Solve the inequality 12x < 22 + x.

Answer:

x = 7.5

Step-by-step explanation:

2/3x + 2= 21/3

Subtract 2 from each side

2/3x + 2-2= 21/3-2

2/3x = 21/3 - 6/3

2/3x =15/3

2/3x = 5

Multiply each side by 3/2 to isolate x

2/3x * 3/2 = 5 *3/2

x = 15/2

let's label each pump A, B, and C, just for convenience. A fills the tank by 1/50 every minute, B fills the tank by 1/60 every minute, and C drains it by 1/75 every minute. Now we can put them all into one function: t(1/50 + 1/60 - 1/75) = 1, where t = our time in minutes and 1 = the tank being full.

next, we solve for t: t = 300/7 minutes, or approximately 42.86 minutes.

Answer:

73.18

Step-by-step explanation:

equilateral triangle means all sides are the same

A=(√3/4)a^2

A=(√3/4)*13^2

A=73.18 inches square

Answer:

73.18 square inches.

Step-by-step explanation:

To find the area of an equilateral triangle, we use a certain formula.

Where the side length is represented by s, the area is (sqrt(3))/4 * s^2.

Since s = 13, you will have (sqrt(3))/4 * 13^2 = 1.732050808/4 * 169 = 292.7165865/4 = 73.17914662. You can round that to 73.18.

So, the area of the triangle is 73.18 square inches.

Remember to use your units when presenting your answer, and hope this helps!

Answer:

x = 3 ± [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Given

y = x² - 6x - 4

To find the zeros let y = 0, that is

x² - 6x - 4 = 0 ( add 4 to both sides )

x² - 6x = 4

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 4 + 9 , that is

(x - 3)² = 13 ( take the square root of both sides )

x - 3 = ± [tex]\sqrt{13}[/tex] ( add 3 to both sides )

x = 3 ± [tex]\sqrt{13}[/tex] ← exact solutions

Answerr:

Step-by-step explanation:

Answer:

Centimeters might be easier because they can be much more precise than inches when there isn't an ideal length. Kilometers might be easier because it would not require such large numbers to work with.

Step-by-step explanation:

:)

Answer:

1/5

Step-by-step explanation:

total number of socks= 10

randomly selects two socks.

2/10=1/5 probability

Answer:

The answer is 1

Step-by-step explanation:

You can try out all the numbers one by one but I'll just show you why 1 works.

First you need to replace x with 1:

-1+8>6

-1+8=7

7 is greater than 6 so 1 is the answer.

I hoped that helped!

(Brainliest???)

:)

Answer:

Distance of midpoints of the segments AB and CD is 24 cm.

Step-by-step explanation:

Given that

AD = 36 cm

Points C and B are in segment AB.

The ratio of distance AB:BC:CD = 2:3:4

To find:

Distance of midpoints of the segments AB and CD  ?

Solution:

The ratio of distance AB:BC:CD =2:3:4

Let AB = [tex]2x[/tex]

Let BC = [tex]3x[/tex]

Let CD = [tex]4x[/tex]

Now, it is clear that AD = AB + BC + CD

[tex]\Rightarrow 36=2x+3x+4x\\\Rightarrow 36=9x\\\Rightarrow x = 4\ cm[/tex]

Putting the value of x to find AB, BC and CD:

AB = [tex]2\times 4 = 8\ cm[/tex]

BC = [tex]3\times 4 = 12\ cm[/tex]

CD = [tex]4 \times 4 = 16\ cm[/tex]

Now, mid point of AB will be [tex]\frac{8}2 = 4\ cm[/tex] on the right side of point A.

And

mid point of CD will be [tex]\frac{16}2 = 8\ cm[/tex] on the left side of point D.

[tex]\therefore[/tex] If we subtract 4 and 8 from AD we will get distance between mid points of segments AB and CD.

So, Distance of midpoints of the segments AB and CD = 36 - 4 -8 = 24 cm.

Distance of midpoints of the segments AB and CD is 24 cm.

