Thomas is making fruit punch for a party. The recipe calls for 5/8 gallon of orange juice to make a full pitcher of punch.

How many full pitchers of punch can Thomas make with 2 gallons of orange juice

Answer:

x = 6

Step-by-step explanation:

The isosceles triangle is divided into two forming two right triangles

in right triangles the square value of hypotenuse is equal to sum of other two side lengths

x^2 + 4^2 = 52

x^2 + 16 = 52 subtract 16 from both sides

x^2 = 36 find the root for both sides

x = 6

The area covered by the roof would be 84.5 square yards.

To calculate the area covered by the roof the formula that should be used would be the formula for the area of a square;

That is ;

Area = 2(length×width)

= 2(6.5×6.5)

= 2(42.25)

= 84.5 yards²

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Answer:

D 1,433.25

Step-by-step explanation:

1/2(10)(7)=35

35*13=455

455*3.15=1,433.25

Answer:

D

Step-by-step explanation:

You need to find the volume of the attic (I would find the surface area myself -- but this is math. You just have to obey the rules of the question no matter how silly).

The Volume is found by V = B * h1

The base is a triangle.

b = 7 m

h1 = 10 m

Area = 1/2 * 7 * 10

area = 35 m^2

The volume of the attic is

V = B * h

V = 35 * 13

V = 455 m^3

The cost = cost /m^3  * m^3

m^3 = 455

Cost = 3.15 * 455

Cost = 1433.25

Step-by-step explanation:

Arlington is increasing because it has 1.027, if it was 0.27 it would be decreasing

If p(6)= 4107 that means after 6 years there would be a total population of 4107

hi  

x²-25 =  (x+5)  ( x-5)  

As a multiplication can only add up to zero if one of term is  0 ,

there is two solutions  :  

x+5 = 0

x = -5  

and   x-5 = 0

        x = 5  

So two solutions for  x² -25 = 0  which are   -5  and 5

Step-by-step explanation:

The first thing we have to do before we can actually do the problem is turn the words into a math equation.

If we use x as our "number," we see that "The sum of a number and 2" can also be written as x+2. The word "Is" almost always means (=), so now we have (x+2) = . The very last part, "6 less than twice that number," means 2x - 6.

So, our whole equation is, (x + 2) = (2x - 6), which simplifies to -x = -8, or

x = 8

Answer:

y = 8

Step-by-step explanation:

number = y

y + 2 = 2y - 6

y + 2 - 2 = 2y - 6 - 2

y = 2y - 8

y - 2y = 2y - 2y - 8

- y = - 8

- y × - 1 = - 8 × - 1

y = 8

Answer:

The answer for this question is C

Answer:

x + 2

Step-by-step explanation:

[tex]\frac{5x+10}{x^2 -x-6}[/tex] = [tex]\frac{5(x+2)}{(x-3)(x+2)}[/tex]

GCF ( 5x + 10, x² - x - 6) = x + 2

Step-by-step explanation:

5(x+2)/(x+2)(x-3)= 5/(x-3)

GCF: x+2

Answer:

A

Step-by-step explanation:

The tangent- tangent angle x is half the difference of the measures of the intercepted arcs.

minor arc = 360° - 254° = 106° , then

x = [tex]\frac{1}{2}[/tex] (254 - 106)° = [tex]\frac{1}{2}[/tex] × 148° = 74° → A

The value of angle x will be 74°. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

We know that the sum of the minor arc and major arc made by a tangent in a circle will be 360 degrees.

Then the measure of the minor arc will be

⇒ 360° - 254°

⇒ 106°

We know that the angle made by the tangent is half of the major arc to the minor arc.

x = (254° - 106°) / 2

x = 148° / 2

x = 74°

The value of angle x will be 74°.

Then the correct option is A.

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Answer:

Where is the picture of the triangle?

Answer:

(x + 5)(x + 5)

Step-by-step explanation:

[tex]x^2+10x+25\\(x+5)(x+5)[/tex]

Answer:

(x+5)(x+5)

Step-by-step explanation:

x²+10x+25

x²+5x+5x+25    

x(x+5)+5(x+5)            

(x+5)(x+5)

Answer:

31.5 m

Step-by-step explanation:

Let w represent the width of the pool.

Since the length is 15 m greater than the width, it can be represented by w + 15.

