This diagram is a straightedge and compass construction. A is the center of one circle,
and B is the center of the other. Explain how we know triangle ABC is equilateral.

Answer:

30/11 (hours)

Step-by-step explanation:

Pipe A can fill the tank until it is full in 3 hours.

=> In 1 hour, pipe A can fill 1/3 of tank

Pipe B can fill the tank until it is full in 5 hours.

=> In 1 hour, pipe A can fill 1/5 of tank

Pipe C can empty the full tank in 6 hours.

=> In 1 hour, pipe A can empty 1/6 of tank

Assume that we open 3 pipes A, B, and C at the same time.

Then, in 1 hour, the amount of water in tank is:

A =  1/3 + 1/5 - 1/6 = 10/30 + 6/30 - 5/30 = 11/30 (tank)

=> The time to fill up the tank is:

T = 1/A = 1/(11/30) = 30/11 (hours)

Answer:

30/11

Step-by-step explanation:

Imagine the tank can hold x litre of water

So,A can fill x/3 litre water per hour

And B can fill x/5 litre water per hour

And C can reduce x/6 litre of water per hour which is filled by A and B.

So the gross calculation per hour is:

(x/3+x/5)-x/6

=11x/30

Now suppose it tooks 'a' hour to fill the tank.

So, a(11x/30)=x

⇨ a= (30/11x)x

⇨a=30/11

Answer:

1) 27.89

2) 20

Step-by-step explanation:

#1)

9.5x + 75 --> 340

340 - 75 --> 265

265 / 9.5 = 27.89

#2)

120 / 6 =

20 minutes

Answer: 4t - 3 < 12

Step-by-step explanation:

Step-by-step explanation:

from the second:

A=[3 -1]. -2B

[-5 0]

input this into 1

2([3 -1]) -(2B) -B =[1 3]

([-5 0]). [0 5]

[6 -2] -4B-B=[1 3]

[-10 0]. [0 5]

-5B=[1 3] -[3 -1]

[0 5]. [-5 0]

-5B= [1-3 3+1]

[0+5 5+0]

B= [-2/5 4/5]

[1 1]

A=[(19/5) (3/5)]

[-3. 2]

using the formula I derived

that's how I got A

Answer:

D

Step-by-step explanation:

Answer:

same side interior angles

Step-by-step explanation:

<4 and <6 are same side interior angles

Same  side interior angles are on the same side of the transversal and inbetween the two lines

Answer:

7 2/5

Step-by-step explanation:

7.08 to improper fraction:

708/100

= 7 2/25

Answer:

0.25 as a fraction is 25/100, which further simplified becomes 1/4

Answer:

5

Step-by-step explanation:

The midsegment of a trapezoid is equal to one half the sum of the bases.

1. Set up the equation using the midsegment formula: 1/2 (QR + ST)

1/2 (3x + 31) = 8x - 17

2. Solve

1.5x + 15.5 = 8x - 17

32.5 = 6.5x

x = 5

Answer:

[tex]\huge \boxed{23}[/tex]

Step-by-step explanation:

QR < LM < ST

LM is the middle segment, it is in between the length of QR and ST.

LM is also the average or mean of QR and ST.

(QR+ST)/2 = LM

(3x+31)/2 = 8x-17

Multiply both sides by 2.

(2)(3x+31)/2 = (2)8x-17

3x + 31 = 16x - 34

Subtract 16x and 31 from both sides.

3x + 31 - 16x - 31 = 16x - 34 - 16x - 31

-13x = -65

Divide both sides by -13.

(-13x)/-13 = -65/-13

x = 5

Substitute x = 5 for LM.

8(5) - 17

40 - 17

= 23

Answer:

6.68

Step-by-step explanation:

To round 6.675 to the nearest hundredth consider the thousandths’ value of 6.675, which is 5. Therefore, the hundredths value of 6.675 increases by 1 to 8.

6.675 rounded to the nearest hundredth = 6.68

Answer:

New depth of the milk will be 4 cm.

