The sum of the digits of a two-digit number is 14. If the number formed by reversing the digits is less than the original number by 18. Find the original numbers.

Answer:

The value of 9f(3) is 1683.

Step-by-step explanation:

This is a compound function, so let's call it [tex]g[/tex], where it is equal to:

[tex]g = 9*f(3)[/tex]

To solve it, we need to find [tex]f(3)[/tex] and apply it on the expression above, this is done below:

[tex]f(3) = 4*(3)^3 + 8*(3)^2 - 2*3 + 13\\f(3) = 4*27 + 8*9 - 6 + 13\\f(3) = 108 + 72 + 7\\f(3) = 187\\[/tex]

Applying it on [tex]g[/tex] we have:

[tex]g = 9*187 =1683[/tex]

Answer:

1,863

Step-by-step explanation:

First thing to do here is to substitute 3 for the value of x

f(3) =4)3)^3 + 8(3)^2 -2(3) + 13

= 4(27) + 8(9) -6 + 13

= 108 + 72 + 7 = 207

we now multiply this result by 9

= 9 * 207 = 1,863

Answer:

[tex] = {b}^{3} [/tex]

Step-by-step explanation:

[tex] \: \: \: \: \: \: \: \frac{ {b}^{7} }{ {b}^{4} } \\ = {b}^{7 - 4} \\ = {b}^{3} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer: The answers are in the steps hope it helps.

Step-by-step explanation:

First solve or the equation and let it be in slope intercept form

y + 2 = 1/2( x + 2)   apply the distributive property first

y + 2= 1/2x + 1

    -2               -2

y= 1/2x -1      is not in slope intercept form so you could put  in any number for x and five y.

This are the points you could plot then draw a straight line between them.

x        y

0        -1

2         0

4          1

6          2

8           3

10          4

-2          -2

-4            -3

-6            -4

-8             -5

-10             -6

Answer:

[tex]7.040 \times {10}^{3} [/tex]

Step-by-step explanation:

First write this number like this

[tex]7.040[/tex]

Then,

[tex]7.040 \times {10}^{3} [/tex]

To check whether your answer is correct you can do like this

[tex]7.040 \times {10}^{3} [/tex]

[tex] {10}^{3} = 10 \times 10 \times 10 \\ \: \: \: \: \: \: \: \: \: \: = 1000[/tex]

[tex]7.040 \times 1000 \\ = 7040[/tex]

yes, your answer is correct.

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

7.809 g/cm^3

Step-by-step explanation:

Density is mass over volume so we need to find the mass and volume of the steel.

First we find the volume of the wood:

Vw = 9*6*6 = 324 cm^3

now we can find the mass of the wood, as mass = density * volume

mw = .68*324 = 220.32g

subtracting the mass of wood from total mass, we get the mass of steel

970-220.32 = 749.68g

now we can find the volume of the pyramid

Vs = 1/3 *6*6* (17-9) = 96 cm^3

Now we divide mass by volume to get density

749.68/96 = 7.809 g/cm^3

Confirming this with known data, density of steel is roughly between 7.75 and 8.05 g/cm^3 so we know we're correct.

Answer:

3

Step-by-step explanation:

15-12

This is 12 taken away from 15

00000000    _    000000

0000000            000000                    000

15 marbles     --    12 marbles  =     3 marbles  

Answer:

Problem 2) : the gradient is "-2", and the y-intercept is "3"

Problem 3)

A is  [tex]y=2x+2[/tex]

B is [tex]y=x+2[/tex]  

Step-by-step explanation:

Problem 2)

In the line given by the equation:   [tex]y=-2x+3[/tex]

the "gradient" (also known as "slope") is the numerical coefficient that multiplies the variable "x". So in this case the gradient is "-2"

the y-intercept is the numerical term "+3" because that is the y-value result of evaluating the expression for x = 0

[tex]y=-2x+3\\y=-2\,(0)+3\\y=3[/tex]

Problem 3)

Consider the two lines :

[tex]y=x+2[/tex]  and  [tex]y=2x+2[/tex]

notice that both have the same y-intercept (that is the numerical term "2" at the end of both expressions. That means that both lines cross the y-axis at the point y=2.