Answer:

4x

Step-by-step explanation:

When you have a parallel line, the slope of the line is the same. So the slope of (-4,3),(-4,7)=4 would be the same as for example  4x+5  

Answer:

Step-by-step explanation:

Answer:

( y + b - a - 3d)(y + b + a + 3d).

Step-by-step explanation:

y^2 + 2by + b^2 - a^2 - 6ad - 9d^2

= y^2 + 2by + b^2 - (a^2 + 6ad + 9d^2)

= (y + b)^2 - (a + 3d)^2

This is the difference of 2 squares so we have

(y + b - (a + 3d))(y + b + (a + 3d))

= ( y + b - a - 3d)(y + b + a + 3d)

Answer:

[tex]Total = 2.00mL[/tex]

Step-by-step explanation:

Given

Solution: NaCl

Flask 1: 0.25mL of NaCl

Flask 2: 1.75mL of Nacl

Required

Calculate the total amount of the solution

The total amount of the solution is calculated by adding the size of the contents in both flasks

i,e,

[tex]Total = Flask\ 1 + Flask\ 2[/tex]

[tex]Total = 0.25mL + 1.75mL[/tex]

[tex]Total = 2.00mL[/tex]

Answer:

yep it is 2.00

Step-by-step explanation:

Answer:

h(t)=-5t+-500

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

i took the test

Answer:

I think it's 12

Step-by-step explanation:

i just multiplied 60 by 20%

Answer:

isnt it 0

Step-by-step explanation:

They only gave 3 digits

Answer: 10 for each side but in total is 20

Step-by-step explanation: u multiply 5 x 4 = 20 divided by 2 to get 10 meters and another is 4 divided by 2 is 2 x 5 is 10 meters times 2 is 20 total

Answer:

BD = 5

Step-by-step explanation:

∠A = 60°

Since AB = 20 = BC, Then ∠B = 60° resulting in a equilateral triangle with ∠C = 60°.  Then dividing ∠DAE into half gives 4 = angles of 15° yielding each secition of BC being equal to 20/4 = 5.  Do i don't think DE ≈ 9.28 cannot occur.

Answer:

A. tan(x) = 2.4/10

Step-by-step explanation:

The question is incomplete and lacks the required diagram. Find the question and diagram attached below.

Which equation can be used to solve for the measure of angle ABC? tan(x) = 2.4/10 tan(x) =10/2.4 sin(x) =10/10.3 sin(x) =10.3/10

We will use the SOH CAH TOA identity to calculate the equation needed to solve for angle ABC.

In a right angled triangle, the side facing the acute angle ABC is the opposite, the longest side is the hypotenuse and the third side (base) is the adjacent.

From the diagram shown;

AB = hypotenuse = 10.3cm

AC = opposite = 2.4cm

BC = adjacent  = 10cm

To get the angle x, we can use the SOH and TOA identity.

SOH means sin<ABC = opp/hyp

Sin(x) = AC/AB = 2.4/10.3

TOA ≈ Tan(x) = opp/adj

Tan(x) = 2.4/10

The equation that can be used to solve for the measure of angle ABC are therefore sin(x) = 2.4/10.3 OR tan(x) = 2.4/10

Based on the given option,

tan(x) = 2.4/10 is the only correct answer.

Answer:

in short its A.

Step-by-step explanation:

EDGE 2021

Answer:

Bill and Ted are going to order t-shirts for there school clubs. The t-shirts will have the club logo printed on the front. Bill and Ted ask two local t-shirt companies to give them a price. * Patty's Printing charges $21.50 for each t-shirt. * Sandra's shirts has a one-time set up fee for $63 and then charges $18 for each t-sh

Step-by-step explanation:

Part 2: Table Chart:

Number of t-shirts: 2

Patty's cost: 43$

Sandra's cost: : 99$

Number of t-shirts: 4

Patty's cost: 86$

Sandra's cost: : 135$

Number of t-shirts: 6

Patty's cost: 129$

Sandra's cost: : 171$

Number of t-shirts: 8

Patty's cost: 172$

Sandra's cost: : 207$

Number of t-shirts: 10

Patty's cost: 215$

Sandra's cost: : 243$

Number of t-shirts: 12

Patty's cost: 258$

Sandra's cost: : 279$

Number of t-shirts: 14

Patty's cost: 301$

Sandra's cost: : 315$

Number of t-shirts: 16

Patty's cost: 344$

Sandra's cost: : 351$

Number of t-shirts: 18

Patty's cost: 387$

Sandra's cost: : 387$

Part 3: Patty's Printing

Linear equation = equation of a line= y=mx+b

y=21.5x

Part 4: Sandra's Shirts:

Linear equation = equation of a line= y=mx+b

y= 18x+63

Part 5: Note to Jackie

Dear Jackie, I recommend Sandra's shirts.

