The banquet room is being carpeted. A floor plan of the room is shown below. Each unit represents 1 yard. The carpet costs $23.50 per square yard. How much will it cost to carpet the room?

Answer:

Then the solution is (-1/4, 3)

Step-by-step explanation:

Start by eliminating the fractional coefficient 1/4:  multiply all 3 terms in the second equation by 4.  This results in equation (b), below:

4x - 3y = -10   (a)

4x = y -4         (b)  

Substitute y - 4 for 4x in equation (a):

y - 4 - 3y = -10

Combining like terms, we get -2y = -10 + 4, or -2y = -6, or y = 3.

Since x = (1/4)y - 1, if y = 3, then x = (1/4)(3) - 1, or x = 3/4 - 1, or x = -1/4

Then the solution is (-1/4, 3)

Answer:

Step-by-step explanation:

angle 4 is congruent to angle 4 because they are alternate interior angles.

angle 5 is congruent to angle 3 because they are alternate interior angles.

angle 1+angle 2+angle 3 is equal to (=) angle 1+angle 2+angle 3

angle 1+angle 2+angle 3=180 degree(being sum of interior angles of a trianngle)

Answer:

4/3

Step-by-step explanation:

-(16/9) = (p/q) (-4/3)

(-16/9)*(-3/4) = (p/q)

4/3 = p/q

Answer:

Step-by-step explanation:

Let the number be x

[tex]x *\frac{-4}{3}=\frac{-16}{9}\\\\x=\frac{-16}{9}*\frac{3}{-4}\\\\x=\frac{4}{3}[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]x=5,\:x=-11[/tex]

Step-by-step explanation:

We solve this with the quadratic formula.

[tex]x_1=\frac{-6+16}{2\cdot \:1},\:x_2=\frac{-6-16}{2\cdot \:1}[/tex]

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Answer:

196608

Step-by-step explanation:

Answer:x

=4

permiter=6

area=24

Step-by-step explanation:

Answer:

x = 8, area = 364 km^2, perimeter = 80 km

Step-by-step explanation:

to start, we have to recognize that opposite sides of a rectangle are congruent.

therefore ➪

2x + 10 = 4x - 6

2x + 16 = 4x

16 = 2x

x = 8

now just plug that in and you'll find ➪

length = 26km

width = 14km

area = l * w

area = 26 * 14

area = 364 km^2

perimeter = 2(l + w)

perimeter = 2(14+26)

perimeter = 80 km

Answer:

y = -3x+ 4

one equation two unknows can not solve uniquely

4y = -12x + 16

y = -3x+ 4

is the solution set

Step-by-step explanation:

Answer:

[tex]x = \frac{ 16 - 4y}{12}[/tex]

Step-by-step explanation:

12x + 4y = 16

12x + 4y - 4y = 16 - 4y

12x = 16 - 4y

[tex]\frac{12x}{12} = \frac{ 16 - 4y}{12}[/tex]

[tex]x = \frac{ 16 - 4y}{12}[/tex]

Refer to the attachment...

Since the line is parallel to the given equation , slope of required line = slope of the given equation of line

slope = -1/2

Answer:

A

Step-by-step explanation:

Answer:6. =    7. <     8.<     9. >    10. >    11.<.  12.<     13.=

14. 0.51,0.52, 0.59         15. 7.1, 7.15, 7.18         16.  1.03, 1.3, 1.33

Step-by-step explanation:

Answer:

Area = 21.7777 m²

Step-by-step explanation:

Side of the square = 14 / 3.

Area of the square = side²

→ (14/3)²

→ 196/9

→ 21.7777 m²

Answer:

Step-by-step explanation:

Given

[tex] {7}^{4} \div 7[/tex]

Since,

[tex] {a}^{x} \div {a}^{y} = {a}^{x - y} [/tex]

Hence,

[tex] = {7}^{4 - 3} [/tex]

[tex] = {7}^{3} (ans)(as \: a \: single \: power \: of \: 7)[/tex]

Answer:

D

Step-by-step explanation:

Frizzy cola is 4.1 through 4.3 inclusive

This means that the pH Range of frizzy cola is between 4.1 to 4.3(including 4.3)

If the pH value is represented as h :

The the lower bound will be 4. 1

Upper bound will be 4.3

This means :

4.1 less than or equal to h and h is less than or equal to 4.3

4.1 ≤ h ≤ 4.3

Since, 7 is neutral, values below 7 are acidic while above 7 are alkaline ;

The range is below 7, hence, frizzy cola is acidic.

