Please help me with this question and my next one!

f(g(x))  (you plug/substitute g(x) into x)

f(x) = 4x - √x

f(g(x)) = 4(g(x)) - √(g(x))      since g(x) = (x - 5)², you can do:

f(g(x)) = 4(x - 5)² - √(x - 5)²     The ² and √ cancel each other, leaving

f(g(x)) = 4(x - 5)² - (x - 5)      Next factor out (x - 5)² or (x - 5)(x - 5)

f(g(x)) = 4(x² - 10x + 25) - (x - 5)  Now distribute the 4 and the -

f(g(x)) = 4x² - 40x + 100 - x + 5   Simplify

f(g(x)) = 4x² - 41x + 105         Your answer is B

ANSWER

[tex]f(g(x)) =4{x}^{2} - 41x + 105 [/tex]

EXPLANATION

The given functions are:

[tex]f(x) = 4x - \sqrt{x} [/tex]

and

[tex]g(x) = {(x - 5)}^{2} [/tex]

To find

[tex]f(g(x)) = f( {(x - 5)}^{2} )[/tex]

[tex]f(g(x)) =4 {(x - 5)}^{2} - \sqrt{{(x - 5)}^{2} } [/tex]

We expand and simplify to obtain,

[tex]f(g(x)) =4 {( {x}^{2} - 10x + 25)} - (x - 5)[/tex]

[tex]f(g(x)) =4{x}^{2} - 40x + 100 - x + 5[/tex]

Combine similar terms to get;

[tex]f(g(x)) =4{x}^{2} - 41x + 105 [/tex]

The correct choice is B.

Answer:

2-2/3y

Step-by-step explanation:

First, you rearrange the equation, to get 3x=6-2y.

Then, you would divide all of the terms by 3, in order to get the value of x

x=2-2/3y

Answer:

B

Step-by-step explanation:

A sum of cubes has the form

a³ + b³

8x³ = (2x)³ and 125 = 5³

Hence

8x³ + 125 = (2x)³ + 5³ ← a sum of cubes

Answer:

(2,8)

Step-by-step explanation:

Add them together to get rid of the y.

-6x = -4 - y

-7x = -22 + y

=

-13x = -26

Then solve for x.

-13x/-13 = -26/-13

x = 2

Now plug in the x value into either equation and solve for y.

-7(2) = -22 + y

-14 = -22 + y

-14 + 22 = -22 + 22 + y

8 = y

So...

x = 2

y = 8

(2,8)

Answer:

The solution is (-2, -16).

Step-by-step explanation:

-6x = -4-y  can be solved for y:  y = 6x - 4

-7x = -22 + y

In the second equation, substitute 6x - 4 for y:

-7x = -22 + 6x - 4

Grouping like terms:  0 = -22 + 6x + 7x - 4, or

                                   -26  = 13x

So x = -2.  If x = -2, we can obtain the value of y from y = 6x - 4 (see above).

y = 6(-2) - 4 = -16

The solution is (-2, -16).

Answer to this is 8. Letter B

Answer: There are 48 students in the class.

Step-by-step explanation:

Let the number of students = S

Let the number of benches = B

If 4 students sit on each bench, 3 benches are left vacant.

S = 4(B - 3)

S = 4·B - 12 } Equation 1

If 3 students sit on each bench, 3 students still standing.

S = 3·B + 3 } Equation 2

We can match the two equations because they both indicate the same number of students.

4B - 12 = 3·B + 3

on solving this

4·B - 3·B = 3 + 12

B = 15 → number of benches

That is the number of benches, therefore substituting the value for B in equation 1

S = 4·B - 12 Equation 1

S = 4·15 -12

S = 60 - 12 = 48 → number of students

Answer: There are 48 students in the class.

There are 48 students and 15 benches.

If 4 students sit on each bench, 3 benches are left vacant.

48students ÷ 4students/bench = 12 benches are occupied and left 3 vacant benches.

If 3 students sit on each bench, 3 students still standing.

15benches * 3 students/bench = 45 students are sitting and 3 students remain standing.