Write equations:

Sandra's Shirts = 18x+63

Patty's Printing = 21.5x

Sandra's Shirts: 495=18x+63 = 24 shirts

Patty's Printing: 495=21.5x = 23 shirts

Part 6: Refute Jackie

Sandra's Shirts is more expensive at the beginning, but as you buy more shirts (greater than 18), Patty's Printing becomes cheaper.

You should probably add to this, but I can't think of anything else.

Part 7: Equality

At 18 shirts (see table), the shirt cost is equal.

You should probably add to this, but I can't think of anything else.

18x+63=21.5x

Words of encouragement:

Good luck!

Answer:

1.54

Step-by-step explanation:

The cotangent value is referred to as the reciprocal or the opposite of a given tangent value. Cotangent is also referred to as it's short form called cot

Mathematically, Cotangent (cot) = 1/tan

In the above question, we are given a value where:

tan = 33°

Cotangent (cot) = 1/tan 33°

Cotangent (cot) = 1.5398649638

We are told to approximate to the nearest hundredth

= 1.54

Answer:

D.

[tex]u =3[/tex]

[tex]v =\sqrt{3}[/tex]

Step-by-step explanation:

Given

The triangle in the diagram above

Required

Find the missing lengths, u and v

To find the missing lengths, we have to check the relationship between the missing lengths, the given length and the given angle;

From trigonometry;

[tex]sin\ \theta = \frac{Opp}{Hyp}[/tex]; Where Opp = Opposite and Hyp = Hypotenuse

From the attached diagram;

[tex]\theta = 30[/tex]

[tex]Opp = v[/tex]

[tex]Hyp = 2\sqrt{3}[/tex]

[tex]sin\ \theta = \frac{Opp}{Hyp}[/tex]  becomes

[tex]sin\ 30 = \frac{v}{2\sqrt{3}}[/tex]

Multiply both sides by [tex]2\sqrt{3}[/tex]

[tex]2\sqrt{3} * sin\ 30 = \frac{v}{2\sqrt{3}} * 2\sqrt{3}[/tex]

[tex]2\sqrt{3} * sin\ 30 = v[/tex]

In radians, [tex]sin30 = \frac{1}{2}[/tex]

[tex]2\sqrt{3} * \frac{1}{2} = v[/tex]

[tex]\sqrt{3} = v[/tex]

[tex]v =\sqrt{3}[/tex]

Similarly, From trigonometry;

[tex]cos\ \theta = \frac{Adj}{Hyp}[/tex]; Where Adj = Adjacent

From the attached diagram;

[tex]\theta = 30[/tex]

[tex]Adj = u[/tex]

[tex]Hyp = 2\sqrt{3}[/tex]

[tex]cos\ \theta = \frac{Adj}{Hyp}[/tex]  becomes

[tex]cos\ 30 = \frac{u}{2\sqrt{3}}[/tex]

Multiply both sides by [tex]2\sqrt{3}[/tex]

[tex]2\sqrt{3} * cos\ 30 = \frac{u}{2\sqrt{3}} * 2\sqrt{3}[/tex]

[tex]2\sqrt{3} * cos\ 30 = u[/tex]

In radians, [tex]cos30 = \frac{\sqrt{3}}{2}[/tex]

[tex]2\sqrt{3} * \frac{\sqrt{3}}{2} = u[/tex]

[tex]\sqrt{3} * \sqrt{3} = u[/tex]

[tex]3 = u[/tex]

[tex]u =3[/tex]

Answer:

? = 35.

Step-by-step explanation:

According to the diagram...

