“1.) 7x - 18 = 4x + 21
Explain your work”

Answer:

x = 18

Step-by-step explanation:

so we know that 128* and (6x+20)* have the same value so

128* = (6x+20)*

lets subtract both sides by 20

108* = 6x*

divide both sides by 6:

108/6 = 18

6x/6 = x

18 = x

Have a nice day!

and please tell me if I am wrong. :-)

Note: Consider x be the breadth of the box.

Given:

The surface area of the box is 204.25 square feet.

Length of the box = 10 ft

Breadth of the box = x ft

Height of the box = 6.5 ft

To find:

The value of x.

Solution:

The surface area of a cuboid is:

[tex]SA=2(lb+bh+hl)[/tex]

Where, l is length, b is breadth and h is height of the cuboid.

Putting [tex]SA=204.25,  l=10,\ b=x,\ h=6.5[/tex] in the above formula, we get

[tex]204.25=2(10\times x+x\times 6.5+6.5\times 10)[/tex]

[tex]204.25=2(10x+6.5x+65)[/tex]

[tex]204.25=2(16.5x+65)[/tex]

Using distributive property, we get

[tex]204.25=2(16.5x)+2(65)[/tex]

[tex]204.25=33x+130[/tex]

[tex]204.25-130=33x[/tex]

[tex]74.25=33x[/tex]

Divide both sides by 33.

[tex]\dfrac{74.25}{33}=x[/tex]

[tex]2.25=x[/tex]

Therefore, the correct option is B.

Answer:

Step-by-step explanation:

let the length=x

width=y

P=2(x+y)=128

x+y=128/2=64

y=64-x

area A=xy=x(64-x)=64x-x²

[tex]\frac{dA}{dx} =64-2x\\\\\frac{dA}{dx} =0,gives~64-2x=0,x=32\\\frac{d^2A}{dx^2} =-2<0 ,at ~x=32[/tex]

so A or area is maximum if x=32

y=64-32=32

or it is a square of edge=32 meters.

Answer:

x = 4

Step-by-step explanation:

Answer:

c) None of these answers

Step-by-step explanation:

8 students own a cat

In this, we count the students who own both a dog and a cat, and the students who own only a cat.

5 students own both a cat and a dog.

So of the 8 who own a cat, 5 own both a cat and a dog, and 8 - 5 = 3 own only a cat.

So the correct answer is given by option c, as 3 is not an option.

Answer:

22 feet²

Step-by-step explanation:

We are given:

height of tree h = 45 inches

Circumference= πd × inches

But d = 22.2inches

Therefore area will be

Area = 22.2π × 45 inches²

Area = 3137 inches²

Let's convert from inches² to feet², we have:

1 foot = 12 inches.

Therefore,

1 square foot = 1foot × 1foot = 12inches×12inches

= 3137inches² / 144 inches²

= 22feet²

Note: I attached missing data which states that diameter at year 13 is 22.2inches

Answer: 22

Step-by-step explanation:

simple

Answer:yes

Step-by-step explanation:99

h(5) means the value of h(x) at x = 5. So what we have to do is to substitute x = 5 in the function.

We are given the function h(x) below:

[tex] \large{h(x) = \frac{6}{x - 3} }[/tex]

Substitute x = 5 in the equation.

[tex] \large{h(5) = \frac{6}{5 - 3} \longrightarrow \frac{6}{2} }[/tex]

Simplify in the simplest form.

[tex] \large{h(5) = \frac{3}{1} \longrightarrow 3}[/tex]

Thus h(5) is 3.

Answer

Hope this helps! Let me know if you have any doubts.

Answer:

1/4

Step-by-step explanation:

Probability is the number of desirable outcomes divided by the number of total outcomes. We can tell these events depend on each other because the batteries are picked without replacement. To find the probability of two dependent events, event that depend on each other, we can find the probability of the first event and the probability of the second event happens if the first is given and multiply them. In this case, the first event is selecting a used battery and the second is picking a new battery.

