Let f (x) = x – 4 and g(x) = 6 - x
Evaluate g(f(10)).

x = 21

y = 8

=========================================================

Explanation:

Since the y is giving you trouble, I recommend ignoring it for now. Luckily we don't need the y value at first.

Let's solve for x.

The two angles (10x-61) and (x+10) form a straight angle which is 180 degrees.

So,

(10x-61) + (x+10) = 180

10x-61 + x+10 = 180

11x - 51 = 180

11x-51+51 = 180+51 .... adding 51 to both sides

11x = 231

11x/11 = 231/11 .... dividing both sides by 11

x = 21

Since x = 21, the upper right angle (10x-61) is equal to

10x-61 = 10*21-61 = 210-61 = 149

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We can now focus on the (18y+5) angle. This is set equal to 149 since vertical angles are congruent

18y+5 = 149

18y+5-5 = 149-5 ... subtracting 5 from both sides

18y = 144

18y/18 = 144/18 .... dividing both sides by 18

y = 8

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Or we could add the angles (18y+5) and (x+10), set them equal to 180, and solve for y like that

(18y+5)+(x+10) = 180

18y+5 + x+10 = 180

18y+5+21+10 = 180 .... plug in x = 21

18y+36 = 180

18y+36-36 = 180-36 ... subtract 36 from both sides

18y = 144

18y/18 = 144/18 .... dividing both sides by 18

y = 8

We get the same result.

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

As a check, plugging y = 8 into 18y+5 should lead to 149

18y+5 = 18*8+5 = 144+5 = 149

This confirms the y value answer

Answer:

a21 = -61

Step-by-step explanation:

[tex]a_{n}=a_{1}+(n-1)d[/tex]

[tex]-19=a_{1}+(7-1)d[/tex]

[tex]-28=a_{1}+(10-1)d[/tex] (subtract to eliminate a₁)

9 = -3d

d = -3

-19 = a₁ + (6)(-3)

-1 = a

a21 = -1 + (21 - 1)(-3)

= -61

Answer:

-61 (Answer D)

Step-by-step explanation:

The general formula for an arithmetic sequence with common difference d and first term a(1) is

a(n) = a(1) + d(n - 1)

Therefore, a(7) = -19 = a(1) + d(7 - 1), or a(7) = a(1) + d(6) = -19

and a(10) = a(1) + d(10 - 1) = -28, or a(1) + d(10 - 1) = -28

Solving the first equation a(1) + d(6) = -19 for a(1) yields a(1) = -19 - 6d.  We substitute this result for a(1) in the second equation:

-19 - 6d + 9d = -28.  Grouping like terms together, we get:

3d = -9, and so d = -3.

Going back to an earlier result:  a(1) = -19 - 6d.

Here, a(1) = -19 - 6(-3), or a(1) = -1.

Then the formula specifically for this case is a(n) = -1 - 3(n - 1)

and so a(21) = -1 - 3(20) = -61 (Answer D)

Answer:

a. 126 pie cm^3

Step-by-step explanation:

Area of a circle = pi*r²

Volume = area*height

(pi*r²)*14

Since your answers are with Pi omit the Pi and times 3² * 14 = 126 pie cm³

Answer:

A. 126pi cm^3

Step-by-step explanation:

The volume of a cylinder can be found using the following formula.

[tex]v=\pi r^2 h[/tex]

First, we must find the radius. The radius is half of the diameter.

[tex]r=\frac{d}{2}[/tex]

The diameter of the cylinder is 6 cm.

[tex]r=\frac{6cm}{2}[/tex]

[tex]r= 3cm[/tex]

The radius is 3 cm.

Now, we can substitute values into the formula.

[tex]v=\pi r^2 h[/tex]

[tex]r= 3cm\\h=14 cm[/tex]

[tex]v=\pi (3cm)^2*14 cm[/tex]

Evaluate the exponent.

[tex](3cm)^2=3cm*3cm=9cm^2[/tex]

[tex]v=\pi*9cm^2*14cm[/tex]

Multiply 9 cm^2 and 14 cm

[tex]9 cm^2*14cm=126cm^3[/tex]

[tex]v=\pi*126cm^3[/tex]

The answer choices are in terms of pi, so we can simply rearrange our answer:

[tex]v=126\pi cm^3[/tex]

The volume of the cylinder is 126pi cubic centimeters and A is the correct answer.

The table represents a function because each input (x-value) corresponds to exactly one output (y-value)

If we had repeated x values, then that is a sign we don't have a function. So for instance, if we had the two points (1,5) and (1,6) then we don't have a function because the input x = 1 corresponds to outputs y = 5 and y = 6 simultaneously.

