To model the problem containing an unknown number, translate the statement into an equation.

Sixteen is five less than a number.

Which steps would you take to translate the statement?

Replace “is” with =, “less than” with –, and “a number” with n to get 16 = 5 – n.
Replace “is” with =, “less than” with +, and “a number” with n to get 16 = n + 5.
Replace “is” with =, “less than” with –, and “a number” with n to get 16 = n – 5.
Replace “is” with =, “less than” with ÷, and “a number” with n to get 16 = 5 ÷ n.

Answer:

The numbers are 14 and 16.

Step-by-step explanation:

Equation:

x (x - 2) = 224

Solution:

x (x - 2) = 224

x² - 2x = 224

x² - 2x - 224 = 0

Now, we ended up with a trinomial. To find the two numbers, we need to factor it.

Factoring Trinomials

Trinomial is a polynomial with three terms which are connected by plus or minus notations. It is expressed as a² + b + c.

To factor, we need to follow these steps:

1. Find the factors of "ac" that when combined it will result to "b".

2. When "c" is positive, the sign in each binomial is the same as "b".

3. When "c" is negative, the sign in each binomial is different.

4. Write as the product of two binomials ( )( ).

Let us continue.

x² - 2x - 224

(x - 16)(x + 14)

Therefore, x = 16 and x = -14.

Since we are looking for a positive value, we are going to use the positive value of x and that is 16.

Larger number is 16.

x - 2 = 16 - 2 = 14

Smaller number is 14.

Final Answer:

The two numbers are 14 and 16.

Checking:

x (x - 2) = 224

16 (16 - 2) = 224

16 (14) = 224

224 = 224 ✔

Answer:

eight divided h 8 '/. h

Step-by-step explanation:

[tex]\frac{8}{h}[/tex]

An algebraic expression is one that is constructed using integer constants, variables, and algebraic operations.

A quotient is a quantity that is obtained by dividing two numbers.

Phrase is "The quotient of eight and a number [tex]h[/tex]"

Quotient of eight and [tex]h[/tex] means [tex]8 \div h[/tex] that is equivalent to [tex]\frac{8}{h}[/tex]

The phrase can be written as [tex]\frac{8}{h}[/tex]

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Answer:

x= -3

Step-by-step explanation:

you replace y with -2 as the output

then subtract the 7 on both sides to have '-9=3x'

divide by 3 on both sides

x= -3

Answer:

x=-3

Step-by-step explanation:

y=3(-3)+7

y=-9+7

y=-2

Answer:

The equation in standard form is [tex]y(t) = 5.390\cdot \sin (4\pi\cdot t +0.379\pi)[/tex].

Step-by-step explanation:

We use the following trigonometric identity:

[tex]\sin (\alpha + \beta) = \sin \alpha\cdot \cos \beta + \cos \alpha \cdot \sin \beta[/tex], [tex]\forall\,\alpha,\beta\in \mathbb{R}[/tex] (Eq. 1)

If we have formula [tex]y(t) = 2\cdot \sin (4\pi\cdot t)+5\cdot \cos (4\pi\cdot t)[/tex], by direct comparison with (Eq. 1):

[tex]A\cdot \cos \phi = 2[/tex] (Eq. 2)

[tex]A\cdot \sin \phi = 5[/tex] (Eq. 3)

Where:

[tex]A[/tex] - Amplitude, dimensionless.

[tex]\phi[/tex] - Phase angle, measured in radians.

By dividing (Eq. 3) by (Eq. 2), we get that:

[tex]\tan\phi = \frac{5}{2}[/tex]

[tex]\phi = \tan^{-1}\left(\frac{5}{2} \right)[/tex]

[tex]\phi = 0.379\pi\,rad[/tex]

From (Eq. 2) we find the amplitude:

[tex]A = \frac{2}{\cos \phi}[/tex]

[tex]A = \frac{2}{\cos 0.379\pi}[/tex]

[tex]A = 5.390[/tex]

Therefore, we find that equation in standard form is:

[tex]y(t) = A\cdot \sin (\omega\cdot t +\phi)[/tex] (Eq. 4)

Where [tex]\omega[/tex] is the angular frequency, measured in radians per second.

([tex]A = 5.390[/tex], [tex]\omega = 4\pi\,\frac{rad}{s}[/tex], [tex]\phi = 0.379\pi\,rad[/tex])

[tex]y(t) = 5.390\cdot \sin (4\pi\cdot t +0.379\pi)[/tex]

The length of the arc is about 1.758 cm.

First, we need to determine the size of the angle. If we have pi/5 radians, we can convert that to 36 degrees, because pi radians is 180 degrees. Now, we know the measure of the arc is 36 degrees. 36 degrees out of 360 degrees is 10%.

Our arc is 10% of the circumference of the circle.

