Mrs. Webster wants to divide 6 pints of
water into 5-pint servings. How many
servings are possible? Explain how you
found your answer.

The solution is 2 and -7.

To find two numbers that multiply to -14 and add to -5, we can set up a system of equations based on the properties of multiplication and addition of numbers with different signs.

Let x and y be the two numbers we are looking for, with the following conditions:

x * y = -14 (Multiplication condition)

x + y = -5 (Addition condition)

Using the addition rules, we know that if we have two numbers with opposite signs, the sign of the larger (absolute value) number will dictate the sign of the result. Similarly, the multiplication rules tell us that two numbers with different signs will give a product with a negative sign.

Applying these principles, we can guess that one number is positive and the other negative since their product is -14. We also know that the number with the greater absolute value must be negative since their sum is -5. We can begin by listing pairs of factors of 14 (since the product is -14) keeping the sign in mind:

1 and -14

-1 and 14

2 and -7

-2 and 7

From this list, the pair that adds up to -5 is 2 and -7. Hence, the two numbers are 2 and -7.

Answer:

(cos a cos b - sin a sin b)

Step-by-step explanation:

It's easy

X=3.1:

Step-by-step explanation:

Answer:

3/2 m / sec²

Step-by-step explanation:

acceleration = change in velocity / time

Here, that would be

acc'n = 15 m/s  /  10 s = 3/2 m / sec²

Answer:

24 hours

Step-by-step explanation:

Answer:

$219.00.

Step-by-step explanation:

January 1, 10 units @ $8 (10 x 8)          = $80

January 18, 50 units @ $9 (50 x 9)      = $450

February 20, 20 units @ $11 (20 x 11)  = $220

March 15, 10 units @ $12 (10 x 12)        = 120

Ending Inventory = 19 unit

Ending Inventory = (10 x12) + (9 x 11) = $219

Answer:

$219.00 (or $220.00 because it's closest option to $219.00)

Step-by-step explanation:

Final answer:

To find how much money Ethan gave to Dakota, we need to set up and solve an equation based on the given conditions, include the initial difference of $8, the 1/4 transfer of funds, and the resulting 5:2 ratio of their money.

Explanation:

Ethan had $8 more than Dakota. When he gave 1/4 of his money to Dakota, the ratio of Ethan's money to Dakota's became 5:2. To solve this, let's assume Dakota originally had D dollars and Ethan had D + 8 dollars. After giving away 1/4 of his money to Dakota, Ethan would have 3/4 of D + 8, and Dakota would have D plus 1/4 of D + 8.

The new ratio of Ethan's money to Dakota's money is 5/2, leading us to the equation 3/4(D + 8) / (D + 1/4(D + 8)) = 5/2. Solving this equation will not only give us the initial amounts of money each person had but also allow us to calculate the exact amount Ethan gave to Dakota, which is the 1/4 of Ethan's original money.

Answer: x= 178. Meaning that x can only equal 178, so that statement can be true. Any other number makes this statement false.

Step-by-step explanation:

Answer:

Lemme break it down for ya. Something plus seventy- two equal two hundred fifty. And if you want or need the answer, all you got to do is subtract 250 and 72. You're welcome. And please follow me.

Yo sup??

a5=a+4d

a10=a+9d

a20=80=a+19d

a+4d+a+9d=a+19d

a=6d

80=6d+19d

80=25d

d=3.2

a=19.2

a30=a+29d

=19.2+92.8

=112

Hope this helps.

Answer:

7.5 inches.

Step-by-step explanation:

Angular velocity  (ω) in radians per minute

= 16* 2π    (as there are 2π radians in 1 revolution)

= 32π radians per minute.

= ω.

Linear velocity V =  ω r      where r = the radius of the circle.

Therefore:  240π = 32π r

r = 240 / 32

r = 7.5 inches.

Answer:

36.

Step-by-step explanation:

6 times 6 equals 36.

Answer:

b is right on plato

Step-by-step explanation:

Answer: Correct answer is B

Step-by-step explanation:

Answer:

≈268.08 [tex]ft^{3}[/tex]

C. 267.9 [tex]ft^{3}[/tex]

Step-by-step explanation:

Equation of volume of a sphere:

Plug in radius (r) into the equation:

Solve using a calculator:

≈268.08 [tex]ft^{3}[/tex]

Answer:

Step-by-step explanation:

first you find that it is t=Tracy and d= Daniel

so the equation is t= d-38*3 now find the answer

Daniel spent $16.

Let's denote the amount Daniel spent as x dollars.

According to the given information, Tracy spent $38 less than 3 times what Daniel spent. Therefore, Tracy's expenditure can be represented as [tex]\( 3x - 38 \)[/tex] dollars.