[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​

Final answer:

By creating a system of equations from the given conditions, the number of students in the class is calculated to be 48.

Explanation:

To find the number of students in the class based on the provided scenario, we can set up a system of equations based on the given conditions:

If 4 students sit on each bench, 3 benches remain empty.

If 3 students sit on each bench, 3 students remain standing.

Let's use B to represent the total number of benches and S to represent the total number of students. The first condition tells us that when 4 students sit on each bench, there are B - 3 benches filled, which means 4(B - 3) students are seated. The second condition implies that if 3 students sit on each bench, all the benches are filled, and 3 more students are still standing, which can be represented by 3B + 3.

Therefore, we can write two equations as follows:

4(B - 3) = S

3B + 3 = S

Since both expressions equal S, we can set them equal to each other:

4(B - 3) = 3B + 3

Simplifying this equation, we can find the number of benches (B), and then substitute back to find the number of students (S).

4B - 12 = 3B + 3

B = 3 + 12 = 15 benches

Now we substitute B into one of our original equations to find S:

S = 4(B - 3)

S = 4(15 - 3)

S = 4 × 12

S = 48 students

Therefore, there are 48 students in the class.

Answer:

make all the numbers have the same denominator, then simply see what multiplies to equal both fractions. your answer should be -3/10(1/5k+1)

Step-by-step explanation:

ANSWER

[tex]( - \infty , - 7) \cup( - 7 , 0) \cup(0 , 7 )\cup(7 , + \infty )[/tex]

EXPLANATION

The given function is

[tex]h(x) = \frac{9x}{x( {x}^{2} - 49) } [/tex]

This function is defined for values where the denominator is not equal to zero.

[tex]x( {x}^{2} - 49) \ne0[/tex]

[tex]x(x - 7)(x + 7) = 0[/tex]

The domain is

[tex] x \ne - 7, x \ne0, \: and \: x \ne 7,[/tex]

Or

[tex]( - \infty , - 7) \cup( - 7 , 0) \cup(0 , 7 )\cup(7 , + \infty )[/tex]

The domain of the function h=9x/x(x^2-49) is x = -7, x = 7.

The domain of the function h = 9x/(x(x^{2}-49)) can be determined by considering the values of x that make the denominator non-zero. Since division by zero is undefined, we need to find the values that would make the denominator equal to zero. In this case, the denominator is x(x^{2}-49), which factorizes to x(x+7)(x-7). So, the values of x that make the denominator equal to zero are x=0, x=-7, and x=7.

However, we also need to consider that the function is undefined when cancelling out those values of x that would also make the numerator zero. In this case, x=0 would make the numerator zero, so it cannot be a part of the domain.

Therefore, the domain of the function h = 9x/(x(x^{2}-49)) is given by x = -7, x = 7.

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Answer:

56 oz

Step-by-step explanation:

1 pound = 16 ounces

16 * 3.5 = 56

3.5 pounds = 56 ounces

I hope I helped!

Let me know if you need anything else!

~ Zoe

16x3=48 half of 16 is 8 so 48+8=56 :)

The required fraction 40/32 simplifies to 5/4.

To simplify the fraction 40/32, we can find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.

The prime factorization of 40 is 2³ * 5, and the prime factorization of 32 is 2⁵. The common factors between 40 and 32 are 2³, so the GCD is 2³ = 8.

Dividing both the numerator and denominator by 8, we get:

40/32 = (40 ÷ 8) / (32 ÷ 8) = 5/4

Therefore, 40/32 simplifies to 5/4.

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To simplify 40/32, find the greatest common divisor (GCD) of 40 and 32, which is 8. Divide both the numerator and the denominator by 8 to get the simplest form 5/4.

To simplify the fraction 40/32, we need to find the greatest common divisor (GCD) of the numerator (40) and the denominator (32). The GCD is the largest number that can evenly divide both the numerator and the denominator.

Thus, 40/32 simplified is 5/4.

