Solve each system of equations by substitution. 4y=3x+6 2y=x+8

Answer: 258

Step-by-step explanation:

7/9 = 1800

2/9 = ?

= 258

Answer:

[tex]x-2y=3[/tex]

Step-by-step explanation:

[tex]We\ are\ given,\\Line\ passes\ through\ the\ points\ (1,-1) and (9,3). Hence,\ this\ means\ that\ the\\ points\ are\ indeed\ solutions\ of\ the\ equation,\ which\ represents\ the\ line.\\Hence,\\We\ know\ that,\\The\ equation\ of\ a\ line\ (Point-Slope)\ is\ given\ by:\\y-y_1=m(x-x_1),\ where\ m\ is\ the\ slope\ of\ the\ graph.[/tex]

[tex]So\ first,\\Lets\ find\ the\ Slope\ of\ the\ Graph.\\Slope(m)=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}\\Hence,\\Here,\\Considering\ (1,-1)\ as\ the\ First\ Point\ and\ (9,3)\ as\ the\ Second\ Point,\ we\ have:x_1=1,x_2=9\ and\ y_1= -1, y_2=3\\Plugging\ the\ values\ in\ the\ Equation\ for\ the\ Slope,\ we\ have:\\[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-1)}{9-1}=\frac{3+1}{9-1}= \frac{4}{8}=\frac{1}{2}\\Hence,\\Coming\ back\ to\ our\ Point-Slope\ Formula\ for\ the\ equation:\\\ We\ already\ have:\\y-y_1=m(x-x_1)\\Substituting\ m=\frac{1}{2} , x_1=1,\ y_1=-1,\ we\ have: \\y+1=\frac{1}{2}(x-1)\\\therefore 2(y+1)=x-1\\\therefore 2y+2=x-1\\\therefore 2y-x=-3\\Multiplying\ with\ (-1)\ on\ both\ sides:\\\therefore x-2y=3\\Hence,\\x-2y=3,\ is\ our\ desired\ equation.[/tex]

Answer:

option : b, c

Step-by-step explanation:

1 meter = 100 centimeters

45 meters = 4500 centimeters

1000 meter = 1 kilometer

 [tex]45 \ meters = \ \frac{45}{1000} = 0.045 \ kilometers[/tex]

1 meter = 1000 millimeters

45 meters = 45, 000 millimeters

Answer: 12

Step-by-step explanation: Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.

Answer:

Step-by-step explanation:

Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.

Answer:

use the Desmos graphing calculator.  Type the first one in.  Then type your answer choices in.  See which lines are the same.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Just simplify

Answer:

The correct answer is:

(a) 0.54

(b) 0.0385

Step-by-step explanation:

Given:

Restaurant tax,

p = 0.54

Sample size,

n = 168

Now,

(a)

The mean will be:

⇒ μ [tex]\hat{p}= p[/tex]

         [tex]=0.54[/tex]

(b)

The standard error will be:

[tex]\sigma \hat{p}[/tex] = [tex]\sqrt{[\frac{p(1-p)}{n} ]}[/tex]

    = [tex]\sqrt{[\frac{(0.54\times 0.46)}{168} ]}[/tex]

    = [tex]\sqrt{[\frac{(0.2484)}{168} ]}[/tex]

    = [tex]0.0385[/tex]

Answer:

3 gallons of carpet shampoo

Step-by-step explanation:

room area: 16 * 15 = 240 ft

1 gallon carpet shampoo: 80 ft

240/80 = 3

3 gallons of carpet shampoo are needed.

Answer:

4 StartRoot 3 EndRoot units

Hope this answer is right!!

Step-by-step explanation:

Since AD is perpendicular to BC, so ΔABD will be aright-angled triangle. Thus, the length of the altitude is 4√3 units.

The length of the altitude of the equilateral triangle is 4√3  units.

The given parameters;

The half length of the base of the triangle is calculated as follow;

[tex]x = \frac{8 \ units}{2} \\\\x = 4 \ units[/tex]

The height of the triangle is calculated by applying Pythagoras theorem as follows;

[tex]h^2 = L^2 - x^2\\\\h = \sqrt{(8^2) - (4^2)} \\\\h = \sqrt{48} \\\\h = \sqrt{16 \times 3} \\\\h = 4\sqrt{3} \ \ units[/tex]

Thus, the length of the altitude of the equilateral triangle is 4√3  units.

