You have 12 gallons of punch. You estimate that each guest will drink 3 cups. Do you have enough punch for 60 guests?

Answer:

D

Step-by-step explanation:

Plug it in 108 divide by 6

Answer:

y = - ( x + 2 )² + 14

Step-by-step explanation:

f(x) = ax² + bx + c

f(x) = a(x - h)² + k (where (h, k) are coordinates of the vertex.

h = - [tex]\frac{b}{2a}[/tex]

~~~~~~~~~~~~

f(x) = - x² - 4x + 10

a = - 1, b = - 4, c = 10

h = - [tex]\frac{-4}{2(-1)}[/tex] = - 2

k = - ( - 2)² - 4( - 2) + 10 = 14

(h, k) = ( - 2, 14 )

y = - ( x + 2 )² + 14

Answer:

Rounded down to the nearest foot, the length of the garden is nine feet.

Step-by-step explanation:

We're told that the length of the chicken coop, 3x + 12 feet, is equal to the length of the garden, 6x - 16 feet.  Let's put them together then and solve for x:

3x + 12 = 6x - 16

First, we'll subtract 6x from both sides

3x - 6x + 12 = 6x - 6x - 16

-3x + 12 = -16

Now we subtract 12 from both sides:

-3x + 12 - 12 = -16 - 12

-3x = -28

Finally divide both sides by -3

-3x / -3 = -28 / -3

x = 28/3

x = 9 and 1/3

As the question asks for the number of feet only (not inches), the answer is nine feet.

A third of a foot though is four inches, so the more exact answer is nine feet and four inches, or 9'4"

The roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k

The equation is given as:

x^2 + (1 - k).x+k-3 = 0

For an equation to have real root, then the following must be true:

[tex]b^2 \ge 4ac[/tex]

In x^2 + (1 - k).x+k-3 = 0, we have:

a = 1

b = 1 - k

c = k - 3

So, we have:

[tex](1 - k)^2 \ge 4 * 1 * (k - 3)[/tex]

Evaluate

[tex]1 - 2k + k^2 \ge 4k - 12[/tex]

Collect like terms

[tex]k^2 - 2k - 4k + 1 + 12 \ge 0[/tex]

[tex]k^2 - 6k + 13 \ge 0[/tex]

Using a graphing calculator, the value of k is all real numbers

Hence, the roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k

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The value of the function when x=3 is approximately 18.83.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

The function

Now,

we need to substitute x=3 into the function and simplify it. We get:

3(3)−1​+(1+3)2

=8​+16

≈2.83+16

=4

Therefore, by the given function answer will be 4.

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Answer:

2)The answer is x*a^2 because the equation is saying a^b*a^2. And if we knew that a^b = x, then the answer is x*a^2

Step-by-step explanation:

Answer:

I think the answer would be y<4

Answer:

-1/3x+2y=4

Step-by-step explanation:

Substitute the negative reciprocal.

-1/3x+2y=4

Missing information:

How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point

[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]

Answer:

[tex]Rate = 0.935042^\circ /cm[/tex]

Step-by-step explanation:

Given

[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]

[tex]T(x,y) =x\sin2y[/tex]

[tex]r = 1m[/tex]

[tex]v = 2m/s[/tex]

Express the given point P as a unit tangent vector:

[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]

[tex]u = \frac{\sqrt 3}{2}i - \frac{1}{2}j[/tex]

Next, find the gradient of P and T using: [tex]\triangle T = \nabla T * u[/tex]

Where

[tex]\nabla T|_{(\frac{1}{2}, \frac{\sqrt 3}{2})} = (sin \sqrt 3)i + (cos \sqrt 3)j[/tex]

So: the gradient becomes:

[tex]\triangle T = \nabla T * u[/tex]

[tex]\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] * [\frac{\sqrt 3}{2}i - \frac{1}{2}j][/tex]

By vector multiplication, we have:

[tex]\triangle T = (sin \sqrt 3)* \frac{\sqrt 3}{2} - (cos \sqrt 3) \frac{1}{2}[/tex]

[tex]\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)[/tex]

[tex]\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5[/tex]

[tex]\triangle T = 0.935042[/tex]

Hence, the rate is:

[tex]Rate = \triangle T = 0.935042^\circ /cm[/tex]

9514 1404 393

Explanation:

