How many solutions does this linear system have?
y = 2/3x+ 2
6x - 4y = -10
• one solution: (-0.6, -1.6)
O one solution: (-0.6, 1.6)
no solution
infinite number of solutions

The required equation of parabola is y = (-1/4)(x-9)² +4

What is a Parabola ?

A parabola is a U shaped Curve , whose all point are at same distance from a point called as Focus and a line called as Directrix.

Let (x,y) be any point on the parabola.

the distance between (x,y) and the focus and the distance between (x,y) and directrix is equal.

The focus is at (9,0) and a directrix at y= - 4

[tex]\rm \sqrt {(x-9)^2 + (y -0)^2[/tex]  = | y +4|

[tex]\rm {(x-9)^2 + (y -0)^2 = (y-4)^2[/tex]

(x-9)²  + y² = y² +16 -4y

On solving this

4y = - (x-9)² +16

y = (-1/4)(x-9)² +4

Therefore this is the required equation of parabola .

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Answer:

A = 55 degrees

B = 35 degrees

C = 90 degrees

side BA = 4.8 units

side AC = 2.7 units

side BC = 3.9 units

Step-by-step explanation:

Hello!

The things we know:

A = 55 degrees

C = 90 degrees

side BA = 4.8 units

AC = adjacent side

BC = opposite side

AB = hypothenuse

B = 180 - 55 - 90 degrees

B = 35 degrees

Let's find side AC

we can use the cos of theta.

cos(55) = AC/4.8

multiply 4.8 on both sides.

4.8cos(55) = AC

AC = 2.7 units

And now we just have to find BC

to calculate BC we can either use tangent or sin.

I will just use sin

sin(55) = BC/4.8

multiply 4.8 on both sides.

4.8sin(55) = BC

BC = 3.9

And now we know everything about the triangle

Hope I Helped!

Answer: 9

Step-by-step explanation:

[tex](f \circ g)(0)=f(g(0))\\\\g(0)=2\\\\\implies f(g(0))=f(2)=\boxed{9}[/tex]

The graph which represents the rational function is; On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

It follows from the task content that the rational function given is; f(x) = 3x-2/x-2.

Hence, since the numerator and denominator polynomials are of the same order, it follows that the horizontal asymptote is the quotient; 3/1 = 3.

Additionally, the vertical asymptote of the function is the value of x which renders the denominator equal to 0 and consequently, the function undefined.

Hence, x -2 = 0 and x= 2.

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Answer: THE PERSON ABOVE IS CORRECT!!

The answer is D.) On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

here u go hope this helps

Answer:

V = 343

Step-by-step explanation:

V = lwh

= 7(7)(7)

= 49(7)

= 343

Answer:

B

Step-by-step explanation:

[tex]\frac{4x}{9}[/tex] - [tex]\frac{2x}{9}[/tex]

since the denominators are common , then subtract the numerators, leaving the common denominator.

= [tex]\frac{4x-2x}{9}[/tex]

= [tex]\frac{2x}{9}[/tex]

Answer:

x=7 and x = 1

Step-by-step explanation:

This is pretty much a quadratic in disguise.
If we multiply both sides by x, we get:
x^2-7=6x
move 6x to the left
x^2-6x-7 = 0
We can either use the quadratic formula, or we can use factoring.
with factoring*, we get:
(x-7)(x+1) = 0 , and so the solution to the equation is x=7, and x=-1

*in a equation: x^2+ax+b = (x+c)(x+d), c+d equals a, and c*d equals b

On to the quadratic formula, a=1, b=-6, and c=-7, so:
(6±sqrt(36+4*7))/2 = x
=(6±8)/2
=3±4
x=7 and x = 1

Answer:

B. 44.93

Step-by-step explanation:

The law of sines states
[tex]\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

where a, b and c are the 3 sides of the triangle and A is the angle opposite side a, B the angle opposite side b and C the angle opposite side c

In this particular problem we have

side a = 44, angle A = 46.7
side c = ? , angle C = 48

So 44/sin(46.7) = c/sin(48) or by multiplying both sides by sin(48)

c = sin(48) * 44/sin(46.7)  = 44.92937 which is 44.93 rounded to 2 decimal places

Let x = number of hours washing cars

Let y = number of hours landscaping

System of equations:

[tex]10x+8y=84\\\\x=2y[/tex]

The correct statement about the matrix is B. B^-1.