Use the perimeter formula, p = 2l + 2w. Plug in the perimeter, and w + 15 as l into the formula:

p = 2l + 2w

96 = 2(w + 15) + 2w

96 = 2w + 30 + 2w

96 = 4w + 30

66 = 4w

16.5 = w

So, the width of the pool is 16.5 m. Add 15 to this to find the length:

16.5 + 15

= 31.5

The length of the pool is 31.5 m

Let the width be w

Length = w + 15

Now

Perimeter = 2(l + w)

96 = 2(w + 15 + w)

96/2 = w + 15 + w

48 = 2w + 15

48 - 15 = 2w

33 = 2w

33/2 = w

16.5 = w

Then,

Length = w + 15

Length = 16.5 + 15

Length = 31.5 m

[tex] \\ [/tex]

Answer:

1. the area of the triangle minus the area of the small, inner rectangle. what did you not understand there ?

the standard formula (hi, internet !) for the area of a triangle is baseline×height/2.

the standard formula (hi, first grade !) for the area of a rectangle is length×width.

that's it.

1.a.

the volume of an object regularity shaped like a silo is always ground area times height.

for this object we only need to imagine to stand the object up sideways on the triangle side.

and don't forget - an area is always a square unit (like cm²,m², ft², ...). and a volume is always a cubic unit (like cm³, m³, ft³, ...).

so then, the triangle area is the ground area. and the original long side line of the object is is height.

as we said in 1. above, the area of a triangle is baseline×height (of the triangle, not of the overall object) divided by 2.

so, we have here 6×4/2 = 6×2 = 12 m²

and now the ground area × object height = 12×8=96 m³

b.

the standard formula for the volume of a ball (hi, internet !) is pi×r³.

so, we have here pi×9³. can you calculate that with your calculator ? that is pi×729 = 2290.221 cm³

2a.

the height of the cone is (as the drawing already suggests) determined via the right-angled triangle of the radius (half of the diameter) of the ground circle, the height of the cone and the length of the sideline on the outside mantle of the cone. this sideline is the Hypotenuse (the baseline of the triangle opposite of the 90 degree angle).

so, we use Pythagoras

c² = a² + b² (c being the Hypotenuse, a and b being the sides).

11² = 8² + h²

121 = 64 + h²

h² = 57

h = 7.55 cm

2b.

the standard formula for the volume of a cone (hi, internet !) is

pi×r²×h/3

pi×8²×7.55/3 = pi×64×7.55/3 = 506 cm³

Step-by-step explanation:

all of that you could easily search on the internet and since it yourself way faster than putting things in here and waiting for responses.

as there is really nothing to explain but just to use the standard formulas with the given numbers.

Answer:

380

Step-by-step explanation:

This is a bit nasty. It depends on how you read the 20 miles more and what you do with it. The best and most careful way to do it is do it a long way setting up the two equations carefully.

Second day

Let the time travelled = t

Let the speed travelled = 60 mph

d2 = 60*t

First Day

40*(t + 2) = d1

but d1 = d2 + 20 because he travelled 20 miles further on d1

40 * (t + 2) = d2 + 20

d2 however = 60*t

40*(t+2 ) = 60*t + 20          Remove the brackets

40t + 80 = 60t + 20           Subtract 20 from both sides

40t + 60 = 60t                   Subtract 40t from both sides

60 = 20*t                           Divide by 20

t = 60/20

t = 3 hours.

Day 2 = 60 + t = 180

Day 1 = 40*5  = 200

Total distance = 380

Where did that 20 miles go? It was just an observation about the difference in distance travelled between the 2 days.

The total distance the driver traveled in the two days is 260 miles

From the question, on the first day, the driver was going as a speed of 40 mph.

Let s be speed

∴ [tex]s_{1}= 40mph[/tex]

On the second day, he increased the speed to 60 mph

∴ [tex]s_{2}= 60mph[/tex]

From the statement- If he drove 2 more hours on the first day

Let time be t

Then

[tex]t_{1}= t_{2} + 2[/tex] hrs

and traveled 20 more miles

Let d be distance  

Then,

[tex]d_{1}= d_{2} + 20[/tex] miles

From the formula

Distance = Speed × Time

Then,

[tex]d = s \times t[/tex]

∴ [tex]d_{1} = s_{1} \times t_{1}[/tex]

From above,

[tex]d_{1}= d_{2}+20[/tex] miles

[tex]s_{1}= 40mph[/tex]