Use the identities ...

  csc(x) = 1/sin(x)

  cot(x) = cos(x)/sin(x)

__

  [tex]\csc(x)(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{1}{\sin(x)}(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{\sin(x)}{\sin(x)}+\dfrac{\cos(x)}{\sin(x)}=1+\cot(x)\\\\1+\cot(x)=1+\cot(x)[/tex]

Answer:

Simplified - 2x(-x+4), Solution - -2x(-x+4)

Answer:

I think the answer should be.

B

Answer:

B

Step-by-step explanation:Edg 2021

Answer:

470 x 1.1 = 517

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

3/12=x/20

cross multiply

12x=3(20)

12x=60

x=60/12

x=5

Answer:

10,000.

Step-by-step explanation:

The solution is, Total assets is 164754.

Assets are resources controlled by the entity as a result of past events and from which future economic benefits are expected to flow to the entity (AAA).

here, we have,

we know,

Mortgage is recorded separated by the home and is treated as liability

Loan & Auto loan are also liabilities of Matthew

Credit cards balances are only his indication of capacity to buy which is if that happens said transaction would result into an obligation of Matthew to pay or simply his liability

we have,

Based on the data given, assets is computed as follows;

Cash (checking account)= 2000

Cash (savings account)= 10000

Home =120000

Investments =12789

Car= 19965

Total assets is = 164754

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complete question:

Matthew currently has $2,000 in his checking account and $10,000 in a savings account. He owns a home worth $120,000 and he owes $75,900 on his mortgage. His investments in a 401(k) are valued at $12,789. He owes $29,526 on his student loans and just bought a new car. The car is currently valued at $19,965. His auto loan balance is $19,156. He is carrying a balance on two credit cards that adds up to $5,234. What is the value of Matthew's total assets? (Do not include the $ sign or commas in your answer).

Answer:

195

Step-by-step explanation:

Therefore, the monthly change in the frog population over the last four months is [tex]195[/tex].

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

As per the given information,

The monthly change in the frog population over the last four months is [tex]195[/tex].

Hence, the monthly change in the frog population over the last four months is [tex]195[/tex].

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Answer:

$1.53 for tax

Step-by-step explanation:

18 times .085 = 1.53

Answer:

lcm of

Step-by-step explanation:

it is 12and 2.........

Answer:

ummmm, i cant see the graph

Step-by-step explanation:

Answer:

your answer is five

Step-by-step explanation:

and stay safe and happy

Answer:

32

Step-by-step explanation:

15x+19=2(10x+2)

15x+19=20x+4

19-4=20x-15x

15=5x

x=3

PQ=QN

10x+2=

10(3)+2=

30+2=

32

Answer:

No, Yes, No

Step-by-step explanation:

3in by 4in by 5in will not make a triangle.

3in by 4in by 6in will make a triangle.

1m by 2m by 3m will not make a triangle.

The reason two of these triangles cannot be form is because the side lengths do not adhere to the triangle inequality theorem. This theorem states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.

9514 1404 393

Answer:

  224 cubes

Step-by-step explanation:

In terms of 1/4 cm cubes, the dimensions of the prism are ...

  (2 cm)/(1/4 cm/cube) = 8 cubes long

  (7/4 cm)/(1/4 cm/cube) = 7 cubes wide

  (1 cm)/(1/4 cm/cube) = 4 cubes high

The volume in 1/4-cm cubes is ...

  V = LWH = (8)(7)(4) = 224 . . . cubes

224 cubes are required to fill the volume.

Answer:

The answer for the question is 3/10

Answer:

B is the correct answer

Answer:

la respuesta que buscas es bastante simple pero no lo sé

Step-by-step explanation:

Answer:

89.7 is the percent

Step-by-step explanation:

38.41/43.7=0.879 (87.9%).