Answer:

.074 I believe

Step-by-step explanation:

1 meter = 1000 millimeters, so set an equal proportion. x / 72.74mm = 1m / 1000mm. Cross multiply to get 1000x = 72.74; divide both sides by 1000 to get x = 0.07274 m or if you're rounding, 0.07m

[tex]2\sqrt{10}[/tex]

1. Use Distance formula

Important to use distance formula in such problems, so keep this formula memorized for future use.

The formula to find distance amongst two points is

[tex]\sqrt{(x^2-x^1)^2 + (y^2 - y1)^2}[/tex]

2. Plug in the numbers into the formula:

1 -(-1)^2 + 3 - (-3)^2

[tex]2^2=4[/tex]

[tex]6^2 = 36[/tex]

36 + 4 = 40

3. Find the square root of 40.

[tex]\sqrt{40}[/tex]

Simplify further:

[tex]2\sqrt{10}[/tex]

The distance between two points (-1, -3) and (1, 3) in a 2-dimensional Cartesian system is √40 units or approximately 6.32 units.

The subject of this question relates to finding the distance between two points in a 2-dimensional Cartesian system. This can be done using the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. That is the square root of the sum of the squares of the differences of the x-coordinates and the y-coordinates of the two points respectively.

Here, we have points (-1, -3) and (1, 3). Substituting into the distance formula, we get:
d = √[(1--1)² + (3--3)²]
= √[(2)² + (6)²] = √[4 + 36] = √40
So the distance between the points (-1, -3) and (1, 3) is √40 units, which is approximately 6.32 units.

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Answer:

246.61 feet (rounded to 2 decimal places)

Step-by-step explanation:

We multiply 3/4 with previous minute traveling.

Minute #1: travels 75 feet

Minute #2: travels (3/4)*75 = 56.25 ft

Minute #3: travels (3/4)(56.25) = 42.19 ft

Minute #4: travels (3/4)(42.1875) = 31.64 ft

Minute #5: travels (3/4)(31.64) = 23.73 ft

Minute #6: travels (3/4)(23.73) = 17.80 ft

So, in 6 minutes, the car travels  75 + 56.25 + 42.19 + 31.64 +23.73 + 17.80 = 246.61 feet.

Answer:

C

Step-by-step explanation:

Substitute 2x into the equation where x is located. G(x)= (2x)^2=4x^2. This will be a graph which has been vertically stretched has a very steep curve to it facing up. It is C.

Answer:

C

Step-by-step explanation:

ANSWER

[tex]x = \frac{\pi}{6} \: or \: x = \frac{5\pi}{6} [/tex]

EXPLANATION

The given trigonometric equation is

[tex]4 \sin ^{2} x - 4 \sin(x) + 1 = 0[/tex]

This is a quadratic equation in sinx.

We split the middle term to obtain,

[tex]4 \sin ^{2} x - 2 \sin(x) - 2 \sin(x) + 1 = 0[/tex]

Factor by grouping to get,

[tex]2 \sin(x) (2 \sin(x) - 1) - 1(2 \sin(x) - 1) = 0[/tex]

This implies that,

[tex](2 \sin(x) - 1)(2 \sin(x) - 1) = 0[/tex]

[tex] \sin(x) = 0.5[/tex]

This gives us,

[tex]x = \frac{\pi}{6} [/tex]

in the first quadrant.

Or

[tex]x = \pi - \frac{\pi}{6} [/tex]

[tex]x = \frac{5\pi}{6} [/tex]

in the second quadrant.

Answer:

x = [tex]\frac{\pi}{6}[/tex], [tex]\frac{7\pi}{6}[/tex],  [tex]\frac{11\pi}{6}[/tex].

Step-by-step explanation:

The given equation is 4 sin²x - 4 sin x + 1 = 0

(2sinx)² - 2(2sinx) + 1 = 0

(2sinx - 1 )² = 0

Sinx = [tex]\frac{1}{2}[/tex] ⇒ x = sin⁻¹ ( [tex]\frac{1}{2}[/tex])

So between the interval [0, 2π] value of x will be  [tex]\frac{\pi}{6}[/tex],  [tex]\frac{7\pi}{6}[/tex],  [tex]\frac{11\pi}{6}[/tex]

[Since sine is positive in 1st 3rd and 4th quadrant]

So value of x will be x =  [tex]\frac{\pi}{6}[/tex], [tex]\frac{7\pi}{6}[/tex],  [tex]\frac{11\pi}{6}[/tex].