Step-by-step explanation:

If the carton (shaded side) is standing vertically, milk in the box will acquire the dimensions of the box.

Length of the cuboid formed by the the milk = 8 cm

Width = 5 cm

Height = 12 cm

Volume of the cuboid formed by the milk in the carton = Length × width × height

V = 8 × 5 × 12

  = 480 cm³

If the carton is turned so that the carton stands on the shaded face,

Volume of the milk remains unchanged but the dimensions of the cuboid formed by the milk inside the carton will get changed.

Length = 15 cm

Width = 8 cm

Height = h cm

Then volume of the cuboid = Length × width × height

V = 15 × 8 × h

480 = 120h

h = [tex]\frac{480}{120}[/tex]

h = 4 cm

Therefore, new depth of the milk will be 4 cm.

Answer:

C

Step-by-step explanation:

A line parallel to a side of the triangle and it intersects the other two sides, then it divides those sides proportionally, that is

[tex]\frac{a}{b}[/tex] = [tex]\frac{d}{c}[/tex] → C

Answer:

There are 3 ways

Step-by-step explanation:

The formula for a sector's area is:

1. A = (sector angle / 360 ) * (pi *r2)

2. A = (sector angle / (2*pi)) * (pi * r2)

3. A = (fraction of the circle) * (pi * r2)

Answer:

  28 inches

Step-by-step explanation:

The point of intersection of the angle bisectors is the incenter. It is the center of a circle tangent to the three sides of the triangle. The circle has radius 2.

In the attached figure, we have labeled the points of tangency D, E, and F. We know that CE and CF are both of length 2, and we know that the points of tangency are the same distance from an external point where the tangents intersect. That means DA = FA and DB = EB.

The perimeter of the triangle is ...

  P = DA +DB +FA +EB +CF +CE

Using the above relations, this can be written as ...

  P = DA +DB +DA +DB +CF +CE = 2(DA +DB) +2(CE)

We are told that AB is 12 inches, so DA +DB = 12 inches. We also know that CE = 2 inches, so the perimeter is ...

  P = 2(12 in) + 2(2 in) = 28 in

The perimeter of triangle ABC is 28 inches.

Answer:

708

Step-by-step explanation:

We are adding 7 each time

15+7 = 22

22+7 = 29

29+7 = 36

So the common difference is 7

The first term is 15

The formula is

an = a1+d(n-1)  where n is the term number

an = 15+7(n-1)

We want to find the 100th term

a100 = 15+7(100-1)

a100 = 15+7(99)

       = 15+693

     = 708

Answer:

7000 (7 thousand)

700 (7 hundred)

20 (2 tens)

2 (2 units)

Step-by-step explanation:

what is the relationship between the values of the given digits?

1. The 7s in 7,700

2. The 2's in 522

From the knowledge of place values;

7,700 could be broken down thus :

7000 + 700 + 0 + 0

The first 7 depicts thousands as it has 3 trailing digits (7000)

The second 7 depicts hundred as it has 2 trailing digits (700)

522 could be broken down thus :

500 + 20 + 2

From 522

The first '2' has one trailing digit = tens

The ending / last digit ia always = Unit value

Answer:

(7/6, 0) and (0,-7/3)

Step-by-step explanation:

I think you mean x-intercept and y-intercept not z-intercept and y-intercept. The first step is to convert the equation to slope intercept form:

-6x+3y=-7

3y=6x-7

y=6/3x-7/3

y=2x-7/3

Now, to find the x-intercept we find the value of x when y is 0.

