Write an algebraic expression for each verbal expression. 1.One third of a number is twelve less than the number itself 2. Two times the sum of a number and five is twenty

Answers

Answer 1

Answer:

1. ⅓*m = m - 12

2. 2(a + 5) = 20

Step-by-step explanation:

1. Let the number be represented by m

Let one-third of the number m, be ⅓*m

If there is 12 less of an amount of something, it implies 12 is to be subtracted from the initial amount.

Thus, 12 less than the number, m is (m - 12)

》⅓*m = m - 12

2. Let the number be represented by a

The sum of the number and 5 is (a+5)

》2(a+5) = 20


Related Questions

If the outliers are not included what is the mean of the data set 76,79,80,82,50,78,79,81,82

Answers

Answer:

The answer is 80

Step-by-step explanation:

we know that

the outlier is 50, as it is not around the other numbers in the data set.

therefore

mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9

mean=[720]/9

mean=80

Answer:

80

Step-by-step explanation:

mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9

mean=[720]/9

mean=80

Find the measure of arc BC?

Answers

Answer:

129

Step-by-step explanation:

Since,

AD = BC

AD = 3x + 24

BC = 4x - 11

3x + 24 = 4x - 11

4x - 11 = 3x + 24

4x - 3x = 24 + 11

x = 35

BC = 4x - 11

= 4 ( 35 ) - 11

= 140 - 11

BC = 129

Answer:

[tex]AB=BC[/tex]

[tex]3x+24=4x-11[/tex]

[tex]3x-4x=-11-24[/tex]

[tex]x=35[/tex]

[tex]BC=4\times 35-1[/tex]

[tex]=140-11[/tex]

[tex]=129[/tex]

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

Hope it helps..

Have a great day!!

What is the equation of the graph ? ILL pay

Answers

Answer:

Step-by-step explanation:

You have it right it is 6^x -3

You have the right idea, but you don't need to type in the "y=" portion since that is already taken care of. So you just need to type in -3 + 6^x

Someone, please help me on this one

Answers

Answer:

D

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 4x² + 7x - 3 + 6x³ - 7x² - 5 ← collect like terms

= 6x³ - 3x² + 7x - 8

Answer:

D. (f + g )( x ) = 6x³ - 3x² + 7x - 8

Step-by-step explanation:

Given :-

f ( x ) = 4x² + 7x - 3.g ( x ) = 6x³ - 7x² - 5.

To Find :-

( f + g ) ( x ).

Solution :-

(f + g )( x ) = 4x² + 7x - 3 + 6x³ - 7x² - 5.

Arranging like terms.

(f + g )( x ) = 6x³ - 7x² + 4x² + 7x -5 - 3

Combine like terms.

(f + g )( x ) = 6x³ - 3x² + 7x - 8

f(x) = -22 – 14
Find f(9)

Answers

Answer:

-4

Step-by-step explanation:

f(9)=-22-14

f(9)=-36

f multiplied by 9divide by 9=-36divide by 9

f=-4

2z^8- 32z^8
Help plz

Answers

Answer:

-30z^8

Step-by-step explanation:

[tex]2 {z}^{8} - 32 {z }^{8} \\ = - 30 {z}^{8} [/tex]

Answer:

-30z^8

Step-by-step explanation:

2z^8- 32z^8

-30z^8

3 of 9
Express the ratio below in its simplest form.
2:4:2

Answers

Answer:

1 : 2 : 1

Step-by-step explanation:

2:4:2

Divide each  term by 2

2/2:4/2:2/2

1 : 2 : 1

Please helppppp!!!!!!!!

Answers

Answer:

128 cm^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h

where b1 and b2 are the lengths of the bases and h is the height

A =1/2( 10+22) * 8

A = 1/2 (32)8

  = 128

Answer:

A=128 cm²

Step-by-step explanation:

Hi there!

We are given a trapezoid and we want to find the area of it

The area of a trapezoid is given as [tex]\frac{a+b}{2}h[/tex], where a and b are the bases and h is the height

The bases are the parallel sides

They are the sides marked as 10 cm and 22 cm in this case

The height is the distance between the bases

In this case, it is the side marked as 8 cm

We know everything needed for the area, let's just label everything to avoid any confusion

a=10

b=22

h=8

Now substitute into the formula

A=[tex]\frac{a+b}{2}h[/tex]

A=[tex]\frac{10+22}{2}*8[/tex]

add the numbers on the numerator together

A=[tex]\frac{32}{2}*8[/tex]

Divide 32 by 2

A=16*8

multiply

A=128 cm²

Hope this helps!