Note: the y values are allowed to repeat and we still have a function, but this function is not one-to-one because of the repeated value y = 2.

Answer:

No idea dude

Step-by-step explanation:

I just need points

Answer:

C D E

Step-by-step explanation:

Edg

Out of the given options, options C, D and E are a difference of squares.

Difference of Squares, two terms that are squared and separated by a subtraction sign.

Given are, options,

D) (y squared minus x y)(y squared + x y) = (y²-xy)(y²+xy) = y⁴-(xy)²

E) (64 y squared + x squared)(negative x squared + 64 y squared) = (64y²+x²)(64y²-x²) = (64y)⁴-x⁴

C) (3 + x z)(negative 3 + x z) = (3+xz)(3-xz) = 3²-(xz)²

Hence, out of the given options, options C, D and E are a difference of squares.

For more references on difference of squares, click;

https://brainly.com/question/11801811

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Answer: The required ratio is PT:TR  = 1:2.

Step-by-step explanation:

Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².

To find : PT:TR

.i.e. Ratio of PT to TR.

Here, PT:TR[tex]=\dfrac{PT}{TR}[/tex]

[tex]=\dfrac{4\ cm}{8\ cm}[/tex]

Divide numerator and denominator by 4 , we get

[tex]\dfrac{1}{2}[/tex]

Therefore, the required ratio is PT:TR  = 1:2.

Answer: 400

Explanation: To round 372 to the nearest hundred, we first find the digit in the rounding place which in this case is the 3 in the hundreds place.

To decide whether to round up or down, we look

at the digit to the right of the 3, which is 7.

According to the rules of rounding, if the digit to the right of the

rounding place is greater than or equal to 5, we round up.

So in this problem, since 7 is greater than or equal to 5, we round up.

This means that we add 1 to the 3 in the rounding place

to get 4 and all digits to the right of 4 become 0.

So 372 rounded to the nearest hundred is 400.

Answer: 104,805

Step-by-step explanation:

just add

Answer:

104,805

Step-by-step explanation:

add it in each placement form

Answer:

x= 4                x = -5

Step-by-step explanation:

3(x – 4)(x + 5) = 0

Using the zero product property

(x – 4)=0      (x + 5) = 0

x= 4                x = -5

What are the solutions to the equation 3(x – 4)(x + 5) = 0?

x = –4 or x = 5

x = 3, x = 4, or x = –5

x = 3, x = –4, or x = 5

x = 4 or x = –5

Answer:

D. x = 4 or x = –5

Step-by-step explanation:

Answer:

12.57

Step-by-step explanation:

The formula to solve the circumference of a circle is:

2 x PI x R (radius)

=> 2 x PI x 2

=> 4 PI or 12.57

Answer:

7000 (7 thousand)

700 (7 hundred)

20 (2 tens)

2 (2 units)

Step-by-step explanation:

what is the relationship between the values of the given digits?

1. The 7s in 7,700

2. The 2's in 522

From the knowledge of place values;

7,700 could be broken down thus :

7000 + 700 + 0 + 0

The first 7 depicts thousands as it has 3 trailing digits (7000)

The second 7 depicts hundred as it has 2 trailing digits (700)

522 could be broken down thus :

500 + 20 + 2

From 522

The first '2' has one trailing digit = tens

The ending / last digit ia always = Unit value

Answer:

f(x) = 4x² + 48x + 149

Step-by-step explanation:

f(x) = 4(x + 6)² + 5

The above expression can be written as: f(x) = ax² + bx + c, by doing the following:

1. Expand (x + 6)²

(x + 6)² = (x + 6)(x + 6)

(x + 6)(x + 6)

x(x + 6) + 6(x +6)

x² + 6x + 6x + 36

x² + 12x + 36

(x + 6)² = x² + 12x + 36

2. Substitute x² + 12x + 36 for (x + 6)² in

f(x) = 4(x + 6)² + 5

This is illustrated below:

f(x) = 4(x + 6)² + 5

(x + 6)² = x² + 12x + 36

f(x) = 4(x² + 12x + 36) + 5

Clear bracket

f(x) = 4x² + 48x + 144 + 5

f(x) = 4x² + 48x + 149

Therefore, the standard of the function:

f(x) = 4(x + 6)² + 5

is

f(x) = 4x² + 48x + 149

Answer:

[tex]W(t)=5(2^t)[/tex]

Step-by-step explanation:

Given that the Newly planted seedlings approximately double their weight every week and a seedling weighing 5 grams is planted at time t = 0 weeks. This represent an exponential function with an equation in the form:

[tex]W(t)=ab^t[/tex].

