3. Evaluate the expression. If k = 3 and h = 2. (Be sure to show each step)
4k+2(5k-2)-h

9514 1404 393

Answer:

  x = 8/7

Step-by-step explanation:

The only real zero of this linear function is the value of x that makes y=0:

  0 = -7x +8

  7x = 8 . . . . . . add 7x

  x = 8/7 . . . . . .divide by 7

Answer:

solid shade above

Step-by-step explanation:

graph line same way you would if it was an equal sign

all the y's that are greater are above the line

its solid because is greater than OR equal to. Equal to includes the line itself as a set of solutions

9514 1404 393

Answer:

  a.  x + 4y = 160

  b.  160

  c.  40

Step-by-step explanation:

a. We can define the variables as ...

  x = number of 1/2-liter bottles

  y = number of 2-liter bottles

For the total number of liters to be 80, we require

  1/2x + 2y = 80

We can multiply this by 2 to eliminate the fraction.

  x + 4y = 160

__

b. The x-intercept is 160. It is the number of 1/2-liter bottles required when no 2-liter bottles are used.

__

c. The y-intercept is 40. It is the number of 2-liter bottles required when no 1/2-liter bottles are used.

Answer:

x = -5y

Step-by-step explanation:

x = ay

-10 = 2a

a = -5

x = ay

-15 = 3a

a = -5

x = ay

-25 = 5a

a = -5

Answer:

First find the SA of the triangular figure

4 x 3 = 12 cm^2 (the triangles on the sides)

2 x 3 = 6 cm^2 (the back square)

2 x 5 = 10 cm^2 (the slanted square)

*I'm not sure if this question includes the bottom of the triangle but here it is anyways

4 x 2 = 8 cm^2

Including the bottom the SA of the triangular figure is:

12 + 6 + 10 + 8 = 36 cm^2

Find the SA of the rectangular shape

4 x 2 = 8 cm^2 (the bottom square)

2 x 6 = 12 x 2 = 24 cm^2 (the sides)

4 x 6 = 24 x 2 = 48 cm^2 (the front and back)

Add them up

8 + 24 + 48 = 80 cm^2

If you wanted to find the SA of the whole figure it would be:

12 + 6 + 10 + 8 + 24 + 48 = 108 cm^2

Hope this helps!

Answer:

13.96units

Step-by-step explanation:

To get the length of CD, we will use the cosine rule as shown:

CD² = DE²+CE²-2(DE)(CE)cos m<E

Substitute the given values

CD² = 14²+9²-2(14)(9)cos71

CD² = 196 + 81 - 252cos71

CD² =277 - 252cos71

CD² = 277 - 82.0431

CD² = 194.95682

CD = √194.95682

CD = 13.96 units

Hence the length of CD of 13.96units

Answer:

4x^2 + 2x + 4

Step-by-step explanation:

5x^2 + 2x + 4 - x^2

4x^2 + 2x + 4

Answer:

2(2x^2 + x + 2)

Step-by-step explanation:

5x^2+2x + 4-x^2

Re arrange so like terms are next to each other

Keep the same symbol that is at the front of the term when moving it

5x^2 - x^2 + 2x + 4

We will just do the first part first

5x^2 - x^2

5x^2 - 1x^2 (is the same thing as above)

So because they are like terms (are both x^2)

We can just minus 1 from 5

5-1=4

So 4x^2

Now the equation is

4x^2 + 2x + 4

This is as small as it gets but you can also bring it to this

4, 2 and 4 all are divisible by 2 so

2(2x^2 + x + 2)

Answer:

its c

Step-by-step explanation:

Answer:

Area = 96 square m

Step-by-step explanation:

[tex]Area = base \times height = 12 \times 8 = 96 \ m^2[/tex]

Answer:

The area of parallelogram is 96 m ².

Step-by-step explanation:

According to the question , we have given a parallelogram with base 12 m and height is 8 m. We need to find the area of parallelogram.

Using Formula

Area of parallelogram = Base × Height

Substitute the values into this formula

Area of parallelogram = 12 m × 8 m

multiply, we get

Area of parallelogram = 96 m²

Therefore, The area of parallelogram is 96 m ².

Answer:

after 10 months

Step-by-step explanation:

Let x be the number of months and y be the amount they still owe.

Sin Ian borrows $1000 from his parents, then the y-intercept b= 1000 since he owes $1000 when x = 0. He pays them back $60 each month The slope is then m = -60 . Substituting in b = 1000 and m = -60 into the slope-intercept form of a line then gives y= mx + b=-60x +1000.

