You need to buy a carpet that measures 7.5 yards long and 5 yards wide and costs $49.50 per square yard. How much will the carpet for the room cost?

Answer:

c= 13

Step-by-step explanation:

The complementary angles add up to 90° so we use some basic algebra to solve this question. like in the step by step explaination I have provided on paper

Answer:

Step-by-step explanation:

Answer:

[tex]38[/tex] and [tex]68[/tex].

Step-by-step explanation:

Let [tex]x[/tex] be the smaller one of the two number.

[tex]x[/tex] must be a positive integer. The other number would be [tex](x + 30)[/tex].

The question states that the product of the two numbers is [tex]2584[/tex]. In other words:

[tex]x\, (x + 30) = 2584[/tex].

Rearrange this equation and solve for [tex]x[/tex]:

[tex]x^{2} + 30\, x - 2584 = 0[/tex].

The first root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}[/tex].

Similarly, the second root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}[/tex].

Since the question requires that both numbers should be positive, [tex]x > 0[/tex]. Therefore, only [tex]x = 38[/tex] is valid.

Hence, the two numbers would be [tex]38[/tex] and [tex](38 + 30)[/tex], which is [tex]68[/tex].

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Answer:

  38 and 68

Step-by-step explanation:

Let x represent the average of the two numbers. Then their product is ...

  (x -15)(x +15) = 2584

  x^2 = 2584 +225 = 2809 . . . . . . use relation (x -a)(x +a) = x^2 -a^2; add a^2

  x = √2809 = 53

Then the two numbers are ...

  53 +15 = 68

and

  68 -30 = 38

The two numbers are 38 and 68.

_____

Additional comment

Solving the problem in this way is equivalent to writing the quadratic equation for the smallest (or largest) number and solving that by completing the square. The "solution" x = -53 is not relevant in this problem.

Answer:

C) [tex]y = \frac{1}{2}[/tex] × [tex]4^x[/tex]

Answer:

C.    y= 1/2*4^x

Step-by-step explanation:

Answer:

=fx+5f

Step-by-step explanation:

=fx+5f

Answer:

5 + 8 × 4

Assuming "five and eight" means 5 + 8

Answer:

3rd, y=-1/5x

Step-by-step explanation:

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Answer:

  $63.75

Step-by-step explanation:

Mike's final price will be 1-25% = 75% of the marked price.

  ($80 +5)(0.75) = $63.75

The final price for Mike's purchase is $63.75.

Answer:

1st box: 1

2nd box: 1

Step-by-step explanation:

1: 3 * 7 = 21, so only put the 1 and carry the 2.

2: 5 * 6 = 30, but we have a 1 from the previous answer given so 31, but only put the 1.

I hope this helps :)

Answer:

[tex] \frac{3}{4} n = 12[/tex]

Step-by-step explanation:

let the number be n :

[tex] \frac{3}{4} \: of \: n = 12 \\ \\ \frac{3}{4} n = 12[/tex]

further more:

[tex]3n = 12 \times 4 \\ n = \frac{12 \times 4}{3} \\ \\ n = 4 \times 4 \\ n = 16[/tex]

Answer:

3x4=12

Step-by-step explanation:

Answer:

m = -1

Step-by-step explanation:

Find the equation in slope intercept form [ y = mx + b ] for line AB. Find the slope using the formula [ y2-y1/x2-x1 ].

8-5/7-4

3/3

1

Find the y-intercept.

5 = 1(4) + b

5 = 4 + b

1 = b

So the equation of the line AB is y = x + 1.

The slope of a perpendicular line is the opposite reciprocal of the original line.

1 -> -1/1 -> -1

Best of Luck!

Answer:

the answer is "B"

the "a" (as in ax^2) is negative thus the parabola "goes downward"

Step-by-step explanation:

The equation of parabola is,

y = - 1/2x²

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.