ANSWER

See below

EXPLANATION

To solve the triangle means to find all sides and angles.

The right triangle has an angle of 38 degrees and an opposite leg of 12 yards

The third angle is 90-38=52°

We use the sine ratio to find the hypotenuse, h.

[tex] \sin(38 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex] \sin(38 \degree) = \frac{12}{h} [/tex]

[tex]h = \frac{12}{ \sin(38) } [/tex]

[tex]h = 19.49[/tex]

The hypotenuse is 19.49 yards to the nearest hundredth.

We can find the adjacent leg using the cosine ratio.

[tex] \cos(38) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(38) = \frac{a}{19.49} [/tex]

[tex]a = 19.49 \cos(39) [/tex]

[tex]a = 15.36[/tex]

to the nearest hundredth.

Answer:

Option D

Step-by-step explanation:

we now that

The increase of the temperature is equal to the absolute value of the difference of the temperatures

Let

x-----> the increase of the temperature

[tex]x=\left|-8-23\right|=31\°F[/tex]

or

[tex]x=\left|23-(-8)\right|=31\°F[/tex]

The expression to represent the increase in temperature is 23 - (-8). To find the increase in temperature, we subtract the initial temperature (-8) from the final temperature (23).

The expression to represent the increase in temperature is 23 - (-8).

To find the increase in temperature, we subtract the initial temperature (-8) from the final temperature (23).

Therefore, the correct expression is 23 - (-8).

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Answer:

Second is the answer

Step-by-step explanation:

Slope = rise/run = y /x = m

Solve y to get y = mx

The slope of a line is rise over run, which would be Y over X.

The second answer is the correct one.

................. ...............

area of rectangle is 5800.

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

ΔABC:

A(2, 5), B(5, 5), C(5, 9)

[tex]AB=\sqrt{(5-2)^2+(5-5)^2}=\sqrt{3^2+0^2}=\sqrt{9+0}=\sqrt9=3\\\\AC=\sqrt{(5-2)^2+(9-5)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\\\\BC=\sqrt{(5-5)^2+(9-5)^2}=\sqrt{0^2+4^2}=\sqrt{0+16}=\sqrt{16}=4[/tex]

ΔDEF:

D(-7, 8), E(-4, 8), F(-4, 4)

[tex]DE=\sqrt{-4-(-7))^2+(8-8)^2}=\sqrt{3^2+0^2}=\sqrt{9+0}=\sqrt9=3\\\\DF=\sqrt{(-4-(-7))^2+(4-8)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\EF=\sqrt{(-4-(-4))^2+(4-8)^2}=\sqrt{0^2+(-4)^2}=\sqrt0+16}=\sqrt{16}=4[/tex]

AB ≅ DE

AC ≅ DF

BC ≅ EF

Therefore ΔABC ≅ ΔDEF

Answer:

168

Step-by-step explanation:

you would times 3.75 by 82 and subtract the answer from 2071.50 and get 1764 then divide 1764 by 10.50 and get 168

Answer:

168 adult adult ticket were sold

Step-by-step explanation:

Hello

The tickets cost for adults is     $10.50

The tickets cost for students is $3.75

number of adult ticket sold:       A

number of student  ticket sold:  B

10.50A+3.75B=2071.50     Equation 1

B=82                                   Equation 2

replacing equation 2 in equation 1

10.50A+3.75(82)=2071.50

10.50A=2071.50-307.50

[tex]A=\frac{1764}{10.50} \\\\A=168\\\\\\[/tex]

168 adult adult ticket were sold

Have a great day.

Answer:

I think Christina caught 23 fish and Sarah caught 8 fish.