Given that Tracy spent $10, we can set up the equation:

[tex]\[ 3x - 38 = 10 \][/tex]

Now, let's solve for x:

[tex]\[ 3x = 10 + 38 \][/tex]

[tex]\[ 3x = 48 \][/tex]

[tex]\[ x = \frac{48}{3} \][/tex]

[tex]\[ x = 16 \][/tex]

So, Daniel spent $16.

The complete Question is given below:

While shopping for clothes, tracy spent $38 less than 3 times what daniel spent. write and solve an equation to find out how much daniel spent. let x represent how much daniel spnet. tracy spent 10$

Answer:

the total mass is 456 grams.

Step-by-step explanation:

After adding his phone/internet/cable, electric bill, and health insurance premium costs, Chester spends $696 on bills each month. With monthly earnings of $2800, he therefore should have around $2104 left over after paying these bills.

To figure out how much money Chester will have left after paying his bills, you first have to add up all his bills. So, he pays on average $120 for his phone/internet/cable service, $277 for his electric bill, and $299 for his health insurance premium.

To add these together: 120 + 277 + 299 = $696. This is the total amount Chester pays for his bills each month.

Now, subtract this total from Chester's monthly earnings. So, Chester earns $2800 per month, and his bills total $696. So, 2800 - 696 = $2104. Therefore, Chester will have around $2104 left each month after paying these bills.

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The ratios 26:169 and 36 to 78, when expressed as fractions in simplest form, are 2/13 and 6/13, respectively, after identifying and dividing by their greatest common factors.

The task is to express each ratio as a fraction in its simplest form. Let's tackle each ratio one at a time.

A. 26:169

To convert the ratio 26:169 into a fraction in simplest form, we observe that both numbers are divisible by their greatest common factor (GCF), which is 26. Dividing both terms by 26, we get 1/6.5. However, to express this in terms of whole numbers, multiplying numerator and denominator by 2 gives us 2/13, which is the fraction in its simplest form.

B. 36 to 78

For the ratio 36 to 78, first, we convert it into fraction form, which is 36/78. The GCF of 36 and 78 is 6. Dividing both the numerator and the denominator by 6, we get 6/13. Therefore, the simplest form of the ratio 36 to 78 is 6/13.

Answer:

4√10

Step-by-step explanation:

√(8) √(20)

= √(8 x 20)

= √(160)

= √(16 x 10)

= √(16) x √(10)

= 4 x √10

= 4√10

Answer:

4[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

[tex]\sqrt{8}[/tex] × [tex]\sqrt{20}[/tex]

= [tex]\sqrt{8(20)}[/tex]

= [tex]\sqrt{160}[/tex]

= [tex]\sqrt{16(10)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{10}[/tex]

= 4[tex]\sqrt{10}[/tex]

Answer:

x=7

Step-by-step explanation:

3x + 2(4 + 6x)= 113

you multiply 2 to 4 that gives you 8 and 2 to 6 that gives you 12x because the 6 has x on it

so it will be 3x + 8 + 12x= 113 then you add 3x to 12x

then you would have 15x+8=113 then subtract 8 to 113 then divide that number to 15 and you get x=7

Answer: [tex]Percent\ change=37.5\%[/tex]  (It is an increase)

Step-by-step explanation:

You need to use the following formula to find the Percent change:

[tex]Percent\ change=\frac{V_2-V_1}{|V_1|}*100[/tex]

Where [tex]V_1[/tex]  is the Initial value and [tex]V_2[/tex] is the Final value.

According to the information given in the exercise, there were 800 visitors on Saturday and 1,100 visitors on Sunday. Then, you can identify that:

[tex]V_1=800\\\\V_2=1,100[/tex]

Then, knowing these values, you must substitute them into the formula:

[tex]Percent\ change=\frac{1,100-800}{|800|}*100[/tex]

Finally, you must evaluate in order to find the Percent change from the number of park visitors on Saturday to the number of park visitors on Sunday.

You get that this is:

[tex]Percent\ change=\frac{300}{|800|}*100\\\\Percent\ change=37.5\%[/tex]

Since it is positive, it is an increase.

Answer:

37.5 percent

Step-by-step explanation:

Answer:

  π

Step-by-step explanation:

The integral decomposes into the sum ...

  [tex]\displaystyle\int_{-2}^2{\left(x^3\cos{\dfrac{x}{2}}\right)\sqrt{4-x^2}}\, dx+\dfrac{1}{2}\int_{-2}^2{\sqrt{4-x^2}}\, dx[/tex]

The first term of this sum is the integral of an odd function, so is zero. The second term of this sum is 1/2 the area under a semicircle of radius 2, so is ...

  A = (1/2)(1/2)π·2² = π

The value of the integral is π.