[tex]t_{1}= t_{2} + 2[/tex] hrs

Putting these into

[tex]d_{1} = s_{1} \times t_{1}[/tex]

[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex] ...... (1)

But,

[tex]Time = \frac{Distance}{Speed}[/tex]

∴ [tex]t_{2}= \frac{d_{2} }{s_{2} }[/tex]

From above, [tex]s_{2}= 60mph[/tex]

∴ [tex]t_{2}= \frac{d_{2} }{60}[/tex]

Put this into equation (1)

[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex]

[tex]d_{2} + 20 = 40\times (\frac{d_{2}}{60} +2)[/tex]

[tex]d_{2} + 20 = \frac{2}{3}d_{2} +80\\d_{2} = \frac{2}{3}d_{2} +80-20\\d_{2} = \frac{2}{3}d_{2} +60[/tex]

Multiply through by 3

[tex]3\times d_{2} = 3\times \frac{2}{3}d_{2} +3 \times 60\\3d_{2} = 2d_{2} + 120\\3d_{2} -2d_{2} = 120[/tex]

∴ [tex]d_{2} = 120[/tex] miles

∴The distance traveled on the second day is 120 miles

For the distance traveled on the first day,

Substitute [tex]d_{2}[/tex] into the equation

[tex]d_{1}= d_{2}+20[/tex] miles

∴ [tex]d_{1}= 120+20[/tex]

[tex]d_{1}= 140[/tex] miles

∴ The distance traveled on the first day is 140 miles

The total distance traveled in the two days = [tex]d_{1} + d_{2}[/tex]

The total distance traveled in the two days = 120 miles + 140 miles

The total distance traveled in the two days = 260 miles

Hence, the total distance the driver traveled in the two days is 260 miles

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Answer:

the third option=C -2,3

Step-by-step explanation:

solve simultaneously

Answer:

(-2,3)

Step-by-step explanation:

The solution to the system is where the two lines cross

x= -2

y = 3

(-2,3)

Answer:

Letter B. Hyperbole is your answer

Answer:

I say it's a

Step-by-step explanation:

I hope this help

Answer:

B

Step-by-step explanation:

each of the numbers is just adding 1.25 on to it

Answer: Choice B

16.00, 17.25, 18.50, 19.75, ...

==========================================================

Explanation:

We start with $16.00 as the first term, as this is the amount the boss pays him initially. Then we add on 1.25 to get 16+1.25 = 17.25 to represent the next wage after that first raise.

Then after the second raise he gets, he'll then earn 17.25+1.25 = 18.50 an hour. This process theoretically can go on forever, but realistically the boss will likely set some kind of limit.

We say that this sequence { 16.00, 17.25, 18.50, 19.75, ... } is arithmetic with the first term of 16.00 and common difference 1.25

The common difference is the gap width between any two neighboring terms, and it's the amount the wage goes up each time he gets a raise.

Answer: Pretty sure that it's y=-5/3x+8

Step-by-step explanation: Since the slope-intercept form is y=mx+b with b as the y-intercept and m as the slope. b would be 8 since that's where the line intercepts the y-axis and the slope is -5/3 (negative bc the line is slanted down)

Answer:

y = - [tex]\frac{8}{5}[/tex] x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (0, 8) and (x₂, y₂ ) = (5, 0 ) ← 2 points on the line

m = [tex]\frac{0-8}{5-0}[/tex] = [tex]\frac{-8}{5}[/tex] = - [tex]\frac{8}{5}[/tex]

The line crosses the y- axis at (0, 8 ) ⇒ c = 8

y = - [tex]\frac{8}{5}[/tex] x + 8 ← equation of line

Answer: [tex]270\ in.^3[/tex]

Step-by-step explanation:

Given

Volume of a gas varies inversely with pressure i.e.

[tex]V\propto \dfrac{1}{P}\\\\PV=\text{constant}[/tex]

Initially, [tex]V_1=450\ in.^3,P_1=3\ psi[/tex]

Then, pressure increases to [tex]P_2=5\ psi[/tex]

[tex]\therefore P_1V_1=P_2V_2\\\Rightarrow 3\times 450=5\times V_2\\\Rightarrow V_2=3\times 90\\\Rightarrow V_2=270\ in.^3[/tex]

Thus, volume decreases to [tex]270\ in.^3[/tex].