The total number of outcomes the basically the total amount of batteries that can be chosen. This is 15 + 10 or 25 outcomes. 10 of these batteries are used, and that would correspond to the amount of desirable outcomes because we want to pick a used one. From this, we can say the probability of picking a used battery is 10/25 which simplifies to 2/5.

To find the probability of picking a new battery after picking a used one, we can start by stating the amounts of each battery before the second draw. Since we already picked a used battery, our new totals will be 24 batteries, which 9 are used and 15 are new. Now, we can do the same thing a before, the number of desirable outcomes over the total. We get 15/24 which simplifies to 5/8.

To find the total probability, we multiply the two getting: 2/5 * 5/8 = 1/4.

Answer:

X= 9//

Step-by-step explanation:

abc = efg

ac + cd = eg + gh

9 + (x+2) = 6 + (2x-4)

9 - 6 = 2x-4 - (x+2)

3 = x - 6

3+6 = x

9 = x//

Answer: 8

Hope this helps

Answer:

P = 660,592

Step-by-step explanation:

p = [tex]222,000 (1+.0875)^{t}[/tex]

P = [tex]222,000 (1+.0875)^{13}[/tex]

P = 660,592

Answer:

the side length of the hot tub = 4.8ft

Step-by-step explanation:

Scale Factor = 5

Also,

B'C' = 24 feet

Since both are squares so both have all sides equal.

Square A'B'C'D' is dilated by a scale factor of 5

So,

AB = BC = CD = DA = 24/5 = 4.8 ft.

i hope this helps you

The length of the one side of the hot tub is 4.8 ft.

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

Here, Richardo wants to build a square pool of the hot tub using a scale factor of 5.

If the each side of the pool is 24 ft.

The length of one side of hot tub = 24/5 = 4.8 ft.

Thus, the length of the one side of the hot tub is 4.8 ft.

Learn more about Scale Factor from:

https://brainly.com/question/22312172

#SPJ2

Answer:

Step-by-step explanation:

1. 882/24 = 36.75 or 37 crates of milk

2. 3712 x 6 = 1902 yoghurts were sold

3. 94291 - 63512 = 30779

4. 91429 is greater by (91429-42929) = 48500.

10. 7 hours 55 mins

1 month and 3 days or 33 days.

Next bus would pass at 8:15am

Step-by-step explanation:

9514 1404 393

Answer:

  17

Step-by-step explanation:

If you number the rows starting with 0 for the row that is 1, then row n has sum 2^n. 131072 = 2^17, is the sum of row 17.

row 0: 1

row 1: 1 1

row 2: 1 2 1

...

row 17: 1 17 136 680 2380 6188 12376 19448 24310 24310 19448 ...

Answer:

165 square ft

Step-by-step explanation:

Answer:

b. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p > .05).

Step-by-step explanation:

The critical value for one tailed test is t ∝(7) > 1.895

A one tailed test is performed to test the claim that advertisements were viewed more in the morning (before noon) or in the evening (after 5pm)

The null and alternative hypotheses are

H0: μm = μe   vs     Ha μm > μe

where μm is the mean of the morning and μe is the mean of evening.

The calculated value of t = -1.152587077  which is less than the critical region hence the null hypothesis cannot be rejected .

P(T<=t) one-tail 0.143458126 > 0.05

If two tailed test is performed the critical region is t Critical two-tail 2.364624252

and the calculated t value is  -1.152587077  which again does not lie in the critical region .

Hence μm =  μe or    μm ≤ μe

P(T<=t) two-tail 0.286916252  > 0.025

Therefore

b. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p > .05).

Option b gives the best answer.

Answer: Well this one is simple too.

ATQ Angle 4 is 73° so the vertically opposite angle that is angle to will be the same, 73°.

now for the rest two.

lets find angle 1 first. If we find any one from this we can automatically get the other as they are vertically opposite angles.