The circumference is 2(pi)r or 2(3.14)2.8 = 17.58 cm

Now, multiply 17.58 by 0.1 to get a total of 1.758 cm.

Answer:

7)A 8)D

Step-by-step explanation:

Answer:

7 is d and 8 is a

Step-by-step explanation:

Answer:

4(t-3)^2-64

3 months

Step-by-step explanation:

1) Vertex form of the equation of the parabola is [tex]v(t)=4(t-3)^2-64[/tex]

2)3 months after its creation the company will reach its lowest net value.

The net value of the company after t months is given as:

[tex]v(t) = 4t^2-24t-28[/tex]

The above parabolic equation can be written as

[tex]v(t)=4(t^2-6t+9)-64[/tex]........(1)

The general equation of a parabola is:

[tex]y = a(x-h)^2 +k[/tex]

where (h,k) is the vertex of the parabola.

So, (1) can be written in the vertex form as

[tex]v(t)=4(t-3)^2-64[/tex]

So, the vertex of the given parabola is (3, -64).

[tex]v'(t) = 8t - 24[/tex]

[tex]v''(t) =8[/tex]

So, from the second derivative test

t value corresponding to v'(t) =0 will give minimum value

[tex]8t-24=0[/tex]

[tex]t=3[/tex]

So,  3 months after its creation the company will reach its lowest net value.

Therefore, 1) Vertex form of the equation of the parabola is [tex]v(t)=4(t-3)^2-64[/tex]

2)3 months after its creation the company will reach its lowest net value.

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Answer:

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square.

Step-by-step explanation:

Answer:

93.5 dollars during Monday.

Step-by-step explanation:

Morning: 12:15 - 8     = 4hours 15 minutes

Afternoon: 17:15 - 13 = 4 hours 15 minutes

Total Time working = 4 hours 15 minutes + 4 hours 15 minutes

Total time working = 8 hours 30 minutes

30 minutes = 1/2 hour = 0.5 hours

Total time = 8.5 hours

Wage = 8.5 * 11 = 93.5 dollars for Monday.

Answer: Well 2 x 23 = 46, So the 23rd floor

Step-by-step explanation: :)

Answer:

You will need 3 buses and you will not have any seats left.

9514 1404 393

Answer:

  ∠3 = 115°

Step-by-step explanation:

Angles 4 and 6 are "same-side interior angles", so are supplementary.

  ∠4 +∠6 = 180°

  (x +5) +(2x -5) = 180

  3x = 180

  x = 60

The angles marked 3 and 6 are alternate interior angles, so are congruent. The measure of angle 3 is ...

  ∠3 = ∠6 = (2x -5)° = (2(60) -5)°

  ∠3 = 115°

This should be simple, just simply multiply the area of base with height.

A - 24 * 4 =  96 ft³

B - 9.5 * 5 = 47.5 ft³

C - 16 * 6 = 96 ft³

D - 48 * 2 = 96 ft³

E - 9 * 5.3 = 47.7 ft³

Therefore, only option A, C, D is correct.

Answer:

(9+3)*6

Step-by-step explanation:

Remember the order of operation: (PEMDAS)

Problem: (9+3)*6

Step 1 add 9+3 =12

Step 2 multiply 12*6

Step 3 your answer to solving the problem 72

Given:

The value of y is directly proportional to the value of x.

y = 45 when x = 180.

To find:

The value of y when x = 80.

Solution:

Since the value of y is directly proportional to the value of x, therefore

[tex]y\propto x[/tex]

[tex]y=kx[/tex]      ...(i)

where, k is constant of proportionality.

Putting y=45 and x=180, we get

[tex](45)=k(180)[/tex]

[tex]\dfrac{45}{180}=k[/tex]

[tex]k=\dfrac{1}{4}[/tex]

Substituting [tex]k=\dfrac{1}{4}[/tex] in (i), we get

[tex]y=\dfrac{1}{4}x[/tex]

Put x=80 in this equation.

[tex]y=\dfrac{1}{4}(80)[/tex]

[tex]y=20[/tex]

Therefore, the value of y is 20 when x=80.

Answer:

c to a a to f

Step-by-step explanation:

Answer: 2.87

Step-by-step explanation:

Answer:

repel and attract is correct answer

Answer:

repel; attract

Step-by-step explanation:

think of magnets, N and N repel and N and S attract

Answer:

x=3...

Step-by-step explanation:

Given:T is the midpoint of SU.....

To find: x

Proof: ST=TU ( T is the midpoint of SU)

         8x+11=12x-1

         11+1=12x-8x

          12=4x

           12/4=x

             x=3.

Answer:

the answer is the first one

Answer:

A

Step-by-step explanation:

Answer:

4y

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Given the following question:

[tex]17,9,11,7[/tex]

To find the mean of any given data set we need to add all the values together and then divide that answer by the total amount of values in the data set.

[tex]17,9,11,7[/tex]
[tex]17+9+11+7[/tex]
[tex]9+11=20[/tex]
[tex]20+17=37[/tex]
[tex]37+7=44[/tex]
[tex]=44[/tex]

Now divide the answer by the total amount of values:
[tex]44[/tex]
[tex]a=4[/tex]
[tex]44\div4=11[/tex]
[tex]m=11[/tex]

Which means the mean of this given data set is "11."

Hope this helps.

Answer:

Step-by-step explanation:

The mean is the average number of the data.

To calculate the mean of the data, divide the sum of the data by the total numbers in the data. The quotient will be the average of the data.

[tex]\dfrac{17 + 9 + 11 + 7}{\text{Total digits in the data}}[/tex]

We can see 4 digits included in the data. Thus, the sum of the data will be divided by 4.

[tex]\dfrac{17 + 9 + 11 + 7}{4}[/tex]

Now, let's solve for the mean.

[tex]\dfrac{17 + 20 + 7}{4}[/tex]

[tex]\dfrac{44}{4} = 11[/tex]

Thus, 11 is the mean.

Robert is designing hexagonal tiles that are made up of 12 identical right triangles, as shown. Write three equations robert can use the find the area A of the hexagonal tile in square centimeters.

we know 12 triangles make up hexagon so we can say

12× Area of triangle = Area of hexagon

[tex]12 \times ( \frac{1}{2} \times base \times height) = area \: of \: hexagon[/tex]

[tex]12 \times \frac{1}{2} \times 3 \times 4 = area \: of \: hexagon \\ 12 \times 3 \times 2 = area \: of \: hexagon \\ 12 \times 6 = area \: of \: hexagon \\ 72cm {}^{2} = area \: of \: hexagon[/tex]

we can see that there is a rectangle in the middle of the hexagon and 4 triangles (identical ) on 2 sides

According to question:-

so area of hexagon= area of square+ 4 area of triangle

[tex]( l \times b ) + (4( \frac{1}{2} \times b \times h)) = area \: of \: hexagon[/tex]

[tex] (8 \times 6 ) + 4(\frac{1}{2} \times 4 \times 3) = area \: of \: hexagon \\ 48 + 24= area \: of \: hexagon \\ 72 {cm}^{2} = area \: of \: hexagon[/tex]

we can see 2 square at the sides of the 4 triangle at the middle so we can say

Area of hexagon =4× area of triangle + 2 area of square

[tex]area \: of \: hexagon = (4\frac{1 }{2} × 4×3)+2(5×5) [/tex]

[tex]area \: of \: hexagon = 24+ 50 \\ area \: of \: hexagon = 74cm² \\ area \: of \: hexagon = 72 cm ² approx [/tex]

This approximation turn out bez in your question the area of 4 identical triangle is not equal to square formed by them

4 area of triangle = area of square

4×6 = 24 cm² not equal to 5² = 25 cm²

thats why there is approximation of 2 cm²

Answer:

x is 76

Step-by-step explanation:

im pretty sure, i just sloved it

Answer:

76.

Step-by-step explanation:

Simplifying

-4(x + -26) = -200

Reorder the terms:

-4(-26 + x) = -200

(-26 * -4 + x * -4) = -200

(104 + -4x) = -200

Solving

104 + -4x = -200

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-104' to each side of the equation.

104 + -104 + -4x = -200 + -104

Combine like terms: 104 + -104 = 0

0 + -4x = -200 + -104

-4x = -200 + -104

Combine like terms: -200 + -104 = -304

-4x = -304

Divide each side by '-4'.

x = 76

Simplifying

x = 76

Answer:

Percent: Approx 41.6%

Fraction: 10/24 = 5/12

10 in 24

Step-by-step explanation:

There are 10 red balloons out of a total of 24. The rest is self-explanatory.

Hope this helps! Have a great day!

Answer:

after it is folded into 4 the new area is 112

Step-by-step explanation:

450 divided by 4 is 112

Answer:

k=24

Step-by-step explanation:

k/6=4 (multiply both sides by 6)

k/6(6)=4(6)

k=24

k= 24 is the answer

Step-by-step explanation:

6×4=24

Answer:

B. 90

Step-by-step explanation:

Simplify

20 + 3(11) + 5 + 2(16)

Expand

20 + 33 + 5 + 32

Simplify

= 90

9514 1404 393

Answer:

  ∠2 = 45°

Step-by-step explanation:

Angles 1 and 2 are same-side interior angles where the transversal crosses parallel lines. That means they are supplementary angles.

  ∠1 +∠2 = 180° . . . . . supplementary angles total 180°

  135° +∠2 = 180° . . . . substitute the given value

  ∠2 = 180° -135° . . . .  subtract 135°

  ∠2 = 45°