We have to given that;

In a parabola,

Vertex = (0, 0)

Since, We know that;

Standard form of equation of parabola is,

y = a (x - h)² + k

Where, (h, k) = (0, 0) = vertex

Hence, We get;

y = a (x - 0)² + 0

y = ax²

Here, A point on parabola is, (2, - 2)

- 2 = a (2)²

a = - 2 / 4

a = - 1/2

Hence, The equation of parabola is,

y = - 1/2x²

Learn more about parabola visit:

https://brainly.com/question/29635857

#SPJ7

Answer:

because P(x) has factors of (x-2) and (x+1) => x = 2 and x = -1 are the solutions of P(x)

so we have:

[tex]\left \{ {{2^{4}+2^{3}a-2^{2}+2b-12 =0} \atop {1-a-1-b-12=0}} \right.\\=>\left \{ {{8a+2b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{4a+b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{a=4} \atop {b=-16}} \right.[/tex]

=> [tex]P(x)=x^{4} + 4x^{3}-x^{2} -16x-12[/tex]

With P(x) = 0

=> [tex]x^{4}+4x^{3}-x^{2} -16x-12 = 0[/tex]

=> ........

Step-by-step explanation:

Answer:

So coming back to the question; No, there is no rational number that is not an integer but is a whole number. The number is called as a rational number if it can be expressed as p/q where p & q are integers & q is not 0. All negative integers are rational numbers but those are not whole numbers.Jan 1, 2020

Step-by-step explanation:

Answer:

3=g/-4  -5

3+5=g/-4

8= g/-4

8x(-4)=g

g=-32

Step-by-step explanation:

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Explanation:

If you can't operate a calculator, perhaps you can do long division. The attachment shows the work for that.

__

  [tex]\dfrac{20}{8}=\dfrac{5\cdot4}{2\cdot4}=\dfrac{5}{2}\\\\=\dfrac{5\cdot5}{2\cdot5}=\dfrac{25}{10}=2.5[/tex]

We assume that you know dividing by 10 moves the decimal point one place left.

Answer:

1360

Step-by-step explanation:

there are 1200 seconds in 20 minutes. if Ella can do 17 jumps in 15 seconds, you would divide 1200 by 15 (which equals 80) because that would be the number of 15 seconds in 20 minutes. then you would divide 80 by 17, which gives you your final answer of 1360 jumps in 20 minutes.

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Answer:

Step-by-step explanation:

The speed difference between boat and current is the upstream rate:

  (448 km)/(8 h) = 56 km/h

The sum of speeds of boat and current is the downstream rate:

  (440 km)/(5 h) = 88 km/h

The rate of the boat is half the sum of these:

  (56 +88)/2 = 72 . . . km/h

The rate of the current is half their difference:

  (88 -56)/2 = 16 . . . km/h

The rate of the boat is 72 km/h; the rate of the current is 16 km/h.

Answer:

Step-by-step explanation:

answer: 9

Step-by-step explanation:

x = - 4; y = 3; z = 2;2 x² - 2 z^4 + y² - x² + z^4 = = 2 * (-4)² - 2 * 2^4 + 3² - ( -4)² + 2^4 == 2 * 16 - 2 * 16 + 9 - 16 + 16 = = 32 - 32 + 9 - 16 + 16 = 9

-7/10 + (-5/6) = -(7/10 + 5/6) =

= -(21/30 + 25/30) = -46/30 =

= -1 16/30 = -1 8/15 ← the end

Answer:

5 more matches was won by yu-na kim

Answer:

23.8 years

Step-by-step explanation:

Assuming this is compound interest, we'll use the compound interest formula

A = P(1 + r)ⁿ

A = Final amount (2000)

P = Initial amount (500)

r = Annual interest rate (.06)

n = ?

Our equation will look like this

2000 = 500(1.06)ⁿ

First, divide both sides by 500

2000/500 = (500(1.06)ⁿ)/500

(1.06)ⁿ = 4

Then we have to take the log₁.₀₆ out of both sides

n = log₁.₀₆(4)

n = 23.79132

Answer:

D . p = 50

Step-by-step explanation:

To find the value of p we first need to find the values of inner angles

180 - 140 (linear pair)

= 40

180 -90 (linear pair)

= 90

now use angle sum property of triangle

40 + 90 + p = 180

130 + p = 180

p = 180 - 130

p = 50

Answer: The length of LK is 40.

Step-by-step explanation:

LK = 6x+10

KM = 2x+8

LM = 58

so

LM = LK + KM

or, 58 = 6x+10+2x+8

or, 58 = 8x + 18

or, 58-18 = 8x

or, 8x = 40

so, x = 5

now

LK = 6x + 10

     = 6*5+10

     = 30 +10

     = 40

Answer:

I belive I might be c not completely sure but pretty positive