The volume of the cylinder is [tex]1539 cm^3[/tex]

Step-by-step explanation:

The volume of a cylinder is given by the equation

[tex]V=\pi r^2 h[/tex]

where

[tex]\pi r^2[/tex] is the area of the base, with r being the radius

h is the height

For the cylinder in this problem we know:

h = 10 cm (height)

c = 44 cm (circumference of the base)

The circumference is given by

[tex]c=2\pi r[/tex]

So the radius is

[tex]r=\frac{c}{2\pi}=\frac{44}{2\pi}=7 cm[/tex]

Therefore, the volume of the cylinder is:

[tex]V=\pi (7)^2 (10)=1539 cm^3[/tex]

Learn more about volume of a solid:

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[tex]\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 5\log(x)+6\log(x+7)\implies \log(x^5)+\log\left[ \left( x+7 \right)^6 \right] \implies \log\left[ x^5\left( x+7 \right)^6 \right][/tex]

Answer: log(x^5(x+7)^6)

Hope that helps! (:

They are not all squares because a rhombus has all sides of equal length, but NO right angles. A square is a rhombus WITH right angles.

Hope that clears things up.

Answer:

Step-by-step explanation:

Given system of equations are

   y= -3x+4

⇔3x+y=4 .........(1)

 x= 2y+6

⇔x-2y=6...........(2)

Equation (1) ×2 +equation (2)

6x +2y+x-2y =8+6

⇔7x=14

[tex]\Leftrightarrow x= \frac{14}{7}[/tex]

⇔x = 2

Putting the value of x in equation (1)

3.2+y=4

⇔y+6=4

⇔y=4-6

⇔y=-2

Therefore x=2 and y=-2

Answer:

the answer is x=-1 and y=9. Hope this helps!

PLEASE GIVE BRAINLEST

Step-by-step explanation:

The given system of linear equations:

x - 2y = 8                        ........ (1)

and 4x + y = 5               ........ (2)

To find, the values of x and y = ?

Multiplying equation (2) by 2, we get

2(4x + y) = 5 × 2  

⇒ 8x + 2y = 10                ........ (3)

Adding equations (1) and (3), we get

x - 2y + (8x + 2y) = 8  + 10  

⇒ x - 2y + 8x + 2y = 8  + 10

⇒ 9x = 18

⇒ x = 2

Put x = 2 in (1), we get

2 - 2y = 8        

⇒ 2y =2 - 8

⇒ 2y = - 6

⇒ y = - 3

∴  x = 2 and y = - 3

Answer:

El encuentro se producirá a 240 km de Morelia

Step-by-step explanation:

Velocidades Relativas

Este es un caso donde las velocidades son sumativas, pues ambos móviles van a su encuentro mútuo. La distancia total de 660 km será cubierta por ambos móviles con una velocidad relativa de 70 km/h + 40 km/h = 110 km/h

Ya que :

[tex]\displaystyle v=\frac{x}{t}[/tex]

Tenemos que

[tex]\displaystyle t=\frac{x}{v}[/tex]

[tex]\displaystyle t=\frac{660}{110}= 6 \ h[/tex]

Tomás anda a 70 km/h, así que en 6 horas recorre

[tex]x_t=6\times 70 = 420\ Km[/tex]

Claudia anda a 40 km/h, así que en las mismas 6 horas ha recorrido

[tex]x_c=6\times 40 = 240\ Km[/tex]

Se puede decir entonces, que el encuentro se producirá a 240 km de Morelia

Answer:

       [tex]\large\boxed{\large\boxed{240km}}[/tex]

Explanation:

Since the question is in Spanish, I will give you the answer in Spanish.

En el punto de encuentro las distancias recorridas por Tomás y Claudia suman la distancia que existe entre Ixtapa y Morelia.

La distancia que recorre cada uno es igual al producto de su velocidad por el tiempo de recorrido.

         [tex]distancia=velocidad\times tiempo\\ \\ d_{Tomas}=70km/h\times t[/tex]

          [tex]distancia=velocidad\times tiempo\\ \\ d_{Claudia}=40km/h\times t[/tex]

Los tiempos, [tex]t[/tex] , son los mismos al momento de encuentro, así que puedes crear una ecuación con una sola incógnita:

           [tex]d_{Tomas}+d_{Claudia}=660Km=70km/h\times t+40km/h\times t[/tex]

Puedes obviar las unidades para resolver la ecuación:

         [tex]660=70t+40t\\ \\ 660=110t\\ \\ 660/110=t\\ \\ 6=t\\\\ t=6[/tex]

El resultado es en horas: t = 6 horas.

         [tex]d_{Claudia}=40km/h\times t=40km/h\times6h=240km[/tex]

Y esa es la respuesta. Se encontrarán a 240 km de Morelia.