0=2x-7/3

7/3=2x

7/6=x so the x-intercept is (7/6,0)

Now, to find the y-intercept we find the value of y when x is 0.

y=2(0)-7/3

y=0-7/3

y=-7/3 so the y-intercept is (0,-7/3)

Answer:

Part one:

In terms of price;

[tex]2x + \frac{5}{2} y = 19 \\ \\ 4x + 5y = 38 - - - (equation \: \: 1)[/tex]

In terms of people, each person will get one snack:

[tex]x + y = 8 - - - (equation \: \: 2)[/tex]

Part two:

[tex]in \: equation \: 2 : \\ x = 8 - y \\ substitute \: for \: x \: in \: 1 : \\ 4(8 - y) + 5y = 38 \\ 32 - 4y + 5y = 38 \\ y = 6 \\ \\ therefore : x = 2[/tex]

Sam bought 2 bags of chips

Answer:

x+4

.....................

Answer

[tex] \boxed{x + 4}[/tex]

Option C is the correct option

Step by step explanation

Let's find the expression which represents the length of the box:

[tex] \mathsf{length \times width \times height \: of \: prism \: = \: volume \: of \: prism}[/tex]

[tex] \mathsf{lengh \times \: (x - 1) \times (x + 8) = {x}^{3} + 11 {x}^{2} + 20x - 32}[/tex]

[tex] \mathsf{length = \frac{ {x}^{3} + 11 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }[/tex]

Write 11x² as a sum

[tex] \mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }[/tex]

Write 20x as a sum

[tex] \mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)}}[/tex]

Factor out x² from the expression

[tex] \mathsf{ = \frac{ {x}^{2}(x - 1) + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)} }[/tex]

Factor out 12 from the expression

[tex] \mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32x - 32 }{(x - 1)(x + 8)} }[/tex]

Factor out 32 from the expression

[tex] \mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32(x - 1) }{(x - 1)(x + 8)} }[/tex]

Factor out x+1 from the expression

[tex] \mathsf{ = \frac{(x - 1)( {x}^{2} + 12x + 32) }{(x - 1)(x + 8)} } [/tex]

Factor out 12x as a sum

[tex] \mathsf{ = \frac{(x - 1)( {x}^{2} + 8x + 4x + 32) }{(x - 1)(x + 8)} }[/tex]

Reduce the fraction with x-1

[tex] \mathsf{ = \frac{ {x}^{2} + 8x + 4x + 32 }{(x + 8)} }[/tex]

Factor out x from the expression

[tex] \mathsf{ = \frac{x(x + 8) + 4x + 32}{(x + 8)} }[/tex]

Factor out 4 from the expression

[tex] \mathsf{ = \frac{x(x + 8) + 4(x + 8)}{x + 8} }[/tex]

Factor out x+8 from the expression

[tex] \mathsf{ = \frac{(x + 8)(x + 4)}{x + 8} } [/tex]

Reduce the fraction with x+8

[tex] \mathsf{ = x + 4}[/tex]

hence, x+4 is the expression that represents the length of a box.

Hope I helped!

Best regards!

Answer:

y = 1/27

Step-by-step explanation:

[tex]y^{\frac{-2}{3}} = 9\\[/tex]

Cube both sides

[tex](y^{\frac{-2}{3}})^{3}=9^{3}\\\\y^{\frac{-2}{3}*3}=9*9*9\\\\y^{-2}=729\\\\\frac{1}{y^{2}}=729\\\\1=729*y^{2}\\\\\frac{1}{729}=y^{2}\\[/tex]

[tex]y^{2}=\frac{1}{27^{2}}\\\\y^{2}=(\frac{1}{27})^{2}\\[/tex]

y = 1/27

Answer:

A: (draw figure 3 and on the right end add two more tiles on the top and bottom stack of tiles)

B: Figure 10 will have 20 tiles because each figure is increasing by 2 tiles.

Step-by-step explanation:

The figures are increasing by 2 so we can multiply 2 by 10 to get the number of tiles on the 10th figure.

Answer:

3 hours and 27 minutes

Step-by-step explanation:

2:05 pm = 14:05 hours

1 hour = 60 minutes

14:05 = 13 hours + 60 minutes + 5 minutes = 13 hours + 65 minutes

then:

 13h  65m

- 10h  38m

=  3h  27m

they drive:

3 hours and 27 minutes

Answer:

7x+14

Step-by-step explanation:

The distributive property is when you multiply the number on the outside of rhe parenthesis with the numbers on the inside.