Step-by-step explanation:

If I did this right, we have to find the equation to represent this situation. Christina caught one less than 3 times as many as Sarah caught. Since we do not know how many Sarah has, we have to use a variable so let's go with x. One less than 3 times as many would be 3x - 1 because one less means subtracting 1 and 3 times means multiply by three. So we have x for Sarah and 3x - 1 for Christina. We add those together to get x + 3x - 1 = 31 (since they caught 31 fish, the total would be 31). We simplify it down to 4x - 1 = 31. Add one to both sides to cancel it out and we get 4x = 32. Divide by 4 on both sides and we get x = 8. Since Sarah was x, Sarah caught 8 fish. To find Christina we just plug in the 8. 3(8) -1. 3 times 8 is 24 and 24 minus 1 is 23. To check our answers we add 8 and 23 together which comes out to be 31.

Please correct me if I'm wrong! (Now I'm not sure what you mean by a 5D table but if this is right I hope it helps)

The number of fish caught by Sarah = 8

And, The number of fish caught by Christina = 23

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Christina and Sarah went on a fishing trip and caught 31 fish.

Now,

Let number of fish caught by Sarah = x

So, The number of fish caught by Christina = 3x - 1

Here, Christina and Sarah went on a fishing trip and caught 31 fish.

Hence, We get;

⇒ x + (3x - 1) = 31

⇒ 4x - 1 = 31

⇒ 4x = 31 + 1

⇒ 4x = 32

⇒  x= 8

Thus, The number of fish caught by Sarah = x

                                                                  = 8

So, The number of fish caught by Christina = 3x - 1

                                                                   = 3×8 - 1

                                                                   = 23

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if this is some kind of riddle then i think its 5

The next term in the given sequence is 4

Given the sequence of values

93 27 14

The product of the two digits of each term will give the subsequent term. From the sequence given for instance;

93 = 9 * 3  = 27 (next term)

27 = 2 * 7 = 14 (3rd term)

For the next term;

14 = 1 * 4 = 4 (This will given the next term in the sequence)

Hence the next term in the sequence is 4

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Without additional context or a defined pattern, it's not possible to definitively determine the next number in the sequence 93, 27, 14. The sequence could potentially be arithmetic, geometric, quadratic, or even something more complex, but with only three terms provided, it's not possible to identify a clear pattern.

The given sequence in the question is 93, 27, 14. The solution to this sequence isn't immediately clear, as a standard mathematical pattern - such as addition, subtraction, multiplication, or division - doesn't seem to apply across all elements. Unfortunately, without additional context or a defined pattern to follow, it's not possible to definitively determine the next number in the sequence. Sequences can follow a vast array of potential patterns, including (but not limited to) geometric sequences, arithmetic sequences, quadratic sequences, or even patterns that incorporate elements of probability, set theory, or number theory.

For example, if we were looking for a simple arithmetic pattern in the given sequence, an initial glance might suggest that we are subtracting 66 and then 13 to find the second and third terms respectively. However, continuing this pattern does not result in a logical (-1) for the 'fourth' term in the sequence.

The sequence could also potentially be following a more intricate pattern - it could be geometric (each term multiplied or divided by a consistent number), quadratic (based on square or cube numbers), or even something more complex. However, with only three terms provided, it's not possible to identify a clear pattern of this nature.

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Answer:

12y-8

Step-by-step explanation:

so what you do is to distribute the 2 to both 6y and -4 so 2 times 6y is 12y and 2 times -4 equals -8

The equivalent expression for the given expression is 12y-8.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 2(6y-4)

= 12y-8

Therefore, the expression is equivalent to 2(6y-4)​ is 12y-8.