? / 42 = 30 / (66 - 30)

? / 42 = 30 / 36

? / 42 = 5 / 6

6 * ? = 42 * 5

? = 7 *  5

? = 35

Hope this helps!

Answer:  35

Step-by-step explanation:

Set up the proportion as follows:

[tex]\dfrac{66}{30}=\dfrac{42+x}{x}\\\\\\66x=30(42+x)\\\\\\66x=1260+30x\\\\\\36x=1260\\\\\\x=\dfrac{1260}{36}\\\\\\x=\large\boxed{35}[/tex]

Step-by-step explanation:

you can split triangle in two 90-:80 triangles

Answer:

14 units

Step-by-step explanation:

We apply the Theorem of reflection over parallel lines.

Theorem: The composition of two reflections over parallel lines that are h units apart is the same as a translation of 2h units.

Given that the two parallel lines are 7 units apart

h=7 units

2h= 2 X 7 =14 units

Therefore, the preimage and the final image will be 14 units apart.

Answer:

8.7 cm

Step-by-step explanation:

The question is a 2-two-step Pythagoras theorem. (c^2 = a^2 + b^2)

Consider as such, If I were to draw a diagonal line along the base of the cube what is the length of the diagonal line. To find out that we use the theorem. We can substitute a for 5 and b for 5 as well. So

a^2 +b^2 = c^2

5^2 + 5^2 = c^2

25 + 25 = c^2

√50 = c

Then since the line side of the cube is on a 3d angle we need to do the same process again but now using the imaginary diagonal line that we just calculated and the height (5).

a^2 +b^2 = c^2

√50^2 + 5^2 = c^2

50 + 25 = c^2

√75 = c

c = 8.6602...

when rounded to 1 d.p.

c = 8.7

Line AB is 8.7 cm long.

Answer:

Option D is the correct option.

Step-by-step explanation:

Let the points be A and B

A ( 7 , 35 ) -----> ( x1 , y1 )

B ( 7 , 21 ) -------> ( x2 , y2 )

Now, finding the distance between these two points:

[tex] \sqrt{(x2 - x1) ^{2} + {(y2 - y1)}^{2} } [/tex]

Plug the values

[tex] = \sqrt{(7 - 7) ^{2} + {(21 - 35)}^{2} } [/tex]

[tex] = \sqrt{ {0}^{2} + {( - 14)}^{2} } [/tex]

0 raised to any positive power equals 0

[tex] = \sqrt{0 + {( - 14)}^{2} } [/tex]

When adding or subtracting 0, the quantity doesn't change

[tex] = \sqrt{ {( - 14)}^{2} } [/tex]

Reduce the index of the radical and exponent with 2

[tex] = 14 \: units[/tex]

Hope this helps...

Best regards!

~ a music lover

Answer:

y = 21/5x

Step-by-step explanation:

y is directly proportional to x

y = kx

Find k constant.

21 = 5k

21/5 = k

Plug k as 21/5.

y = 21/5x

Answer:

y=21/5x

Step-by-step explanation:

When y is 21, x is 5.

5(21/5)=21, so we have y=21/5x

Step-by-step explanation:

If you are not a gerbil, then you are not a pet owner. False; if you are not a gerbil, you can be a human who owns pets.

If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets.

If you do not have a gerbil, then you are not a pet owner. False; you could have a dog or a cat.

If you are not a pet owner, then you do not have a gerbil. True, since if you do not own any pets, you will not have any animals, so you will not have a gerbil.

Hope this helps!

Answer:

If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=27.8

A rectangle has 4 sides. Two of the sides have the same length, and the other two sides have the same length. Therefore, two sides are x+4 and the other two are equal to x.

Your equation will be (x+4)+(x+4)+x+x=48

When you solve for x, you get 10.

Since your length is x+4, you will do 4+10 which is 14 as your final answer

FINAL ANSWER: 14''

Please let me know if this helped you!!

Answer:. Width=10 Length = 14

Step-by-step explanation:

2w + 2(w+4) = 48

2w +2w + 8 = 48

4w = 48-8

4w = 40

W=10. L= 14

10+10+14+14 = 48