4.1 ≤ h ≤ 4.3 ; acidic

Answer:

18 N

Step-by-step explanation:

Let F denote the force, m denote the mass of the object and a denote the acceleration of the object.

[tex]F=ma[/tex]

[tex]m = \frac{F_{1} }{a_{1} }=\frac{63}{7} =9 kg[/tex]

[tex]F_{2} =ma_{2}=9*2=18N[/tex]

Answer:

D or C

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The graph goes up meaning it is positive.

Hey there!

[tex]\mathsf{\dfrac{3^4}{14-5}\times2}[/tex]

[tex]\mathsf{3^4}[/tex]

[tex]\mathsf{= 3 \times 3 \times3 \times3}[/tex]

[tex]\mathsf {= 9\times9}[/tex]

[tex]\mathsf{= \bf 81}[/tex]

[tex]\mathsf{14 - 5}[/tex]

[tex]\mathsf{= \bf 9}[/tex]

[tex]\mathsf{\dfrac{81}{9}\times2}[/tex]

[tex]\mathsf{\dfrac{18}{9}}\\\\\mathsf{= 81\div9}[/tex]

[tex]\mathsf{\bf = 9}[/tex]

[tex]\mathsf{9\times2}[/tex]

[tex]\mathsf{= \bf 18}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: \bf18}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

[tex]Given,[/tex]

∠CBA=(7x+6)°

∠EBD=(9x-24)°

[tex]Now,[/tex]

∠CBA=∠EBD (vertically opposite angles)

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

hope it helps...

have a great day!!

Answer:

(6x + 5)(x + 2)

Step-by-step explanation:

x coefficients must multiply to 6

so 6 * 1 or 2*3

10 must be 5*2 or 1* 10

(6x + 5)(x + 2) = (6x² + 12x + 5x + 10) = 6x² + 17x + 10

Answer:

50°

Step-by-step explanation:

The sum of the internal angles of a triangle is always 180°. The PQR triangle have 70° + 60° = 130°, so it need to have more 50° to complete 180°, and the angle x have the same size that this "missing angle" from the PQR triangle because the angle x is formed by the same segments, so it have 50°

Answer:

x = 10

Step-by-step explanation:

The secant- secant angle 3x is half the difference of the intercepted arcs, that is

3x = [tex]\frac{1}{2}[/tex] (4x + 50 - 30 )

3x = [tex]\frac{1}{2}[/tex] (4x + 20) = 2x + 10 ( subtract 2x from both sides )

x = 10

Answer: The longest possible length of the shelves =  18 inches

Step-by-step explanation:

Given: Lengths of two boards are  72-inches and 54 inches.

To make as many shelves as he can while using up all the wood we will find the longest possible length of the shelves = HCF ( 72, 54)

72 = 2 x 2 x 2 x 3 x 3

54 = 2 x 3 x 3 x 3

HCF(72,54) = 2 x 3 x 3 = 18

Hence, the longest possible length of the shelves =  18 inches

Answer:

Step-by-step explanation:

11 ÷ 4 = 2 + 2 = 4

1 + 4 + 4 = 9

19 ÷ 4 = 4

Answer:

all real values

Step-by-step explanation:

there is no value for x, where the operations in f(x) would run into an undefined or outright invalid situation. whatever x we can think of, f(x) will calculate a valid y.

Part (a)

The angles would stay the same. This is because similar figures keep the same shape, but the size will shrink or grow.

A real world application is to simply move your head closer to the page and the figure will appear to get larger. The angles themselves stay the same but the side lengths will get larger.

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

Part (b)

While the angles stay the same under a dilation operation, the side lengths do not. As the instructions state: "The side lengths are 3 times longer" (paraphrased).

So we multiply each side length in the diagram by 3

Refer to the diagram below. I've used the resize feature to enlarge the image to make figure DEFG

Question 1 (The wood question)

Answer: 14 7/8

Explanation: (see attached photo!)

Question 2 (The graph question)

Answer: multiply the number of weeks by 3

Explanation: Look at the point where it's between 2 and 4

I hope this helps!

Answer:

p = 6x + 10

Step-by-step explanation:

p = 2(l + w)

p = 2(6 + (3x - 1))

Simplify terms inside parenthesis

p = 2(3x + 5)

Distribute

p = 6x + 10

Answer:

x= 15

Step-by-step explanation: