Bradley is preparing a presentation to show the CEO of his company. He wants to emphasize that the profits of their competitor have increased slowly over the past 16 months.

9514 1404 393

Answer:

  A

Step-by-step explanation:

The second equation differs from the first in that -9 is a term added to both sides of the equation. The addition property of equality tells you that doing this will not change the value of the variable.

_____

The reason (not justification) for doing this is that the sum of 9 and its additive inverse is 0, the additive identity element. This means the equation can be simplified to 3x = 12, which is the point of making that step (subtracting 9).

[tex]\longrightarrow{\green{a\:=\:2}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]

➡[tex]\:4a + 1 = a + 7[/tex]

Combining like terms, we have

➡[tex]\:4a - a = 7 - 1[/tex]

➡[tex]\:3a = 6[/tex]

➡[tex]\:a = \frac{6}{3} [/tex]

➡[tex]\:a = 2[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

➪ [tex] \: 4 \times 2 + 1 = 2 + 7[/tex]

➪ [tex] \: 8 + 1 = 9[/tex]

➪ [tex] \: 9 = 9[/tex]

➪ [tex] \: L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]

Answer:

HCF = 1

Step-by-step explanation:

Smallest 2 digit composite number = 10

Smallest  3 digit prime number = 101

Factors of 10 = 1 , 2 , 5

Factors of 101 = 1 , 101

HCF = 1

Answer:

slope = [tex]\frac{2}{7}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (4, 4)

m = [tex]\frac{4-2}{4-(-3)}[/tex] = [tex]\frac{2}{4+3}[/tex] = [tex]\frac{2}{7}[/tex]

Answer:

= 2

7

Step-by-step explanation:

slope = y2 - y1

x2 - x1

=4 - 2

4 - -3

= 2

7

y - 4 = 2

x - 4 7

7(y - 4) = 2(x - 4)

7y - 28 = 2x - 8

7y = 2x - 8 + 28

7y = 2x + 20

7 7 7

Gradient = 2

7

The set {1, 2, 3} has 8 subsets.

A set with 'n' elements in it can have 2n subsets.

Answer: 1.8 s

Step-by-step explanation:

Given

The height of the spring mass system above the table is given by

[tex]h(t)=6.85\cos (3.42t)+9[/tex]

The mass is performing S.H.M with frequency [tex]\omega =3.42[/tex]

and [tex]\omega T=2\pi[/tex]

[tex]\therefore T=\dfrac{2\pi }{\omega}[/tex]

time when mass returns to its original position

[tex]T=\dfrac{2\pi }{3.42}\\\\T=1.8\ s[/tex]

The number of seconds, to the nearest tenth, will it take for the mass to return to its original position is 1.8 seconds.

Since the equation h(t)=6.85cos(3.42t)+9, where the height is in inches and the time, t, is in seconds

So here the time should be

[tex]= 2\pi \div 3.42\\\\= 2\times 3.14\div 3.42[/tex]

= 1.8 seconds

Therefore, The number of seconds, to the nearest tenth, will it take for the mass to return to its original position is 1.8 seconds.

Learn more about time here: https://brainly.com/question/24308516

Answer:

D

Step-by-step explanation:

Have a great summer :)

Answer:

C

Step-by-step explanation:

The slope is negative, so we can exclude the graph A and D

If we substitute y with 2 and x with -3 we have

2 = -4/3 (-3) -2

2 = 4 - 2

2 = 2

the equality is verified so C is the answer

Answer:

29.2 cm

Step-by-step explanation:

The two leg lengths are 15 and 25 cm and we are to find the length of the hypotenuse.  The Pythagorean Theorem applies here because this is a right triangle.  

a^2 + b^2 = c^2 becomes 15^2 + 25^2 = 225 + 625 = 850

The hypotenuse length is thus √850 ≈ 29.2 cm

Answer:

no

Step-by-step explanation:

since;

(4--3)/(4-1)≠(8-4)/(5-4)

Answer: The ASAP Math program provides an opportunity for additional small group instruction for students who find the math program challenging. Students in grades 1 to 4 will come to the ASAP room two to three times a week during the math block.

Answer:

1/2

Step-by-step explanation:

2, 3, and 5 are the prime numbers. Therefore, it would be 3/6 or 1/2 chance she rolls a prime number.

Answer:

34 because the shape is split.

Step-by-step explanation:

Answer:

B. 14 and 15

hope this helps

have a good day :)

Step-by-step explanation:

the square root of 200 is 14.14213562 so it has to be between 14 and 15

Answer:

sin = opposite / hypotenuse

cos = adjacent/hypotenuse

sin U = 4/5

cos U = 3/5

sin T = 3/5

cos T= 4/5

Answer:

5P5 × 20P15

Step-by-step explanation:

i think...

sorry if im wrong

good luck

Answer:

5

Step-by-step explanation:

The highest power is 5 so the degree of the monomial is also 5.

Answer:

7.5 minutes

Step-by-step explanation:

Given

See attachment for complete question

Let

[tex]t \to time[/tex]

[tex]y \to capacity[/tex]

From the question, we have the following points

[tex](t_1,y_1) = (0,7)[/tex] --- When he first sees it

[tex](t_2,y_2) = (3,5)[/tex] --- 3 minutes later

First, we calculate the rate (m)

[tex]m = \frac{y_2 -y_1}{t_2 -t_1}[/tex]

[tex]m = \frac{5 -7}{3 -0}[/tex]

[tex]m = -\frac{2}{3}[/tex]

The discharge rate is 2/3 gallons per minute

To calculate the additional minute, we simply consider the capacity of the tank at the later time. i.e. 5 gallons

To calculate time (t), we have:

[tex]Rate * Time = Capacity[/tex]

[tex]\frac{2}{3} * t = 5[/tex]

Solve for t

[tex]t = 5 *\frac{3}{2}[/tex]

[tex]t = \frac{15}{2}[/tex]

[tex]t = 7.5[/tex]

Answer:

D

Step-by-step explanation:

Here, we want to select the correct choice of answer

Looking at the two dot plots, we can see that for the class A, we have the clustering from 4-6 and from 10-12

With this, we can see that this clustering is essentially around two areas only

The beginning parts and the mid parts are left empty only for the two parts to be populated by data points

Answer:

[tex] < b = 180 \degree - (2x + 40)\degree \\ =( 140 - 2x)\degree[/tex]

Answer:

m∠B = 50º

Step-by-step explanation:

B = 180 - (2x + 40) = 180 - 2x - 40 = -2x + 140

C = 180 - (3x - 45) = 180 - 3x + 45 = -3x + 225

From the Exterior Angle Theorem

B + C = 140

-2x + 140 - 3x + 225 = 140

-5x + 365 = 140

-5x = -225

x = 45

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

B = -2x + 140

B = -2(45) + 140

B = -90 + 140

B = 50º

Answer:

length- 10cm, width- 5cm

Step-by-step explanation:

You want to convert this into an algebraic equation.

Since a=lw, in this case, 50=lw. Subbing (x+3) for l and (x-2) for w, we get the equation (x+3)(x-2)=50.

Using FOIL, we can expand the brackets to make x²-2x+3x-6=50 and collect like terms to x²+x-6=50.

We want all the numbers on one side (to use the null factor law), so we subtract 50 from both sides. This gives x²+x-56=0.

From there, we factorise it, which becomes (x-7)(x+8)=0. (I used the cross method for this)

With the null factor law, one of the brackets must be equal to 0, meaning x-7=0 or x+8=0. This gives x as either 7 or -8.

With measurement, units must be positive, meaning it has to be 7. We can sub this for x in the 2 equations (length and width) to get the answers.

Length=x+3 becomes 7+3, which is 10cm.

Width=x-2 becomes 7-2, which is 5cm.

**This content involves writing, expanding, and factorising quadratic equations, and the null factor law which you may wish to revise. I'm always happy to help!

Answer:

Step-by-step explanation:

To find the roots of a quadratic equation, you need to solve the quadratic equation by using the quadratic formula.

OR

You can use the (Equation/Function) mode on the calculator.

[tex]\frac{-b+-\sqrt{b^{2} -4ac } }{2a} x \neq 0[/tex]

For this equation,

a = 3

b = 15

c = -5

X1 = [tex]\frac{-15+\sqrt{15^{2} -4(3)(-5) } }{2(3)} x \neq 0[/tex]

X2 = [tex]\frac{-15-\sqrt{15^{2} -4(3)(-5) } }{2(3)} x \neq 0[/tex]

Solving this on the calculator and you should get

X1 = [tex]\frac{=15+\sqrt{285} }{6}[/tex] X2 = [tex]\frac{=15-\sqrt{285} }{6}[/tex]

a, b, c = constants, where a ≠ 0

x  = the unknown

Answer:

Distribute 1.2 to 6.3 and -7x

Combine 3.5 and 7.56

suhtract 11.06 from both sides

Answer:

The answer is C≈49.64

Answer:

C=2πr=2·π·7.9≈49.63716

Step-by-step explanation:

brainliest??

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

r=x(a+b)/x

r/x=a+b-b

r/x-b=a

Answer: 360 is a complete circle meaning the figure will be back where it was originally

Step-by-step explanation:

Answer:

2 cm²

Step-by-step explanation:

Perimeter of a rectangle = perimeter of a square + perimeter of a square

2 congruent squares, side by side

The perimeter of the two squares = 6*sidelength.

Perimeter of a rectangle = 6 cm

The perimeter of the two squares = 6 * length

= 6l

Perimeter of a rectangle = The perimeter of the two squares

6 = 6l

l = 6/6

l = 1

Length = 1 cm

What is the total area of the squares.

Area of a square = lenght²

Area of two squares = 2(length ²)

= 2(1²)

= 2(1)

= 2 cm²

Given:

A figure of a rectangular prism with length l, width w and height h.

To find:

The surface area of the rectangular prism.

Solution:

The product of twice of the length l and the width w is:

[tex]2\times l\times w=2lw[/tex]          ...(i)

The product of twice of the length l and the height is:

[tex]2\times l\times h=2lh[/tex]           ...(ii)

The product of twice of the width w and the height h is:

[tex]2\times w\times h=2wh[/tex]       ...(iii)

The surface area of the prism is the sum of (i), (ii) and (iii). So, the expression for the surface area is:

[tex]A=2lw+2lh+2wh[/tex]

[tex]A=2(lw+lh+wh)[/tex]

Therefore, the required expression is [tex]2(lw+lh+wh)[/tex].