From the information, it can be seen that the matrix is 2 by 2. Based on the information about the matrix, 1/3AB = 1/3BA.

From this, it can be depicted that the inverse of B illustrates that:

A(1/3B) = (1/3B)

This illustrates that the correct is B.

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Answer:

Tan p is 20/21

Tan q is 21/20

Step-by-step explanation:

Tan is short for tangeant.

tangeant means opposite/adjacent

the opposite of vertices p is 20.

the adjacent of vertices p is 21.

so tan p= 20/21

The opposite of vertices q is 21

the adjacent of vertices q is 20

so tan q is 21/20

Answer:

B and D

Step-by-step explanation:

A

[tex]\frac{5}{6}[/tex] × 13 = [tex]\frac{5(13)}{6}[/tex] = [tex]\frac{65}{6}[/tex] = 10 [tex]\frac{5}{6}[/tex] < 13

B

4 × 13 = 52 > 13

C

[tex]\frac{3}{4}[/tex] × 13 = [tex]\frac{3(13)}{4}[/tex] = [tex]\frac{39}{4}[/tex] = 4 [tex]\frac{3}{4}[/tex] < 13

D

[tex]\frac{10}{10}[/tex] × 13 = 1 × 13 = 13

Band D are equal to or greater than 13

Answer:

Complementary angles are:

∠ORS and ∠SRQ

Supplementary angles are:

∠ORP and ∠PRQ

Answer: y(-3y^7+18y^4+10)

Step-by-step explanation:

Answer:

The new store will have a profit of $5400 after its fifth month.

(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9

(Use 5 for x)

(R-C)(5) = 9(5) + 9 = 45+9 = 54

Answer:Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.Which expression can you use to find 23% of 52? ✔ 0.23 × 5223% of $52 is $✔ 11.96.An easy way to check your answer is to use the friendly ✔ 25%and divide 52 by ✔ 4to get ✔ 13

Step-by-step explanation:

Answer:

17 square centimeters.

Step-by-step explanation:

Divide the rectangle into a 3x5 rectangle and a 2x1 rectangle.

(3x5)+(2x1)=17

17 square centimeters.

Answer:

1±i sqrt(7/2)

Step-by-step explanation:

For this equation you would need to use quadratic formula: x=(-b+-square root b^2-4ac)/2a

Answer:the answer is option E (see pic)

Step-by-step explanation:

One root would be: x =(4-√88)/-4=1+1/2√ 22 = 1.345

Answer:

c = 75.36 cm

Step-by-step explanation:

The equation of the circumference is:

[tex]c=\pi d[/tex]  In which "d" represents the measurement of the diameter

in this case d= 24cm, π = 3.14

Calculate the circumference:

[tex]c=\pi d=(3.14)(24)=75.36cm[/tex]

Hope this helps

A circle has a diameter of 24cm. The circumference of the circle is c = 75.36 cm.

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

Given information;

A circle has a diameter of 24cm.

"d" represents the measurement of the diameter, so

d= 24cm, π = 3.14

Radius = d/ 2 = 12

Calculate the circumference:

The circumference of the circle = 2πr

= 2 ( 3.14 ) ( 12)

= 75.36

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The length of the rectangle is 8m and width of the rectangle is 7m

Given that the length and width of a rectangle are consecutive integers

Let the length of the rectangle be x+1 meter

Let the breadth of the rectangle be x meter

Also given that perimeter of the rectangle is 30 meters

To find length and breadth of the rectangle

We know that perimeter of the rectangle is P = 2 (l+b)

30 = 2 (x+x+1)

15 = 2x + 1

2x = 14

x = 7

x+1 = 8

Hence, the length of the rectangle is 8m and width of the rectangle is 7m

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The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

Total rupees withdraw from saving account is $149

Let total amount in account before withdrawing is X= $500

Amount left after withdraw the money is calculated by a

AMOUNT LEFT = TOTAL AMOUNT - WITHDRAW AMOUNT

So, put the values then

Y= X($500) - $149

Y= $500 - $149

Y= $351

If we represent the balance of saving account in the integer form then it become the Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

So, The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

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Answer:

y = -x + 1

(Image of what graph looks like is attached)

Step-by-step explanation:

x = 1 - y can be rewritten into y = mx + b format.

x = 1 - y (subtract 1 from both sides)

x - 1 = -y (multiply by -1 to both sides)

y = -x + 1

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The total weight of the packed box is 9 lb 6 oz

According to question:

The weight of 12 jars is 12 times the weight of one jar

The weight of jars and box together is the sum of those weights.

... 12 × (10 oz) + 1 lb + 14 oz = 1 lb + 134 oz

... = 1 lb + 8 × (16 oz) + 6 oz . . . . . . 1 lb = 16 oz

... = 9 lb 6 oz

1 ounce (oz) is equal to 0.0625 pounds (lb).

1 oz = (1/16) lb = 0.0625 lb

The mass m in pounds (lb) is equal to the mass m in ounces (oz) divided by 16:

m(lb) = m(oz) / 16

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Answer: After working for 33 [tex]\frac{1}{3}[/tex] hours a week

Step-by-step explanation:

     Let us write equations to represent these two places. Let x be hours worked and y be money earned.

   Tim Hortons:

$200 + $5x = y

    McDonalds:

$300 + $2x = y

    Now, to find the conditions of which Tim Hortons is the better employer (on the basis of money earned) we must find the interval that Tim Hortons pays more. This can be found by setting up another equation, or by graphing. I have shown both. See attached for the graph.

$200 + $5x > $300 + $2x

$5x > $100 + $2x

$3x > $100

x > [tex]\frac{100}{3}[/tex]

x > 33.3334

    Tim Hortons is the better employer after an employee has worked for 33 [tex]\frac{1}{3}[/tex] hours a week.

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Answer:

[tex]m\angle{ABC}=144^{\circ}[/tex]

Step-by-step explanation:

By using Angle Addition Postulate, it holds:

[tex]m\angle{ABD}+m\angle{DBC}=m\angle{ABC}[/tex]

Substitute [tex]m\angle{ABD}=76^{\circ}[/tex] and [tex]m\angle{DBC}=68^{\circ}[/tex] into the equation:

[tex]76^{\circ}+68^{\circ}=m\angle{ABC}[/tex]

Add the measures:

[tex]m\angle{ABC}=144^{\circ}[/tex]

The sale price of the car as a percentage of the original price is 142%

Sale price as a percentage of the original price = sale price / buying price

= 1280/900 × 100

= 1.42222222222222 × 100

= 142.22%

Approximately,

142%

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The distance from Bobby to the plane is 154.7 yards.

Sine law can be used to find the distance of the plane to Bobby.

Therefore,

x / sin 40 = 240 / sin 95

cross multiply

Hence,

x sin 95 = 240 sin 40

divide both sides by sin 95

x  =  240 sin 40 / sin 95

x = 240 × 0.64278760968 / 0.99619469809

x = 154.08 / 0.9961

x = 154.683264732

x = 154.7 yards

Therefore, the distance from Bobby to the plane is 154.7 yards.

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Step-by-step explanation:

x + 2x + 7x

72 = 9x

72 - 9 = x

63 = x

63 ÷ 3 = 21

piece 1 = 21

piece 2 =21+2 = 23

piece 3 =21+7 = 28

21+23+28 = 72 This proves the above is correct.

Answer:

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