Sin Ken borrows $600 from his parents, then the y-intercept b = 600 since he owes $600 When x= 0. He pays them back $20 per month so the amount he owes decreases $20 each month. The slope is then m = -20 . Substituting in

b= 600 and m = -20 into the slope-intercept form then gives y = mx +b = -20x + 600.

They will owe the same amount when they have the same y-coordinate. Therefore -60x+ 1000= y= -20x+600. Solve this equation for x:

-60x+ 1000 = -20x+ 600

1000 = 40x+ 600

400 = 40x

10=x

They will then owe the same amount after 10 months.

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {D. \:= 2 {x}^{2} - \frac{1}{3} x}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

[tex] \frac{1}{3} x \: ( \: 6x - 1 \: )\\[/tex]

[tex] = \frac{x \: ( \: 6x - 1 \: )}{3}\\[/tex]

[tex] = \frac{6 {x}^{2} - x}{3} \\[/tex]

[tex] = \frac{6 {x}^{2} }{3} - \frac{x}{3}\\ [/tex]

[tex] = 2 {x}^{2} - \frac{1}{3} x\\[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]

Answer:

27

Step-by-step explanation:

The expected count in a χ² test can be obtained thus :

Expected count for each each point in a two way table ::

(row total * column total) / total

Therefore, expected count for cell corresponding to people from United Kingdom whose favorite sport is tennis :

Row total = (51+14+86+29) = 180

Column total = (25 + 29) = 54

Total = 360

Hence,

Expected count = (180 * 54) / 360

Expected count = 27

Answer:

F(-2)= g(-2)

Step-by-step explanation:

F(-2)= g(-2), both function have the same points of intersect.

Step-by-step explanation:

Given: [∀x(L(x) → A(x))] →

[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

To prove, we shall follow a proof by contradiction. We shall include the negation of the conclusion for

arguments. Since with just premise, deriving the conclusion is not possible, we have chosen this proof

technique.

Consider ∀x(L(x) → A(x)) ∧ ¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

We need to show that the above expression is unsatisfiable (False).

¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

∃x¬((L(x) ∧ ∃y(L(y) ∧ H(x, y))) → ∃y(A(y) ∧ H(x, y)))

∃x((L(x) ∧ ∃y(L(y) ∧ H(x, y))) ∧ ¬(∃y(A(y) ∧ H(x, y))))

E.I with respect to x,

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ ¬(∃y(A(y) ∧ H(a, y))), for some a

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ (∀y(¬A(y) ∧ ¬H(a, y)))

E.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b))) ∧ (∀y(¬A(y) ∧ ¬H(a, y))), for some b

U.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Since P ∧ Q is P, drop L(a) from the above expression.

(L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Apply distribution

(L(b) ∧ H(a, b) ∧ ¬A(b)) ∨ (L(b) ∧ H(a, b) ∧ ¬H(a, b))

Note: P ∧ ¬P is false. P ∧ f alse is P. Therefore, the above expression is simplified to

(L(b) ∧ H(a, b) ∧ ¬A(b))

U.I of ∀x(L(x) → A(x)) gives L(b) → A(b). The contrapositive of this is ¬A(b) → ¬L(b). Replace

¬A(b) in the above expression with ¬L(b). Thus, we get,

(L(b) ∧ H(a, b) ∧ ¬L(b)), this is again false.

This shows that our assumption that the conclusion is false is wrong. Therefore, the conclusion follows

from the premise.

15

Answers:

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

Explanation:

The simple interest formula is

i = p*r*t

where in this case,

So,

i = p*r*t

i = 3000*0.10*0.25

i = 75 is the amount of interest earned

This adds onto the initial deposit to get the final balance when the CD matures (ie when you're able to withdraw the money without penalties)

The balance at maturity is p+i = 3000+75 = 3075 dollars

---------------

In short, you deposit $3000 into the CD and have to wait 3 months for the amount to update to $3075.