Angle 1= 180 - Angle 4

Angle 1 = 180-73=107°

We found this coz the Angle 1 and 4 are on the same line which will form a straight angle.

hence, Angle 4 and 2 = 73°

Angle 1 and 3= 107°

Hope it helps. Pls mark brainliest

Answer:

2 non real solutions.

Step-by-step explanation:

We need to use discriminant,

for ax²+bx+c=0

The discriminat is b²-4ac

If the discriminant is,

→ less than 0, then 0 real solutions

→ equal to 0, then 1 real solutions

→ more than 0, then 2 real solutions

Given that,

7x²−4x+3=0

a=7, b=-4, and c=3

→ (-4)²-4(7)(3)

→ 16-84

→ -68

You can see this is less than 0, then non real solutions. [2 nonreal solutions]

Answer:

Solution given:

7x²-4x+3=0

taking common 7

7(x²+4/7*x+3/7)=0

x²+2*x*2/7+(2/7)²-(2/7)²+3/7=0

(x+2/7)²=-17/49

x+2/7=[tex]\sqrt{\frac{17}{49}}[/tex]

x=±√(17)/7-2/7

taking positive

x=√(17)/7-2/7

x=0.39

taking positive

x=-√(17)/7-2/7

x=-0.87

2:unreal number

Answer:

a. 24 woman

b. 28 men and 24 women

Step-by-step explanation:

a.

given: men to women = 7:6

find: number of women

solution: 28 / 7 = 4, 4 * 6 = 24 women

b.

given: number of men

find: number of men and women

solution: 28 men and 24 women

hope this helps....

Answer:

A) 24 women

B) 52 men and women are at the meeting

Step-by-step explanation:

A)

Let y = women at the meeting

7:6 = 28:y

7/6 = 28/y

6×38 = 7y

6×28⁴/7¹ = 7y¹/7¹

y= 6×24

y=24

B)

Number of women at the meeting = 24

Number of men at the meeting = 28

Total number of people at the meeting = 24+28

= 52

Answer:

A = 60° , B = 30°

Step-by-step explanation:

[tex]sin(A+B ) = 1\\\\\ \ \ (A + B) \ = \ \ sin^{-1} 1\\\\A + B = 90^\circ --(1)\\\\ \ tan (A - B) = \frac{1}{\sqrt{3}}\\\\(A-B) = tan^{-1}\frac{1}{\sqrt3}}\\\\A - B = 30^\circ --(2)\\\\ (1) + (2) => 2A = 120^\circ\\[/tex]

                   [tex]A = 60^\circ[/tex]

[tex]from \ (1) \\A + B = 90^\circ\\60^\circ + B = 90^\circ\\B = 90^\circ - 60^\circ\\B = 30^\circ[/tex]

Let the numbers be n, n+2, n+4

Sum equals too= 13+2(n+4), which is 2n+21

a) Equation--> n+n+2+n+4= 2n+21

b) Solution--> 3n+6= 2n+21

                      => n= 15

c) Second number--> 17 (15+2)

   Third number--> 19 (15+4)

d) 15+15+2+15+4=30+21

   => 51= 51

So, the equation is true.

And pls mark me brainliesttt :)))

Step-by-step explanation:

Let the number be n. Then: 2n + 9

Answer:

Yes.

Step-by-step explanation:

I don't really know how to explain this other than use a calculator.

Hope that this helps!

Answer:

3 :2.

Step-by-step explanation:

1.5 : 1

Multiply both numbers by 2:

i this gives 3:2

Answer:

A. 300π units³

Step-by-step explanation:

Formula for volume of a cone = ⅓πr²h

Where,

radius (r) = ½(10) = 5 units

height (h) = 36 units

Plug in the values and find the volume in terms of π

Volume of the cone = ⅓*π*5²*36

Volume of the cone = 300π units³