Learn more about equilateral triangle here: https://brainly.com/question/15294703

Answer:

The non-negative zero of the function f(x) is x = 2.

Step-by-step explanation:

For a given function f(x), the "zeros" of the function are the values of x such that:

f(x) = 0

In this case, we have the function:

f(x) = 6*x^2 - 9*x - 6

If we want to find the zeros of this function, we need to solve:

f(x) = 0 =  6*x^2 - 9*x - 6

To solve this, we can use the Bhaskara's formula, which says that for a general quadratic equation:

0 = a*x^2 + b*x + c

The zeros are:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

In this case our equation is:

0 =  6*x^2 - 9*x - 6

then, in the above notation, we have:

a = 6

b = -9

c = -6

Replacing these in our general formula, we get:

[tex]x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4*6*(-6)} }{2*6} = \frac{9 \pm 15 }{12}[/tex]

Then we have two zeros:

x = (9 + 15)/12 = 24/12 = 2

x = (9 - 15)/12 = -6/12 = -1/2

But we want only the non-negative, so we can discard the second one.

Concluding, the non-negative zero of the function f(x) is x = 2.

Answer:

good point I don't know that either

Answer:

[tex]M = (0,0)[/tex]

Step-by-step explanation:

Given

[tex](4,-5)[/tex] and [tex](-4,5)[/tex]

Required

The midpoint (M)

This is calculated as:

[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]

So, we have:

[tex]M = \frac{1}{2}(4-4,-5+5)[/tex]

[tex]M = \frac{1}{2}(0,0)[/tex]

[tex]M = (0,0)[/tex]

Given:

Line A goes through (0,y) and (-2,0).

Line B goes through (1,2) and (3,10).

To find:

The value of y for which the system of given linear equation (equation of line A and line B) has no solutions.

Solution:

Two linear equation has no solutions if they are parallel line.

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We know that the slopes of two parallel lines are the same.

So, the given system of given linear equation has no solutions if

Slope of line A = Slope of line B

[tex]\dfrac{0-y}{-2-0}=\dfrac{10-2}{3-1}[/tex]

[tex]\dfrac{-y}{-2}=\dfrac{8}{2}[/tex]

[tex]\dfrac{y}{2}=4[/tex]

Multiply both sides by 2.

[tex]\dfrac{y}{2}\times 2=4\times 2[/tex]

[tex]y=8[/tex]

Therefore, the required value of y is 8.

Answer:

Adult ticket = 38

Student ticket = 17

Step-by-step explanation:

Let :

Adult ticket = x

Student ticket = y

x + y = 55 - - - - (1)

Cost per x = 3.75

Cost per y = 2

3.75x + 2y = 176.50 - - - (2)

From (1):

x = 55 - y

Put in (2)

3.75(55 - y) + 2y = 176.50

206.25 - 3.75y + 2y = 176.50

-1.75y = - 29.75

y = - 29.75 / - 1.75

y = 17

From :

x = 55 - y

x = 55 - 17

x = 38

Answer:

D. None of the above

Step-by-step explanation:

The two right triangles have different sizes. Therefore, their areas cannot be the same as well.

Congruent triangles have the same three angles that are congruent to each other and three side lengths that are congruent or equal to each other. The two triangles only have equal angles bit different corresponding side lengths. Therefore, they cannot be congruent.

The correct answer is "None of the above".

Answer:

PROPORTIANAL SIDE LENGTHS

Step-by-step explanation:

I JUST TOOK THE TEST

Given:

Two dice are thrown.

[tex]E_1[/tex] is the event that the sum of their dots is a prime number

[tex]E_2[/tex] is the event that 5 is the dot on the top of second die.

To find:

Whether [tex]P(E_1\cap E_2)=P(E_1)\cdot P(E_2)[/tex] is true or false.

Solution:

If two dice thrown, then the total possible outcomes are:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).

[tex]E_1[/tex] is the event that the sum of their dots is a prime number.

[tex]E_1=\{(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)\}[/tex]

[tex]P(E_1)=\dfrac{15}{36}[/tex]

[tex]P(E_1)=\dfrac{5}{12}[/tex]

[tex]E_2[/tex] is the event that 5 is the dot on the top of second die.

[tex]E_2=\{(1,5), (2,5),(3,5),(4,5),(5,5),(6,5)\}[/tex]

[tex]P(E_2)=\dfrac{6}{36}[/tex]

[tex]P(E_2)=\dfrac{1}{6}[/tex]

The intersection of these two events is:

[tex]E_1\cap E_2=\{(2,5),(6,5)\}[/tex]

[tex]P(E_1\cap E_2)=\dfrac{2}{36}[/tex]

[tex]P(E_1\cap E_2)=\dfrac{1}{18}[/tex]

Now,

[tex]P(E_1)\cdot P(E_2)=\dfrac{5}{12}\cdot \dfrac{1}{6}[/tex]

[tex]P(E_1)\cdot P(E_2)=\dfrac{5}{72}[/tex]

[tex]P(E_1)\cdot P(E_2)\neq P(E_1\cap E_2)[/tex]

Therefore, the given statement is false because [tex]P(E_1\cap E_2)\neq P(E_1)\cdot P(E_2)[/tex].

Answer:

Step-by-step explanation:

What points were you given to choose from?

Answer:

thiếu giữ liệu không thể trả lời được

Step-by-step explanation:

Answer:

1/6 * 1/2 = 1/12

Step-by-step explanation:

1 number on a 6 sided die is 1 out of 6 (1/6) and an even number (2,4,6) on a 6 sided die is 3/6 or 1/2 (always simplify when multiplying fractions)

so 1 times 1 = 1 and 6 times 2 = 12 making it 1/12

Answer:

8 miles

Step-by-step explanation:

I'm going to assume the question said that she "couldn't" repair the tire and was forced to walk back home, that makes more sense.

With that in mind:

She rode her bike 2 miles.

She walked 4 miles on the way there, and 6 miles on the way back.

You can deduce that it was a 6 mile walk back because of the 2 mile bike ride, then the 4 mile walk that it took to get there.

All in all that rounds out to 10 mile walking, and 2 mile biking. That is 8 miles more walking than biking.

Answer:

yes but can be simplified

Step-by-step explanation:

area of shaded part = ( area of square - area of circle ) / 4

= [tex]\frac{12^2-\pi (6)^2}{4}[/tex]

= [tex]\frac{144-36\pi }{4}[/tex]

= [tex]\frac{144}{4}[/tex] - [tex]\frac{36\pi }{4}[/tex]

= 36 - 9π

Answer:

[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]

Step-by-step explanation:

Poorly formatted question.

The given parameters can be summarized as:

[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex] ----- the series

Required

Determine [tex]e^\frac{1}{5}^x[/tex]

We have:

[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex]

Substitute [tex]\frac{1}{5}x[/tex] for x

[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{(\frac{1}{5}x)^k}{k!}[/tex]

Split

[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]

Answer:

Oval frames = 17

Rectangular frames = 51

Step-by-step explanation:

Given that :

Paintings on wall are either oval or rectangular ;

Let :

Oval painting = x

Rectangular painting = y

According to the information given :

x + y = 68 - - (1)

Rectangular frames = 3 times oval frames

y = 3x - - - (2)

Put y = 3x in equation (1)

x + 3x = 68

4x = 68

x = 68/4

x = 17 frames

From :

x + y = 68

17 + y = 68

y = 68 - 17

y = 51

Oval frames = 17

Rectangular frames = 51

Answer:g(x) = 3/2x + 2 and a half?

Step-by-step explanation: sorry not good at college math, but at least i tried.

Answer is

5 gives the range of possible values for x.

Answer:

650 adult tickets and 250 children's tickets.

Step-by-step explanation:

Answer:

2x^2 + 4

Step-by-step explanation:

f(g(x)) just means to first solved g(x) and put the solution into f(x).

Therefore, it becomes f(x)=(10x^2+5)/5 + 3, and you can simplify that into

2x^2 + 4.

the answer is b no trend