F(x) = 6x+2, find f (x+3)

Answers

Answer:

6x+20

Step-by-step explanation:

F(x) = 6x+2

f(x+3) means replace x with x+3

F(x+3) = 6(x+3)+2

         = 6x+18+2

         = 6x+20

Answer:

A; F(x+3) = 6x^2 + 20x + 6

Step-by-step explanation:

To find it you just would multiply F(x) onto the other side. So it would look like this:

           F(x+3) = 6x + 2 (x+3)            

          F(x+3) = 6x^2 + 2x + 18x + 6            *combine like terms getting you

           F(x+3) = 6x^2 + 20x + 6    

Hope this helped!!

look at photo! please help needed! 1.

Answers

Answer:

5/12

Step-by-step explanation:

it says in the question that 1/4 +1/3 is used so in order to make it simple we have to find the common denominator that is 12. so converting 1/4 is 3/12 and 1/3 is 4/12.so u add the numerator and u get 7 over 12 .so now the whole container of peanuts is 12/12 but 7/12 is used so 12-7= 5. so ur ans is 5/12

Make x the subject of the formula y=4x²-2​

Answers

Step-by-step explanation:

y=4x²-2y+2=4x²√(y+2)/4=xx=√(y+2)/4

hope it helps.stay safe healthy and happy....

Which values for h and k are used to write the function f(x) = x2 + 12x + 6 in vertex form?
h=6, k=36
h=-6, k=-36
h=6, k=30
hs-6, k=-30

Someone please help me with this I can’t fail this test !

Answers

i gotchu bro you ain’t getting this wrong

ITS D!!! h = -6 k = -30

The equation of a vertical parabola in vertex form is equal to

f(x)= a(xh)² + k

where

a is a coefficient

(h,k) is the vertex

we have

f)x) = x² + 12x + 6

Convert to vertex form

Complete the square

f)x) 6= x² + 12x

f)x) - 6+36= (x² + 12x +36)

f)x)+ 30 = (x² + 12x +36) -

f)x)+30= (x+6)²

f)x) = (x+6)² – 30. -----> equation in vertex form

therefore

The vertex is the point (-6,-30)

h=-6, k=-30

Wendy brought 4 cakes and 2 pies for $20. The cost of a cake is twice the cost of 1 pie. A) What was the cost of one cake b)What was the cost of 1 pie?

Answers

Answer:

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Step-by-step explanation:

Let the cost of cake be C.Let the cost of pie be P

C = 2P  .....equation 1

4C + 2P = 20  .....equation 2

Substituting eqn 1 into eqn 2, we have;

4(2P) + 2P = 20

8P + 2P = 20

10P = 20

P = 20/10

Pie, P = $2

Next, we would determine the cost of a cake;

From equation 1;

C = 2P

Substituting the value of "P" we have;

C = 2 * 2

Cake, C = $4

Therefore, we would have the following answers;

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Check:

From equation 2;

4C + 2P = 20

4(4) + 2(2) = 20

16 + 4 = 20

20 = 20

Help Please
Find The Surface Area Of The Prism

Answers

Answer:

360 cm^2

Step-by-step explanation:

Find the area of each face of the triangular prism.

Imagine the triangular prism as its net, it is composed with 2 triangular faces (these are tye bases of the prism) and 3 rectangular faces.

Areas of the 2 triangular bases (they are similar triangles):

1/2 x 8 cm x 6 cm = 24 cm^2

24 x 2 = 48 cm^2

Area of the rectangular face:

8 x 13 = 104 cm^2

Area of another rectangular face:

6 cm x 13 cm = 78 cm^2

Area of another rectangular face:

13 cm x 10 cm = 130 cm^2

Add up all the areas of all faces:

48 + 104 + 78 + 130 = 360

So the SA is 360 cm^2

Factor of 3x^3-x^2-20x-12

Answers

Answer:

(−3)(+2)(3+2)

Step-by-step explanation:

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(32+8+4)

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(+2)(3+2)

True or false..?

In a parallelogram, consecutive angles are supplementary.

Answers

Answer:

True

Step-by-step explanation:

Both pairs of opposite angles are congruent. parallelogram, rectangle, rhombus, square. Both pairs of opposite sides are congruent. parallelogram, rectangle, rhombus, square. All consecutive angles are supplementary. parallelogram, rectangle, rhombus, square. diagonals bisect each other. parallelogram, rectangle, rhombus, square.

Answer:

true

Step-by-step explanation:

any 2 consecutive angles are supplamentary

What is the probability of rolling 2 standard dice which sum to 9?

Answers

Answer: 1/9

Explanation: Tbh I can’t explain how my brain just clicks sometimes

Can some one help me solve these 3 questions?

Answers

7. A
8. Is the 1st picture
9.is the second picture

find the LCM and hcf of 72 and 162 , leaving the LCM in prime factors

Answers

Answers:  LCM = 2^3*3^4HCF = 18

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

Explanation:

Find the prime factorization of 72 and 162

72 = 8*9 = 2^3*3^2162 = 2*81 = 2*9^2 = 2*(3^2)^2 = 2*3^4

Here's a simplified version of each

72 = 2^3*3^2162 = 2*3^4

We have these unique primes: 2, 3

Circle the terms that have the largest exponents for each of those unique primes. So you'll circle 2^3 and 3^4. Those items circled will multiply together to get the LCM.

This means 2^3*3^4 is the LCM (lowest common multiple).

2^3*3^4 turns into 648, but your teacher wants you to keep the LCM in prime factor form.

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

Now onto the HCF (highest common factor; aka GCF).

Looking at

72 = 2^3*3^2162 = 2*3^4

We again see '2's and '3's as the unique primes. Both have at 1 copy of '2' between them. They also both have 3^2 between them. It might help to think of 3^4 as 3^2*3^2.

Those common factors you circled are then multiplied.

Overall, the HCF is 2*3^2 = 2*9 = 18

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

Side note: The HCF is useful to help reduce fractions, while the LCM is useful to help find the LCD (lowest common denominator) when adding or subtracting fractions of different denominators. There are other applications of each of these.

Answer:

LCM= 648

HCF= 18

Step-by-step explanation:

Help fast please in a test and don’t know the answer I have tried Googling and everything please help

Answers

Answer:

Surface Area = 3,543.7 cm²

Step-by-step explanation:

Surface area of the cylinder = 2πr(h + r)

Where,

radius (r) = 12 cm

height (h) = 35 cm

Plug in the values into the surface area formula

S.A = 2*π*12(35 + 12)

S.A = 24π(47)

S.A = 3,543.71651 cm²

≈ 3,543.7 cm² (approximated to the nearest tenth)

Sarah earned 45 1/2 dollars in 5 3/4 minutes. What is the unit rate in dollars per
minute?

Answers

Answer:

7 21/23 dollars per minute

Step-by-step explanation:

Total amount Sarah earns = 45 1/2 dollars

Time taken to earn = 5 3/4 minutes

What is the unit rate in dollars per

minute?

unit rate in dollars per

minute = Total amount Sarah earns / Time taken to earn

= 45 1/2 ÷ 5 3/4

= 91/2 ÷ 23/4

= 91/2 × 4/23

= (91 * 4) / (2 * 23)

= 364/46

= 7 42/46

= 7 21/23 dollars per minute

unit rate in dollars per

minute = 7 21/23 dollars per minute

Strat with k add 2 multiply by 6 then subtract 8

Answers

Answer:

6(k+2) -8

Step-by-step explanation:

Start with k

k

Add 2

(k+2)

Multiply by 6

6(k+2)

Then subtract 8

6(k+2) -8

6(k+2)-8 is a required answer.

Answer:

Solution given:

Start with k.

K

add 2

k+2

multiply by six

(k+2)*6

subtract by 8

6(k+2)-8

SECTION B
A matatu and Nissan left town A for town B 240km away at 8.00 a.m travelling at 90km/hr
and 120km/hr respectively. After 20 minutes the Nissan had a puncture which took 30
minutes to mend.
(5mks
a) How far from town A did the Nissan catch up with the matatu?

Answers

9514 1404 393

Answer:

  180 km

Step-by-step explanation:

The Nissan had traveled (120 km/h)(1/3 h) = 40 km when it had the puncture. It started from that location when the puncture was repaired at t = (1/3+1/2) = 5/6, where t is in hours. Then the two vehicles met (again) when ...

  Matatu distance = Nissan distance

  90t = 40+120(t -5/6)

  0 = 40 +30t -100 . . . . . . subtract 90t, eliminate parentheses

  60 = 30t . . . . . . . . . . . add 60

  2 = t . . . . . . . . . . . . . 2 hours after leaving, the cars meet again

That distance from town A is ...

  y = 90t = 90(2) = 180 . . . . km

help asap no wrong answers----------------------

Answers

Answer:

[tex]y=-2(sin(2x))-7[/tex]

Step-by-step explanation:

1. Approach

Given information:

The graph intersects the midline at (0, -7)The graph has a minimum point at ([tex]\frac{\pi}{4}[/tex], 9).

What conclusions can be made about this function:

The graph is a sine function, as its y-intercept intersects the midlineThis graph has a negative coefficient, this is because after intersecting the midlines at the y-intercept, the function has a minimum.This graph does not appear to have undergone any horizontal shift, as it intercepts the midlines with its y-intercept

Therefore, one has the following information figured out:

[tex]y=-n(sin(ax))+b[/tex]

Now one has to find the following information:

amplitudemidlineperiod

2. Midline

The midlines can simply be defined as a line that goes through a sinusoidal function, cutting the function in half. This is represented by the constant (b). One is given that point (0, -7) is where the graph intersects the midline. The (y-coordinate) of this point is the midline. Therefore, the midline is the following:

y = -7

2. Amplitude

The amplitude is represented by the coefficient (n). It can simply be defined by the distance from the midline to point of maximum (the highest part of a sinusoidal function) or point of minimum (lowest point on the function). Since the function reaches a point of minimum after intercepting the (y-axis) at its midlines, the amplitude is a negative coefficient. One can find the absolute value of the amplitude by finding the difference of the (y-coordinate) of the point of minimum (or maximum) and the absolute value of the midline.

point of minimum: [tex](\frac{\pi}{4},9)[/tex]

midline: [tex]y=-7[/tex]

Amplitude: 9 - |-7| = 9 - 7 = 2

3. Period

The period of a sinusoidal function is the amount of time it takes to reach the same point on the wave. In essence, if one were to select any point on the sinusoidal function, and draw a line going to the right, how long would it take for that line to reach a point on the function that is identical to the point at which it started. This can be found by taking the difference of the (x- coordinate) of the intersection point of the midline, and the (x-coordinate) of the point of minimum, and multiplying it by (4).

point of minimum: [tex](\frac{\pi}{4},9)[/tex]

midline intersection: [tex](0, -7)[/tex]

Period: [tex]4(\frac{\pi}{4}-0)=4(\frac{\pi}{4})=\pi[/tex]

However, in order to input this into the function in place of the variable (a), one has to divide this number by ([tex]2\pi[/tex]).

[tex]a=\frac{2\pi}{\pi}=2[/tex]

4. Assemble the function

One now has the following solutions to the variables:

[tex]n =-16\\a=2\\b=-7\\[/tex]

Substitute these values into the function:

[tex]y=-2(sin(2x))-7[/tex]

Jernel has to figure out the area of her square garage. She knows that one side of the garage is equal to the length of her rabbit pen. The dimensions of the rectangular rabbit pen are 13 by 10.

Answers

Answer:169

Step-by-step explanation:13 x 13 = 169

You would take the larger side of the pen (13) or else it wouldn’t fit if you chose 10.

what is constant in graphing ?

Answers

Answer:

the constant is the number without an x attaches to it.

Ex:

y = 2x + 9

9 is a constant because it is not attached to any x

y = x^3 + 2x^2 + 10x + 19

19 is a constant because it is not attached to any x

The equation of the line with slope −4 that goes through the point (8,−3)
can be written in the form y=mx+b
where m is:
and where b is:

Answers

Answer:

y = -4x + 29

Step-by-step explanation:

-3 = -4(8) + b

-3 = -32+b

29=b

The equation whose slope is -4 and passes through (8,-3) is y=-4x+29 where slope is -4.

What is equation?

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

How to form equation?

We have been given slope of line being -4 and point through which it passes (8,-3) and we have to find the equation of line.

The equation from two points can be calculated through the following formula:

y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]) and slope is m.

Putting the values of points and slope in the formula given above.

y-(-3)=-4(x-8)

y+3=-4(x-8)

y+3=-4x+32

y=-4x+32-3

y=-4x+29

Hence the equation is y=-4x+29 where slope is -4.

Learn more about equation at https://brainly.com/question/2972832

#SPJ2

ASAP please help meeeeeeeeeee

Answers

Answer:

Step-by-step explanation:

1/16 + 1/2 = 1/16 + 8/16 = 9/16

what is 3 over 4 divided by 1 over 6

Answers

The answer is eighteen
3 over 4 of 6 over 1
18 divided by 4
4.5

Find the percentage of the following:
20/60
18/60
21/60
31/60​

Answers

Answer:

20/60 = 33%

18/60 = 30%

21/60 = 35%

31/60 = 52%

Step-by-step explanation:

Just divide em'

Simple as that.

Answer:

20/60 = 33%18/60 = 30%21/60 = 35%31/60 = 51.67%

I hope th is helps you I just divided the fractions by the way :)

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