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The answer is 6

Explaination:

Step-by-step explanation:

(-)(-) = (+)(+) = (+)

(-)(+) = (+)(-) = (-)

13 + (-12) - (-5) = 13 - 12 + 5 = 1 + 5 = 6

Since [tex]T_n[/tex] is arithmetic, it's given recursively by

[tex]T_n=T_{n-1}+c[/tex]

where [tex]c[/tex] is a fixed number and [tex]T_1[/tex] is the starting term in the sequence. We have

[tex]T_n=T_{n-2}+2c[/tex]

[tex]T_n=T_{n-3}+3c[/tex]

and so on, so that

[tex]T_n=T_1+(n-1)c[/tex]

We're told that [tex]T_4=16[/tex], so

[tex]16=T_3+c[/tex]

and

[tex]T_5=16+c[/tex]

so that

[tex]T_3-T_5=(16-c)-(16+c)=-2c=6\implies c=-3[/tex]

Then the first term in the sequence is [tex]T_1[/tex]:

[tex]T_4=T_1+3(-3)\implies T_1=25[/tex]

and the sequence has general formula

[tex]T_n=25-3(n-1)\implies\boxed{T_n=28-3n}[/tex]

The first negative term occurs for

[tex]28-3n<0\implies28<3n\implies n>\dfrac{28}3[/tex]

[tex]\implies n=10[/tex]

The first negative term in the sequence is [tex]T_{10}=28-3\cdot10=\boxed{T_{10}=-2}[/tex].

6(2x-3)+4 = 16-(-18)

(6)(2x)+(6)(-3)+4 = 16+18

12+ -18+4 = 16+18

(12x)+(-18+4) = (16+18)

12x+ -14 = 34

12x-14 = 34

12x-14+14 = 34+14

12x = 48

12x/12 = 48/12

x = 4

Kyle was 1 minute and 47 seconds faster in a 3-mile race yesterday compared to his normal running time.

Kyle's normal time is 23 minutes and 25 seconds, which is (23 * 60) + 25 = 1405 seconds. Yesterday, Kyle's time was 21 minutes and 38 seconds, which is (21 * 60) + 38 = 1298 seconds.

Now, we subtract the faster time from the normal time: 1405 seconds - 1298 seconds = 107 seconds.

Thus, Kyle was 107 seconds faster yesterday than his normal time. To put it back into minutes and seconds, we divide by 60:  107  \ 60 = 1 minute and 47 seconds.

So, Kyle was 1 minute and 47 seconds faster yesterday.

We can solve for an acute angle in a right triangle if we know the other two angles. In the given hypothetical example, we assumed one angle was 30 degrees and the other was 90 (a right angle). We then subtracted these angles from 180 (the sum of all angles in a triangle) to find the acute angle NPO.

To solve for the acute angle NPO, we would typically need more specific information about the properties of the figure in question. However, let's suppose that triangle NPO is a right triangle and one of the given angles is 30 degrees. In this case, we can use the knowledge that the sum of all angles in a triangle equals 180 degrees.

Therefore, we set up an equation: 30 (degree of the given angle) + 90 (degree of the right angle) + X (angle NPO to be found) = 180. Solving for X gives us that NPO = 180 - 30 - 90 = 60 degrees.

Please remember that solving for an acute angle typically requires specific information about the figure and not all problems are as simple as this example demonstrates.

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A linear pair involves adjacent angles formed when two lines intersect. In this context, <NPO is 40°, and <SPR is 50°, adhering to the linear pair property.

A linear pair is formed when two lines intersect at a single point, creating two adjacent angles. If these angles align in a straight line, they constitute a linear pair, and the sum of their measures is always 180°. These angles are often termed supplementary or additional angles.

In the given scenario, angle <QPO is provided as 140°. According to the linear pair property, the angle <NPO supplementary to <QPO forms a straight line, and their sum equals 180°. Therefore, <NPO is calculated as 180° - 140°, resulting in <NPO being 40 degrees.

Moving on to the second part, three angles <SPN, <SPR, and <RPQ are considered. Applying the linear pair property, the sum of these angles is 180°. Given that <SPN is 90° and <RPQ is already known as 140°, the calculation involves finding <SPR. Thus, 90° + <SPR + 40° equals 180°. Solving for <SPR, it is determined to be 50 degrees.

In summary, for the provided angles:

a) <NPO is found to be 40 degrees.

b) <SPR is determined as 50 degrees through the linear pair property.

The question probable may be:

7.What is the measure of Angle NPO?

8.What is the measure of Angle SPR if the measure of Angle RPQ is 40°?