Now notice that the gradient of one of them is "1"  (for [tex]y=x+2[/tex] ) that is the coefficient that multiplies the variable "x". While for the other line ( [tex]y=2x+2[/tex])  the gradient is "2" and therefore steeper than the previous one.

Then, the line identified as "A" which is the one with steeper gradient, corresponds to the equation   [tex]y=2x+2[/tex], and the line identified with "B" is the one with smaller gradient  [tex]y=x+2[/tex]  .

Answer:

Step-by-step explanation:

Angles x and z are supplementary, meaning that they add up to 180.  From the markings on the diagram, angle z and the angle measuring 20 are complementary, meaning they add up to 90. So the game plan is to find out the measure of angle z first, then use that to find the measure of angle x.

angle z = 90 - 20 so

angle z = 70 degrees. And

angle z + angle x = 180.  Subbing in our value for z:

70 + angle x = 180 and

angle x = 180 - 70 so

angle x = 110 degrees

Answer:

8 ejercicios

Step-by-step explanation:

De acuerdo a la información dada, puedes plantear las siguientes ecuaciones:

x+y= 45 (1)

7x-1y= 19 (2)

x= ejercicios que resolvió bien

y= ejercicios que resolvió mal

Primero, puedes despejar x en (1):

x= 45-y (3)

Segundo, debes reemplazar (3) en (2):

7(45-y)-1y=19

315-7y-1y= 19

315-8y= 19

315-19= 8y

296= 8y

y= 296/8

y= 37

Tercero, debes reemplazar el valor de y en (3) para encontrar x:

x= 45-37

x= 8

De acuerdo a esto, la respuesta es que el hijo ha resuelto bien 8 ejercicios.

Answer:

28

Step-by-step explanation:

x = 2 point questions, y = 3 point questions

x + y = 40

2x + 3y = 92

Solving this we get x = 28, y = 12 so the answer is 28.

Answer: 28

Step-by-step explanation:

Let x be the number of 2 mark questions

Let y be the number of 3 mark questions

x+y=40. ---------------(1)

2x+3y=92 ---------------(2)

Solve equation (1) for y

y=40−x

Substitute

y=40−x in equation (2)

2x+3(40−x)=92

2x+120−3x=92

2x−3x=92−120

−x=−28

x=28

Substitute

x=28 in equation (1)

28+y=40

y=40−28=12

Number of 2 mark questions

=28

Number of 3 mark questions

=12

<AED

Explanation:

B is the mid point of AD.( since AB=BD)

C is the mid point of AB( since AC=BC)

Therefore BC is parallel to DE.

Angle ACB= Angle AEB

Corresponding angles are equal.

And hence, they are congruent.

Hope it helps

Good luck on your assignment

The angle congruent to ∠ACB is B. ∠AED.

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

Congruent Angles have the same angle (in degrees or radians).

Now from the given figure,

In triangle  ABC and triangle AED

AC = CB

BC is parallel to DE

Thus, by law of congruent angles, interior angles are equal,

Thus, ∠ACB = ∠AED

this is the required congruent angle of ∠ACB.

Thus, the angle congruent to ∠ACB is B. ∠AED.

To learn more about congruent angles:

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Answer:

Option (2).

Step-by-step explanation:

This question is incomplete; here is the complete question and find the figure attached.

In the diagram of a circle O, what is the measure of ∠ABC?

27°

54°

108°

120°

m(minor arc [tex]\widehat {AC}[/tex]) = 126°

m(major arc [tex]\widehat {AC}[/tex]) = 234°

By the intersecting tangents theorem,

If the two tangents of a circle intersect each other outside the circle, measure of angle formed between them is half the difference of the measures of the intercepted arcs.

m∠ABC = [tex]\frac{1}{2}[m(\text {major arc{AC})}-m(\text{minor arc} {AC})][/tex]

             = [tex]\frac{1}{2}(234-126)[/tex]

             = 54°

Therefore, Option (2) will be the answer.

Answer:

B.

Step-by-step explanation:

Answer:

Ratio = 4 : 15 or

[tex] \frac{4}{15} [/tex]

Step-by-step explanation:

Here letters from I to W are written on a separate index card.

I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W

Counting the letters, they are 15 in number.

To find the probability that a letter in the word MILK will be selected on first try, we'll get the following:

Possible event / total number

Since the word MILK contains 4 letters, the probability =

[tex] \frac{4}{15} [/tex]

Therefore, ratio that represents the probability that a letter in the word MILK will be selected on the first try is 4 : 15

Answer:

222x + 888 = 303030

Step-by-step explanation:

If he raises the amount of push-ups he does by 222, then we can put the x with it, which represents the number of days. Since we are adding onto the 888 a day we can put that without the variable. If you were to solve this equation you would get the amount of days it would take to reach 303030 push-ups a day.

Hope this helps!

Answer:

8+2x=30

Step-by-step explanation:

did it on khan its correct

Answer:

Simplified Expression a ) 2n^2 + 7n - 5,

Simplified Expression b ) 8n^2 - 11n - 10,

When n = 3 part a ) 34,

When n = 2 part a ) 17,

When n = 3 part b ) 29,

When n = 2 part a ) 0

Step-by-step explanation:

Consider the " simplification " process at hand;

[tex]a ) (5n^2 + 3n -4) + (-3n^2 + 4n -1),\\5n^2+3n-4-3n^2+4n-1,\\5n^2-3n^2+3n+4n-4-1,\\\\Simplified Expression = 2n^2+7n-5[/tex]

[tex]b ) (7n^2 - 5n - 2) - (-n^2 + 6n + 8),\\7n^2-5n-2+n^2-6n-8,\\\\Simplified Expression = 8n^2-11n-10[/tex]

For each part ( a and b ) I removed the ( ) and grouped like elements to receive the simplified expression;

Value of each polonomial;

[tex]a ) 2n^2 + 7n - 5,\\2 * ( 3 )^2 + 7 * ( 3 ) - 5,\\34\\\\2 * ( 2 )^2 + 7 * ( 2 ) - 5\\17[/tex]

[tex]b ) 8n^2 - 11n - 10,\\8 * ( 3 )^2 - 11 * ( 3 ) - 10,\\29\\\\8 * ( 2 )^2 - 11 * ( 2 ) - 10,\\0[/tex]

Each expression was solved through substitution and algebra.

" Simplified " Solution - See in answer above

* I hope the answer wasn't too confusing, for further information look through my response thoroughly

Answer:

Linear Function

Step-by-step explanation:

8x-3y = -2

-3y = 8x-2

3y = -8x+2

y = [tex]\frac{-8x+2}{3}[/tex]

y = [tex]-\frac{8}{3}x+\frac{2}{3}[/tex]

Linear Function

Answer:

13 = 15(x) - 23

x = 12/5 or 2 2/5

Answer:

(x+3)(x-3)

Step-by-step explanation:

It is a difference of squares so it is sqrt of x^2 gives x and sqrt of 9 gives +3, -3.  So we get (x+3)(x-3).

Answer:

[tex]\angle I = 21.6 ^\circ[/tex] is the correct answer.

Step-by-step explanation:

Please refer to the attached figure.

[tex]\triangle IJK[/tex] is shown with the following measurements:

[tex]\angle K = 90^\circ[/tex]

Side KI = 5.3 ft

Side JK = 2.1 ft

To find : [tex]\angle I[/tex] = ?

Using trigonometric identity for tangent of an angle:

[tex]tan\theta = \dfrac{\text{Perpendicular}}{\text{Base}}[/tex]

Here [tex]\theta = \angle I[/tex]

Perpendicular is side JK.

Base is side KI.

Putting the values in above formula:

[tex]tan\theta = \dfrac{\text{JK}}{\text{KI}}\\\Rightarrow tan\theta = \dfrac{2.1}{5.3}\\\Rightarrow tan\theta = 0.3962\\\Rightarrow \theta = 21.6^\circ[/tex]

Hence, [tex]\angle I = 21.6 ^\circ[/tex] is the correct answer.

Answer:

0< h ≤ 15

Step-by-step explanation:

A = 1/2 * base * height = 1/2*16*h = 8h

A no more is ≤.

A ≤ 120

8h ≤ 120

h ≤ 15

0< h ≤ 15

Height should be  more than 0 feet and no more than 15 feet.

The required volume of the rectangular prism is 765792 cubic centimeters. None of the options are correct.

To find the volume of a rectangular prism, you can use the formula:

Volume = length (l) * width (w) * height (h)

Given:

l = 412 cm

w = 312 cm

h = 6 cm

Volume = 412 cm * 312 cm * 6 cm
Volume = 128544 * 6 cubic centimeters
Volume = 771264 cubic centimeters

Thus, the volume of the given rectangular prism is 771264 cubic centimeters.

Learn more about volume here:

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Answer:

-2/3

Step-by-step explanation:

Perpendicular slopes have lines that multiply to -1

m* 3/2 = -1

Multiply each side by 2/3

m* 3/2 * 2/3 = -1 * 2/3

m = -2/3

The slope of the perpendicular line is -2/3

Answer:

The answer is B

I use an online graphing calculator called Desmos. You should check it out some time :)

Answer:

x=6

Step-by-step explanation:

Because of the Pythagorean theorem, you know that the square of the two legs of a right triangle will be equal to the square of the hypotenuse. Conversely, the square of one of the legs will be equal to the square of the other leg subtracted from the square of the hypotenuse. Therefore:

[tex]x^2=10^2-8^2 \\\\x^2=100-64\\\\x^2=36\\\\x=6[/tex]

Hope this helps!

Answer:

6

Step-by-step explanation:

By Pythagoras theorem

10^2 = 8^2 + x^2

100= 64 + x^2

X^2 =100-64

X^2= 36

[tex]x = \sqrt{36} \\ x = 6[/tex]

Hope this helps..

Answer:Box A contains 13.75 cubic feet more space than Box B. I just took the test. hope this helps ;)

Step-by-step explanation:

Answer:

1) 275

2)60

Step-by-step explanation:

1) 55 x 5 =275

2) 12 x 5 = 60

Hope it helps!

Answer:

2 vans and 7 busses

Step-by-step explanation:

Let x=# of busses

Let y=# of vans

55x+12y=409

x=y+5

55(y+5)+12y=409

55y+275+12y=409

67y+275=409

134=67y

y=2

There were two vans, and y+5 (7) busses

Answer:

C) 13

Step-by-step explanation:

f(x) = 5x -2

f(3) = 5(3) -2

f(3) = 15 - 2

f(3l) = 13

Answer:

Section A

Volume of the cylindrical tool = 1413.72cm³

Section B

1) Curved Surface Area of the right circular cone = 251.33cm²

2) Volume of the right circular cone = 402.12cm³

Step-by-step explanation:

Section A

We are asked to find the volume of the cylindrical moulding tool.

Volume of a cylinder = πr²h

From the question, the cylindrical tool had a diameter of 10cm. This means the radius of the tool = Diameter ÷ 2 = 10cm ÷ 2 = 5cm

The height of the cylindrical tool = 18cm

Volume of the cylindrical tool = π × (5cm)² × 18cm

1413.7166941cm³

Approximately = 1413.72cm³

Section B

The height of a right circular cone is 6cm and its radius is 8cm.

1) Calculate its curved surface area.

The formula for the curved surface area of a right circular cone =

πrl

r = radius = 8cm

h = height = 6cm

l = √(r² +h²) = √(8² + 6²) = √100

l = 10cm

The curved surface area = πrl

= π × 8cm × 10cm

= 251.33cm²

2) Calculate the volume of the cone.

The formula for the volume of a cone=

1/3πr²h

radius (r) = 8cm

height (h) = 6cm

1/3πr²h

1/3 × π × 8² × 6

= 402.12cm³

Answer: £2598.80

Step-by-step explanation:

Let those under 16 be x

Those over 16 be y

49 + y = 155

y = 155-49

y = 106 = over 16

for over 16, y * 18.60

= 106 * 18.60 = 1971.60

For under 16, x * 12.80

= 49 * 12.80 = 627.20

Answer:

(-3.5,2.5)

Step-by-step explanation:

[tex]m=\left( \dfrac{-6+-1}{2},\dfrac{-2+5}{2} \right)=\left( \dfrac{-7}{2},\dfrac{3}{2}\right)=\left( -3.5,2.5 \right)[/tex]

Hope this helps!