W(t) is the weight in t weeks, t is the weeks and a is the weight when t = 0. At t = 0, W = 5 g:

[tex]W(t)=ab^t\\W(0)=ab^0\\5=ab^0\\a=5[/tex]

Since the weight double every week, b = 2. The exponential function is given as:

[tex]W(t)=ab^t\\\\W(t)=5(2^t)[/tex]

Answer:

120°

Step-by-step explanation:

We can see that b=a by opposite exteriors.

So a+1/2a=180

1.5a=180

a=180/1.5=120

And since b and a are equal, b also equals 120°

Answer:

2(x-5)

Step-by-step explanation:

Answer:

the answer to your question is 5xa^2

or you can use symbolab calculator online

Answer:

x= 6 degrees

Step-by-step explanation:

x+x+54 = 90

2x+54 = 90

x= 90- 54 /2

x =6

Answer:

x = 6

Step-by-step explanation:

90 - 54 = 36

x + 5x = 6x

36 + 6x = 90

90 - 36 = 6x

36/6x = 6

x = 6

Answer:

y = 32,000(1.08)^x

Step-by-step explanation:

The exponential growth equation is y = a(1 + r)^x, where a is the initial amount, r is rate as a decimal, and x is the time.

In this situation, 32,000 is the initial amount (a) and 0.08 is the rate (r)

If we plug these into the equation, we get the equation y = 32,000(1.08)^x

So, y = 32,000(1.08)^x is the correct answer.

Answer:

A

Step-by-step explanation:

on edge 2020

Answer:

a) 55 degrees

b) 350 ft.

Step-by-step explanation:

a- the sum of angles of triangle=180

( since it is right angle , one angle is 90 degrees), x be the acute angle

x+35+90=180

x=180-125

x=55 degrees

b) tan 35= height of a tree/ length of a shadow

height of a tree=tan35*500=350.103≅350 ft ( rounded to nearest tens)

c)  hypotenuse²=350.1²+500²

c=√350.1²+500²

c=610.385 ft

d) no because the distance is more than 500

Answer:

Composition and vertical translation must be done in the parent function.

Step-by-step explanation:

Let be [tex]j(x)[/tex] the parent function, if [tex]g(x) = j(4\cdot x) -27[/tex], then two transformation must be done in the following order:

Composition

[tex]j \circ h (x) \rightarrow j(h(x))[/tex], where [tex]h(x) = 4\cdot x[/tex]

Vertical translation

[tex]g(x) = j(4\cdot x) -27[/tex]

Composition and vertical translation must be done in the parent function.

Answer: Option D

Horizontal compression by a factor of 1/4, and a translation 27 units down

Answer:

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos es de $13.90

Step-by-step explanation:

La información dada son;

El valor de la máscara = $ 1.25

El valor del paquete de jabones = $ 2.00

El valor del gel de alcohol = $ 3.00

La cantidad que le quedaba después de pagar = $ 7.65

Por lo tanto, tenemos;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = La cantidad que le quedaba después de pagar + El valor del gel de alcohol + El valor del paquete de jabones + El valor de la mascarilla

Por lo tanto;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = $ 7.65 + $ 3.00 + $ 2.00 + $ 1.25 = $ 13.90.

Answer:

h = (x - 8)/5

Step-by-step explanation:

Step 1: Write out expression

x = 5h + 8

Step 2: Isolate variable h (Subtract 8 on both sides)

x - 8 = 5h

Step 3: Isolate h (Divide both sides by 5)

(x - 8)/5 = h

Step 4: Rewrite

h = (x - 8)/5

Answer:

approaching negative infinity

Step-by-step explanation:

Since as x increases, the values of f(x) are approaching infinity, the function approaches negative infinity as the end behavior.

Answer:

Below.

Step-step-explanation:

As x increases from negative infinity f(x) decreases in value .

As x increases to positive infinity f(x) decreases in value.

For values of x  on the negative side  the graph rises  to the left and on the positive x -axis it falls to the right.

Answer:

Step-by-step explanation:

Cost price of three machines with repairment charge ( CP ) = 5400 × 3 + 4000

= Rs 20200

Selling price of 1 machine = Rs 7000

Selling price of 3 machines ( S.P )= Rs 7000 × 3

= Rs 21000

Since , SP > CP , he made a profit

Profit = SP - CP

= Rs 21000 - Rs 20200

= Rs 800

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

Further more explanation

Profit and loss

In any business , owners have intension to have profit by selling articles. The price at which an article is purchased is called it's Cost price ( C.P ) and the price at which it is sold is called Selling price ( S.P ).

If the selling price is less than cost price of an article then there is a loss.

[tex] \mathrm{Loss \: = \: Cost \: Price \: (C.P) - Selling \: Price \: (S.P)}[/tex]

If the selling price is more than cost price of an article then there is a profit ( gain )

[tex] \mathrm{Profit = Selling \: Price \: (S.P) - Cost \: Price \: (C.P)}[/tex]

So, If S.P > C.P, there is profit in dealing.

If C.P > SP , there is loss in dealing.

Hope I helped!

Best regards!!

Answer:

176m²

Step-by-step explanation:

When we are asked to find the outer surface area of a geometric shape, it means to find the Lateral or Curved Surface Area of the shape. We are given two shapes above.

Step 1

Find the Outer surface area of the cone

Outer / Lateral surface area of a cone =

πrl

Where l = √r² + h²

r = 4 m

h = 3m

Outer surface area = 22/7 ×√4² + 3²

= 22/7 × √16 + 9

= 22/7 × √25

= 22/7 × 5

= 62.83185m²

Step 2

Find the outer surface area of a cylinder

= 2πrh

π = 22/7

r = 4m

h = 4.5

π = 22/7

Outer surface area of a cylinder = 2 × 22/7 × 4 × 4.5

= 113.09734m²

Step 3

The Outer Surface Area of the Tent = Outer Surface Area of the cone + Outer Surface Area of the cylinder

= 62.83185m² + 113.09734m²

= 175.92919m²

Approximately ≈ 176m²

Therefore, the outer surface area of the tent = 176m²

Answer:

see below

Step-by-step explanation:

cos ( x+pi/2) = -sinx

We know that

cos(A + B) = cos A cos B - sin A sin B

Let x = A and pi/2 = B

cos x cos pi/2 - sin x sin pi/2 = -sin x

We know cos pi/2 = 0  and sin pi/2 = 1

cos x * 0 - sin x *1 = -sin x

- sin x = - sin x

Answer:

the answer is c.

Step-by-step explanation:

c is the only reasonable option.

Answer:

2.5 Yards

Step-by-step explanation:

Multiply 5/8 by 4

Answer:

Any one of these three works:

plane MOU

plane MNU

plane NOU

Step-by-step explanation:

A plane can be named by a single letter, such as L in this problem, or by any three non-collinear points that lie on the plane. Non-collinear points are points that do not all lie in a single line.

Points M, N, O, and U lie on plane L, so you can choose any 3 of the 4 points to name the plane with, but make sure all 3 points are non-collinear.

To name plane L with points, you cannot use points MNO together since they are collinear, but you can name it using point U plus any two of the points M, N, and O.

plane L can be named

plane MOU

plane MNU

plane NOU

Do not name it plane MNO

Answer:

The critical value of F for this situation is 2.975.

Step-by-step explanation:

A test is being performed to determine if a particular drug, smartozine, affects maze learning in rats.

The groups are divided as follows:

So, there were in total k = 4 groups with n = 30 rats.

The significance level of the test is, α = 0.05.

Compute the critical value of F as follows:

[tex]F_{\alpha, (k-1, n-k)}=F_{0.05, (4-1, 30-4)}=F_{0.05, (3,26)}=2.975[/tex]

*Use the F-table.

Thus, the critical value of F for this situation is 2.975.

The critical value of F for this situation has been 2.975.

The F value has been the statistical factor that has been used for the determination of the significance of the test.

The high F value has been the representation of the rejected null hypothesis, while the low  F value represents the accepted hypothesis. The study that has been performed with the rats has:

Number of groups of rats = k = 4

Total number of rats = n = 30

The 0.05 significance test has been performed, thus the value of α has been 0.05.

The value of F can be given as:

Critical value = [tex]\rm F_\alpha_\;_,(_k_-_1,_n_-_k_)[/tex]

Substituting the values:

Critical value = [tex]\rm F_0._0_5,_(_4_-_1,_3_0_-_4_)[/tex]

Critical value = 2.975

Thus, the critical value of F for this situation has been 2.975.

For more information about the F value, refer to the link:

https://brainly.com/question/11566053

Answer:

The systems of equation for the amount spent are as follows

[tex]Y= 0.99x+5[/tex]

[tex]Y= 0.79x+10[/tex]

Step-by-step explanation:

In this problem we are expect to give a model or an equation that represents the amount of money spent per month given a fix subscription amount and a variable fee which is based on extra minutes spent.

let Y represent the amount of money spent in total for the month

The first case:

Subscription =$5

charges per minutes = $0.99

therefore the amount spent can be modeled as

[tex]Y= 0.99x+5[/tex]

The second case:

Subscription =$10

charges per minutes = $0.79

therefore the amount spent can be modeled as

[tex]Y= 0.79x+10[/tex]