In this case it will be 7×x and 7×2

7(x+2)=7x+14

Consider plane A with respect to B,

initial relative Altitude [tex] h_{a, b}=h_a-h_b=-972 [/tex]

relative rate of altitude(speed) $r_{a,b}= 55.75-35.5=20.25$

To get at same altitude, they'll take same time, and their relative height will be $0$ So,

$H_{a,b}=h_{a,b}+r_{a,b}t$

$0=-972+20.25t$

$t=48$

and altitude will be, $3028+55.75\cdot 48=5704$

Answer:

Step-by-step explanation:

We can write equations for the altitude of each plane:

  A(t) = 3028 +55.75t . . . . . initially at 3028 ft; gaining at 55.75 ft/s

  B(t) = 4000 +35.5t . . . . . initially at 4000 ft; gaining at 35.5 ft/s

The two altitudes will be equal when ...

  A(t) = B(t)

  3028 +55.75t = 4000 +35.5t . . . . substitute the expressions for A and B

  20.25t = 972 . . . . . . subtract 3028+35.5t

  t = 48 . . . . . . . . . . . . divide by 20.25

The common altitude will be ...

  B(48) = 4000 +35.5(48) = 5704 . . . . feet

The planes will both be at an altitude of 5704 feet after 48 seconds.

Answer:

Step-by-step explanation:

Because of the nature of the information we are given, we have no choice but to use the equation

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

and solve for a.

We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:

[tex]0=a(21-0)^2+84[/tex] and simplifying a bit:

0 = 441a + 84 and

-84 = 441a so

[tex]a=-\frac{84}{441}=-\frac{4}{21}[/tex] Good, a is negative. Your equation is, then:

[tex]y=-\frac{4}{21}x^2+84[/tex]

Answer:

x² = -21y

Step-by-step explanation:

THIS IS THE RIGHT ANSWER I TOOK THE TEST

Answer:

7

Step-by-step explanation:

if the bases of the exponents are the same then we can add the powers. so 2^3 * 2^4 = 2^7 = 128.

Answer:

7

Step-by-step explanation:

2^3⋅2^4= 2^7

2^7=2^x

since it had the same base you wouldn't need to worry about it you can just focus on the exponent.

7=x

swap it over

x=7

angle at center is twice angle at circumference

so therefore the lengths of WU and WV are proportional along with WC and WT.

WU / WV  =  WC / WT

4 / 2  =  11 / x

2 = 11 / x

x = 11 / 2 or 5.5 u

no cheating thanks <3

Answer:

The identities of the terms are;

3 - 53 = y is an equation

7.5 < 2.9 is an inequality

2 + 0 is an expression

t is a term

24" is a term

Step-by-step explanation:

An equation is an expression with the equal to sign

3 - 53 = y is an equation

An inequality is a mathematical expression that contains an inequality sign

7.5 < 2.9 is an inequality

A term is a sole number or variable or the product of variables and numbers that come before and after mathematical operators such as +, ×, -, or ÷

t and 24" are terms.

Answer:

239 ft².

Step-by-step explanation:

Let P represent the price for tiling.

Let S represent the size of the room.

From the question,

Price (P) varies directly as the size (S) i.e

P & S

P = KS

Where K is the constant of proportionality.

Next, we shall determine the value of K as follow

Price (P) = $ 4224

Size (S) = 264 ft²

Constant of proportionality (K) =?

P = KS

4224 = K × 264

Divide both side by 264

K = 4224/264

K = 16

Finally, we shall determine the size of the kitchen that will cost $ 3824 for tiling.

This is illustrated below:

Price (P) = $ 3824

Constant of proportionality (K) = 16

Size (S) =?

P = KS

3824 = 16 × S

Divide both side by 16

S = 3824/16

S = 239 ft²

Therefore, the size of the kitchen is 239 ft².