot 7[/tex]

5 times the quantity 7 minus a number f  

subtract f from the expression we got

[tex]5 \cdot 7 -f[/tex]

Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]

Learn more information about 'Algebraic expression ' here:

brainly.com/question/2193741

A business has $25,000 to spend on training sessions for its employees. It wants 45 of its employees to attend. The business wants to send as many employees as it can to a technology training. The technology training costs $1,000 per person. The customer service training costs $500 per person. Create a system of equations that models how many of each type of training the business should purchase. 1,000x + 500y = 45 x + y = 25,000 1,000x + 500y = 25,000 x + y = 45 1,000x + y = 45 x + 500y = 25,000 x + 500y = 45 1,000x + y = 25,000

Answers

Answer: [tex]x+y=45\\\\1000 x + 500y = $2500[/tex]

Step-by-step explanation:

Let x =  Number of employees taking technology training

y= Number of employees taking customer service training

Given, The technology training costs $1,000 per person. The customer service training costs $500 per person.

Total cost = 1000 x + 500y

Since, Total cost = $25,000 and total employee to attend training= 45 .

That means , the required equations are:

[tex]x+y=45\\\\1000 x + 500y = $2500[/tex]

Answer:

1,000x + 500y = 45

x + y =45

Step-by-step explanation:

So that means answer b is the correct answer, also I took the test.

What are the dimensions of the matrix?

Answers

Answer:

4 x 3

Step-by-step explanation:

The order of a matrix is given by stating the number of rows followed by the number of columns.

The matrix here has 4 rows and 3 columns thus order is

4 x 3

Help now for brainliest,5stars and thanks.Find the values of x in the range 0≤x≤180° for which 15sin^2 x+11cox-17=0

Answers

Answer:

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

Step-by-step explanation:

Given equation is:

[tex]15sin^2 x+11cosx-17=0[/tex]

To find:

Values of [tex]x[/tex] in the range [tex]0^\circ\leq x\leq180^\circ[/tex].

Solution:

First of all, let us recall one identity of square of sine and square of cosine.

Sum of square of sine of an angle and square of cosine of the same angle is equal to 1.

[tex]\bold{sin^2\theta+cos^2\theta=1}[/tex]

So

Putting [tex]sin^2x=1-cos^2x[/tex] in the given equation.

[tex]15(1-cos^2x)+11cosx-17=0\\\Rightarrow 15-15cos^2x+11cosx-17=0\\\Rightarrow -15cos^2x+11cosx-2=0\\\Rightarrow 15cos^2x-11cosx+2=0\\\Rightarrow 15cos^2x-5cosx-6cosx+2=0\\\Rightarrow 5cosx(3cosx-1)-2(3cosx-1)=0\\\Rightarrow (5cosx-2)(3cosx-1)=0\\\Rightarrow cosx=\dfrac{2}{5}, \dfrac{1}{3}[/tex]

So, in the range [tex]0^\circ\leq x\leq180^\circ[/tex]

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

Explain what each of them is.

Answers

Answer:

What are natural numbers?

the positive integers or whole numbers include 1, 2, 3, and etc. sometimes zero.

What are whole numbers?

Whole numbers are 0, 1, 2, 3, 4, 5, 6. Whole numbers include positive integers along with 0.

17, 99, 267, 8107 and 999999999 are examples of whole numbers.

What are rational numbers?

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333

What are irrational numbers?

A real number that can NOT be made by dividing two integers (an integer has no fractional part). "Irrational" means "no ratio", so it isn't a rational number.

Example: π is an irrational number.

What are real numbers?

The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2.

Included within the irrationals are the transcendental numbers, such as π

Which professionals most directly use geometry in their work? A. accountants B. astronomers C. judges D. pharmacists E. politicians\

Answers

Answer:

Astronomers directly use geometry in their work rather than accountants , judges, pharmacist and politicians.

They used geometry to measure velocity , direction, distance, relativity, momentum, and probability. They used it to look at objects in the sky with a telescope by setting a required angle to get a proper view .

But Accountants, judges, pharmacist and politicians are not in use of geometry directly or frequently.

Hence, Option 'B' is correct.

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Use the rule "add 2" to create a sequence of 5 numbers starting with 8.

Answers

Answer:

8 10 12 14 16

Step-by-step explanation:

8+2=10, 10+2=12, 12+2=14, 14+2=16

I need help pppppppllssssssssss​

Answers

Answer:

y=x-1

Step-by-step explanation:

Practice Writing Composite Functions Given: f(x) = x - 7 and h(x) = 2x + 3 Write the rule for h(f(x)).

Answers

Answer:

h(f(x)) = 2x - 11

Step-by-step explanation:

f(x) = x - 7

h(x) = 2x + 3

To find h(f(x)) substitute f(x) into h(x) that's replace every x in h(x) by f(x)

That's

h(f(x)) = 2(x - 7) + 3

h(f(x)) = 2x - 14 + 3

We have the final answer as

h(f(x)) = 2x - 11

Hope this helps you

the sum of three consecutive numbers is 276. What is the smallest of these intengers?

Answers

Answer:

91

Step-by-step explanation:

Let x be the smallest one:

● x is the first number

● x+1 is the second number

● x+2 is the third number

The sum of these numbers is 276

● x+(x+1)+(x+2) =276

● x+x+1+x+2 = 276

● 3x + 3 = 276

Substract 3 from both sides:

● 3x+3-3 = 276-3

● 3x = 273

Divide both sides by 3

● (3x)/3 = 273/3

● x = 91

So the smallest one is 91

The length of a rectangle is seven inches more than its width. Its area is 540 square inches. Find the width and
length of the rectangle.​

Answers

Answer: 20 is the width and 27 is length

a pack of 4 choclates cost 1.80 pounds how much is the price per unit

Answers

Answer:

0.45p

Step-by-step explanation:

4 chocolates = £1.80

1 chocolate =  x

x= 1.80× 1 = 1.80÷4 = 0.45p

1 = 0.45p

I HOPE THIS HELPED :)

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

Answers

Answer:

b

Step-by-step explanation:

Answer:

The answer is D or (10,-9)

Step-by-step explanation:

Since y is already given (and you have to use the substitution method) substitute y into one of the equations. So you should have something like this:

-2x+11=3x+21

After that merely solve for x which should get you x=10. After you get your x value plug 10 in either (of the original) equation and your y value should be -9. For example if you chose y=-2x+11 you should have y= -2(10)+11. In the end your answer should be (10,-9).

If you want to check your work merely plug your answer into both equations (ex: -9=-2(10)+11 --> -9=-9), therefore you know your answer is correct).

Hope this helped!

PLEASE HELP TO BE MARKED THE BRAINLIEST

Answers

Answer:

4.  m_LON + m_MON = m_LON; m_JKL + m_IKH = m_HKJ

Step-by-step explanation:

Both interior angles of each add up to m_LON:m_HKJ

To prove this we show the interior angles add + sign to each prove LON angle, and : colon separates from the proof of m_JKL+m_IKH= m_HKJ.

85 POINTS! PLEASE HELP! Explain how to write an equation parallel to the equation y = 2x + 3 and the new line also includes the ordered pair (1,-2).

Answers

Answer:

[tex]\huge\boxed{\sf y = 2x -4}[/tex]

Step-by-step explanation:

The given equation is:

y = 2x + 3

Where Slope = m = 2 , Y-intercept = b = 3

Parallel lines have equal slopes

So, Slope of new line = m = 2

Now, Finding y-intercept:

Given Point = (x,y) = (1,-2)

So, x = 1 , y = -2

Putting m, x and y in standard form of equation to get b:

[tex]\sf y = mx+b[/tex]

[tex]\sf -2 = (2)(1) + b\\-2 = 2 + b\\[/tex]

Subtracting 2 to both sides

[tex]\sf b = -2-2\\[/tex]

b = -4

So, the standard form og equation for the new line is :

[tex]\sf y = mx+b[/tex]

[tex]\sf y = 2x -4[/tex]

Answer:

y = 2x - 4

Step-by-step explanation:

the problem is called (slope-intercept form)

the equation of the line is y = mx + b

the equation of a line is given as y = 2x + 3

slope = 2

b = y-intercept is where the line crosses the y-axis = 3

so point (x1, y1)  = (1, -2)

by using the equation.

y = mx + b

-2 = 2 (1) + b

-2 -2 = b

therefore b = -4

writing the new equation using the slope intercept form

y = mx + b  would be y = 2x + 4

so the equation parallel to the equation y = 2x + 3 is y = 2x - 4

3/v=2/4? i need help plz

Answers

Answer:

v = 6

Step-by-step explanation:

3/v = 2/4

We can use cross products to solve

2v = 3*4

2v = 12

Divide each side by 2

2v/2 = 12/2

v =6

Answer:

v=6

Step-by-step explanation:

If this is making them equal, then you should know that 2/4 is 1/2 , so you could just multiply 3 by both the 1 and the 2 in 1/2 and 1 times 3 is 3 which is what we have and 2 times 3 is 6 which is v.

There are 8 marbles in a bag, each with a different color. How many different groups
of 4 marbles can we select?

Answers

Answer:

70

Step-by-step explanation:

8 choose 4

= (8!)/(4!*4!)

=(8*7*6*5)/(4*3*2*1)

=1680/24

=70

Answer:

4/8 simplified=1/2

Step-by-step explanation:

i hope this is right sorry if not

What shape best describes the cross-section cut at an angle to the base of a right rectangular prism? Trapezoid Parallelogram Square Rectangle

Answers

Answer:

Parallelogram

Step-by-step explanation:

Answer:

Parallelogram

Step-by-step explanation

the length of rectangle is 6/5 of its breath and perimeter is 132 m find area of rectangle​

Answers

Answer:

1,080 meters squared.

Step-by-step explanation:

Let's say the breadth of the rectangle is x. That means the length of it is 6/5x.

The perimeter is 132 meters. The formula for the perimeter is 2 times the breadth plus two times the length.

2(x) + 2(6/5x) = 132

2x + 12/5x = 132

10/5x + 12/5x = 132

22/5x = 132

22x = 660

x = 30.

That means that the breadth of the rectangle is 30 meters, and the length is (6/5) * 30 = 6 * 6 = 36 meters.

The formula for the area of the rectangle is the breadth times the length, so the area is 36 * 30 = 1,080 meters squared.

Hope this helps!

The function f(x) = 50(0.952)x, where x is the time in years, models a declining feral cat population. How many feral cats will there be in 9 years?

Answers

Answer: B) 32

Work Shown:

f(x) = 50(0.952)^x

f(9) = 50(0.952)^9

f(9) = 32.1146016801717

f(9) = 32 approximately

Side note: the exponential function is in the form a*b^x with b = 1+r = 0.952, which solves to r = -0.048. The negative r value means we have a 4.8% decrease each year.

Another note: you don't even need to use math to answer this question. Note how 50 is the starting population and the population is declining. Only choice B has a value smaller than 50, so we can rule out the others right away.

Answer:

  32

Step-by-step explanation:

The initial value of the population is f(0) = 50(0.952^0) = 50. If the population is declining, it must be less than 50 in 9 years. The only answer choice that is less than 50 is ...

  about 32 feral cats

_____

You can evaluate f(9) to choose the same answer:

  f(9) = 50(0.952^9) ≈ 32.114 ≈ 32

Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. 13.2 and 6.7

Answers

Answer:

6.5<3rd side <19.9

Step-by-step explanation:

Extremely easy. All you have to do to get the first answer is minus 13.2-6.7 which is 6.5. Then add 13.2+6.7 to get 19.9 for the other answer. So the two answers would be 6.5 and 19.9.

Your welcome


Please answer this question now

Answers

Answer:

1471.15

Step-by-step explanation:

What are the solutions to the equation (2x – 5)(3x – 1) = 0? x = or x = 3 x = x = 5 or x = 1

Answers

Answer:

x = 5/2          x=1/3

Step-by-step explanation:

(2x – 5)(3x – 1) = 0

Using the zero product property

2x-5 =0    3x-1 =0

2x=5         3x =1

x = 5/2          x=1/3

Answer:

C on edg 2021

Step-by-step explanation:

The sum of the numerator and denominator of a
fraction is 12. If the denominator is increased by 3,
the fraction becomes 1/2.
Find the fraction.
plz answer step by step​

Answers

[tex]x+y=12\\\dfrac{x}{y+3}=\dfrac{1}{2}\\\\x=12-y\\2x=y+3\\\\2(12-y)=y+3\\24-2y=y+3\\3y=21\\y=7\\\\x=12-7=5\\\\\dfrac{x}{y}=\dfrac{5}{7}[/tex]

Isabelle bought some stationery. 1/3 of them were pencils. 5/8 of the remainder were erasers and the rest were rulers. The cost of the stationery is - a Pencil: $1.20, an eraser: $1 and a ruler: $0.50. She spent a total of 169.50 on all stationery. How much more did she spend on erasers than rulers.

Answers

Answer:

Isabelle spent $52.50 more on Erasers than rulers.

Step-by-step explanation:

Step 1

Find the quantity of each stationery bought in fraction

Let us represent the total fraction of what Isabelle bought as: x

1/3x = quantity of pencils bought

5/8 of the remainder = quantity of erasers bought

The remainder = x - 1/3x = 2/3x

5/8 of 2/3x = 5/8 × 2/3x = 5/12x

Hence, 5/12x = quantity of erasers bought

The rest is rulers

1 - (1/3 + 5/12)

1 - (4 + 5/12)

1 - 9/12

1 - 3/4

= 1/4x

Hence, 1/4 = quantity of rulers bought.

Step 2

We find the number of stationeries that Isabelle bought.

The cost of the stationery is

a Pencil: $1.20

an eraser: $1

a ruler: $0.50.

Total amount spent on stationery = 169.50

We have this equation

1.20 × 1/3x + 1 × 5/12x + 0.50 × 1/4x = 169.50

0.4x + 0.4166666667x + 0.125x =

169.50

0.9416666667x = 169.50

x = 169.50 /0.9416666667

x = 179.99999999

Approximately , the number of stationeries that Isabelle bought = x = 180

Step 3

Find the number and the amount spent on each stationery that Isabelle bought

a) i) Quantity of pencils bought = 1/3 x

x = 180

= 1/3 × 180

= 60 pencils

ii) Amount spent on pencils

If 1 pencil = $1.20

60 pencils =

60 × 1.20 = $72

b) i) Quantity of Erasers bought = 5/12x

x = 180

= 5/12 × 180

= 75 pencils

ii) Amount spent on Eraser

If 1 pencil = $1

75 pencils =

75 × 1 = $75

c) i) Quantity of rulers bought = 1/4 x

x = 180

= 1/4 × 180

= 45 pencils

ii) Amount spent on pencils

If 1 pencil = $0.50

45 pencils =

45 × 0.50 = $22.50

Step 4

We were asked to calculate how much more did she spend on erasers than rulers.

In step 3, the amount spent on Erasers = $75

the amount spent on ruler = $22.5

The difference in the amount spent = $75 - $22.5

= $52.5

Therefore, Isabelle spent $52.50 more on Erasers than rulers.

Adam and his dad share the cost of a meal in the ratio of 2:3.

Adam's dad pays £52.20.

What is the total cost of the meal?

Answers

Answer:

£ 87.00

Step-by-step explanation:

52.20*2/3=52.20/3*2=17.4*2=34.8

52.20+34.80=87.00

what is the answer to 1/8=s-3/4

Answers

Answer:

7/8 =s

Step-by-step explanation:

1/8=s-3/4

Add 3/4

1/8 + 3/4 = s -3/4 +3/4

1/8 + 3/4 = s

Get a common denominator

1/8 + 3/4 *2/2 = s

1/8 + 6/8 =s

7/8 =s

1/8 = s - 3/4

1/8 = s -6/8 ( * 2/2)

7/8 = s

s = 7/8

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