Answer:

Step-by-step explanation:

Given that:

[tex]y^2 (y^2-4) = x^2(x^2 -5)[/tex]

at point (0, -2)

[tex]\implies y^4 -4y^2 = x^4 -5x^2[/tex]

Taking the differential from the equation above with respect to x;

[tex]4y^3 \dfrac{dy}{dx}-8y \dfrac{dy}{dx}= 4x^3 -10x[/tex]

Collect like terms

[tex](4y^3 -8y)\dfrac{dy}{dx}= 4x^3 -10x[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

Hence, the slope of the tangent line m can be said to be:

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

At point (0,-2)

[tex]\dfrac{dy}{dx}= \dfrac{4(0)^3 -10(0)}{4(-2)^3-8-(2)}[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{0 -0}{4(-8)+16}[/tex]

[tex]\dfrac{dy}{dx}= 0[/tex]

m = 0

So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:

(y - y₁ = m(x - x₁))

y + 2 = 0(x - 0)

y + 2 = 0

y = -2

Answer:

Angle A = [tex]77^{o}[/tex]

Step-by-step explanation:

cos A = adjacent / hypotenuse

cos A = 18/82

cos A = 0.22

A = [tex]cos ^{-1}[/tex]0.22

A = [tex]77^{o}[/tex]

Answer:

54 pounds

Step-by-step explanation:

To find out how much flour is needed to make 9 cakes, we first need to find out how much much flour is needed to make 1 cake. For that, we need to divide 6 by 36. That will give you 6. Now that we know how much flour is needed to make 1 cake, we will just have to multiply 6 by 9 to find out how much flour is needed to make 9 cakes. That will give you 54 pounds, which is your final answer.

Answer:

[tex]\displaystyle x \approx 9.9[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 64°

Opposite Leg = x

Hypotenuse = 11

Step 2: Solve for x

Answer:

Hi, there the answer is

These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Hope This Helps :)

Step-by-step explanation:

First degree equations

A first degree equation has the form

ax + b = 0

There are some special cases where the equation can have one, infinitely many or no solution

If , the equation has exactly one solution

If a=0 and b=0 the equation has infinitely many solutions, because it doesn't matter the value of x, it will always be true that 0=0

If a=0 and  the equation has no solution, because it will be equivalent to b=0 and we are saying it's not true. No matter what x is, it's a false statement.

We have been given some equations, we only need to put them in standard form

-5x + 12 = –12x – 12

Rearranging

7x + 24 = 0

It has exactly one solution because a is not zero

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

-5x + 12 = 5x + 12

Rearranging

-10x + 0 = 0

It has exactly one solution because a is not zero

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

-5x + 12 = 5x – 5

Rearranging

-10x + 17 = 0

It has exactly one solution because a is not zero

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

-5x + 12 = -5x – 12

Rearranging

0x + 24 = 0

It has no solution, no matter what the value of x is, it's impossible that 24=0

Answer: These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Answer:

17

Step-by-step explanation:

2a+30 = 4a-4

+4 +4

2a+34 = 4a

-2a -2a

34 = 2a

÷2 ÷2

a=17

Hope this helps! :)

Answer:

A = 17

Step-by-step explanation:

Opposite angles are congruent in a parallelogram

Hence 2a + 30 = 4a - 4

( Note that we've just created an equation that we can use to solve for a)

We now solve for a

2a + 30 = 4a - 4

Add 4 to both sides

2a + 34 = 4a

Subtract 2a from both sides

34 = 2a

Divide both sides by 2

a = 17

Answer:

0

Step-by-step explanation:

Ignore the next 2 numbers after 0.05. To the nearest whole number, round 0.05 to the nearest tenth, 0.1. Then round that to the nearest whole number, 0, which is your answer.

Answer:

D. 3

Step-by-step explanation:

Distance between A and D = AD = 9 units

Distance between A and B = AB = 3 units

[tex] \frac{AD}{AB} = \frac{9}{3} [/tex]

Simplify by dividing

[tex] \frac{AD}{AB} = \frac{3}{1} [/tex]

[tex] \frac{AD}{AB} = 3 [/tex]

The answer is 3

Answer:

100°

Step-by-step explanation:

the lower right angle is 180-149 = 31°

the sum of all three angles in a triangle is 180°.

so the solution is 180-31-49

Answer:

that's my answer

hope it helps

9514 1404 393

Answer:

  (x, y) = (5, -2)

Step-by-step explanation:

Equating expressions for y, we have ...

  x^2 -9x +18 = x -7

  x^2 -10x +25 = 0 . . . . . add 7-x to both sides

  (x -5)^2 = 0 . . . . . . . . factor

The value of x that makes the factor(s) zero is x=5. The corresponding value of y is ...

  y = x -7 = 5 -7 = -2

The solution is (x, y) = (5, -2).

Answer:

Undefined

Step-by-step explanation:

The square root of a negative number does not exist in the set of real numbers so it would be Undefined