9514 1404 393

Answer:

  20 +2√10 ≈ 26.3 units

Step-by-step explanation:

Length AB is given as 10 units. Length AC is given as 2√10 ≈ 6.325 units. The length BC is the difference of the x-coordinates of its end points, since they are on a horizontal line: 5 -(-5) = 10 units.

The perimeter is the sum of the lengths of the sides of the triangle.

  P  = AB +AC +BC = 10 +2√10 +10 = 20 +2√10 ≈ 26.3 . . . units

Answer:

A, E or 1, 5

Step-by-step explanation:

Its not A, D

Answer:

x = 15

Step-by-step explanation:

The two angles form a straight line so they add to 180

6x-5+6x+5 = 180

Combine like terms

12x= 180

Divide by 12

12x/12 =180/12

x = 15

Answer:

Step-by-step explanation:

Equation of circle: (x - h)² + (y - k)² = r²   where (h,k) is the center.

Center( -4 , 4) and r = 5

(x -[-4])² + (y - 4)²= 5²

(x + 4)² + (y-4)² = 25

x²  + 2*4*x +4²  + y²  - 2*y*4 + 4²  = 25

x²  +8x + 16 + y²  - 8y + 16 = 25

x²  + 8x + y²  - 8y + 16 + 16 -25 = 0

x²  + 8x + y²  - 8y +7 = 0

We have that the an equation of a circle given the center (-4,4) and radius r=5  is mathematically given as

(x-4)^2+(y-4)^2=5^2

Question Parameters:

Given the center (-4,4) and radius r=5

Generally the equation for the Equation of a circle   is mathematically given as

(x-x')^2+(y-y')^2=r^2

Therefore, The resultant equation will be

(x-x')^2+(y-y')^2=r^2

(x-4)^2+(y-4)^2=5^2

Hence,an equation of a circle given the center (-4,4) and radius r=5 is

(x-4)^2+(y-4)^2=5^2

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Answer: 825

Step-by-step explanation:

Plug in the values for v = π*r²*h

So, your new equation is v = π*5²*11 (I got 5 because 10 is the diameter, the radius is half the diameter, therefore r = 5.)

The question is also telling us to replace π with 3.

now we solve, after gathering all of our information.

v = 3*5²*11

v=3*25*11

v=75*11

v=825

Answer:

4 1/3 of her hair

Step-by-step explanation:

Just add 2 1/6 + 2 1/6 and there you go

There is the total amount of her hair she cut

Answer:

I don't know search it up I picked B

okay it's 5 and I'm

Answer:

25%

Step-by-step explanation:

let the MP be x

sp without vat =x-16%of x

= 21x/25

sp with VAT = 21x/25 +13% of 21x/25

rs 9492 = 2373x/2500

( 9492*2500)/2373=x

x = 10000

cp = ((21x/25 )*100)/100+5 ( 5= profit percent )

=8000

(10000-8000)×100%/8000

=25%

Answer:

We have, sinx+sin3x+sin5x=0

∴(sinx+sin5x)+sin3x=0

∴2sin(

2

x+5x

)cos(

2

5x−x

)+sin3x=0

∴2sin3xcos2x+sin3x=0

∴sin3x(2cos2x+1)=0

Either sin3x=0 or 2cos2x+1=0

i.e. sin3x=0 or cos2x=−

2

1

Now, cos2x=−cos

3

π

∴cos2x=cos(π−

3

π

)

∴cos2x=cos

3

2π

∴sin3x=0 or cos2x=cos

3

2π

3x=nπ,n∈Z or 2x=2mπ±

3

2π

where m∈Z

Hence, x=

3

nπ

or x=mπ±

3

π

, where n,m∈Z.

Answer:

x=5

Step-by-step explanation:

-2(-3+ x) = -4

Distribute

-2 * -3 + (-2) *x = -4

6 -2x = -4

Subtract 6 from each side

6 -2x-6 = -4-6

-2x = -10

Divide each side by -2

-2x/-2 = -10/-2

x = 5

Answer:

5

Step-by-step explanation:

-2(-3+x)=-4

Use distributive property (Multiply -2 by -3 which gives you 6vand multiply -2 by x which gives you -2x )

6-2x=-4

Bring the 6 over to the other side

-2x=-4-6

-2x=-10

Divide both sides by -2 to get x by itself

x=5