Solve the system of equations using elimination.

4x - 7y = 5
9x – 7y = –15

Answer:

F. y= -[tex]\frac{1}{3\\}[/tex]x

Step-by-step explanation:

A proportional relationship between x and y exists if it can be expressed in the form y/x=k or y=kx. From the choices listed, F. y= -[tex]\frac{1}{3\\}[/tex]x is the only equation expressed in this form.

The correct option is J. [tex]\( y = 2x - 4 \).[/tex]

To determine which equation represents a proportional relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we need to look for an equation where [tex]\( y \)[/tex] is a constant multiple of [tex]\( x \)[/tex], and passes through the origin (0,0). A proportional relationship can be expressed in the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.

Let's analyse each option:

F. [tex]\( y = -\frac{1}{3}x \)[/tex]

This equation represents a proportional relationship with a constant of proportionality [tex]\( k = -\frac{1}{3} \)[/tex].

G. [tex]\( y = -x + 1 \)[/tex]

This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is 1).

H. [tex]\( y = \frac{3}{2}x + \frac{3}{2} \)[/tex]

This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is [tex]\( \frac{3}{2} \))[/tex].

J. [tex]\( y = 2x - 4 \)[/tex]

This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is -4).

Answer:

The measure of each interior angle of the dodecagon is 150 degrees.

Step-by-step explanation:

(n - 2) x 180 = 1800       Use the equation to find the number of sides

n - 2 = 10                        Divide by 180 on both sides

  + 2  + 2                        Add 2 to both sides

n = 12

Take the sum of the interior angles divided by the number of sides to find the measure of each angle

1800/12 = 150 degrees for each angles of the dodecagon.

Answer:

Step-by-step explanation: so, u would do 80 times 30 which equals 2400. Then u would divide 2,400 by 4 which gives u ur answer which is 60ft long! :)

Answer:

if im right its 110ft

Step-by-step explanation:

Answer:

Its height is 24.71 centimeters.

Step-by-step explanation:

Given:

The volume of a rectangular pyramid  is 10,500 cubic centimeters.

It has a  length of 15 centimeters and a width of  85 centimeters.

Now, to find the height.

Let the height be [tex]h.[/tex]

Volume of rectangular pyramid  = 10,500 cubic centimeters.

Length (l) = 15 centimeters.

Width (w) = 85 centimeters.

Now, to get the height by putting formula:

[tex]Volume=\frac{l\times w\times h}{3}[/tex]

[tex]10500=\frac{15\times 85\times h}{3}[/tex]

[tex]10500=\frac{1275h}{3}[/tex]

Multiplying both sides by 3 we get:

[tex]31500=1275h[/tex]

Dividing both sides by 1275 we get:

[tex]24.71 =h\\\\h=24.71\ centimeters.[/tex]

Therefore, its height is 24.71 centimeters.

Answer:

First Option

Step-by-step explanation:

An exponent is how many times you multiply a number by its self, in this case, that's 5 times

Answer:

[tex] \frac{32}{243} \\ [/tex]

Step-by-step explanation:

[tex] = ( { \frac{2}{3})}^{5} \\ \\ = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} [/tex]

The value of B = [tex]\dfrac{2S-NA}{N}[/tex]

Step-by-step explanation:

The given equation,

[tex]S=\dfrac{N}{2}(A+B)[/tex]

To find, the value of B in terms of S, N and A = ?

∴ [tex]S=\dfrac{N}{2}(A+B)[/tex]

By crossmultiplication, we get

⇒ N(A + B) = 2S

⇒ NA + NB = 2S

⇒ NB = 2S  - NA

⇒ B = [tex]\dfrac{2S-NA}{N}[/tex]

∴ The value of B = [tex]\dfrac{2S-NA}{N}[/tex]

Answer:

207.24 inches

Step-by-step explanation:

The formula for circumference is C=[tex]2[/tex][tex]\pi r[/tex]

Apply the formula here

r = 33

[tex]\pi[/tex]=3.14

C=2*3.14*33 = 207.24

Apply units!

207.24 inches

Answer:

$63

Step-by-step explanation:

30% of 90 is 27

90-27=63

Answer:

  [tex]10+\dfrac{x}{6}[/tex]

Step-by-step explanation:

The wording, "the sum of A and B" translates to the math formula A+B.

The wording, "the quotient of A and B" translates to the math formula A/B.

Then "the sum of 10 and the quotient of x and 6" will translate to the math formula ...

  [tex]\boxed{10+\dfrac{x}{6}}[/tex]

Answer:  5 (x + 2y - 3)

Step-by-step explanation:

Answer:

perp. : 1/3= m

y + 8 = 1/3(x -4): answer is c

y + 24/3 = (1/3)x - 4/3

y = (1/3)x - 28/3

Step-by-step explanation:

answer is c

To find the equation of a line perpendicular to y = -3x + 11 that passes through the point (4, -8), we first calculate the negative reciprocal of the original line's slope, which is 1/3. Then we apply this slope and the given point to the point-slope form equation to obtain y + 8 = (1/3)(x - 4).

The student has asked for an equation in point-slope form for a line that is perpendicular to y = -3x + 11 and passes through the point (4, -8). Firstly, we identify the slope of the given line, which is -3.

As we need a perpendicular line, we find the negative reciprocal of this slope, which is 1/3 (since the slope of perpendicular lines are negative reciprocals of each other). Now, using the point-slope form formula, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we plug in our values to get:

y - (-8) = (1/3)(x - 4)

This simplifies to:

y + 8 = (1/3)(x - 4)

Which is the equation of the line perpendicular to y = -3x + 11 that passes through the point (4, -8) in point-slope form.

Step-by-step explanation:

Given , a line passes through the points (1,-3) and (3,1)

The equation of line which passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is

[tex]y - y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Here [tex]x_1 = 1 , y_1= -3[/tex]     and      [tex]x_2 = 3 , y_2= 1[/tex]

The required equation of the line is

[tex]y+3=\frac{1+3}{3-1} (x-1)[/tex]

[tex]\Leftrightarrow y +3 =2(x-1)[/tex]

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

[tex]\Leftrightarrow y =2x-5[/tex]

8.

Given, y varies directly with x and y=24 when x=8

Therefore,

[tex]y\propto x[/tex]

[tex]\Rightarrow y = kx[/tex].........(1)

y = 24 when x=8

[tex]\therefore 24 = 8k[/tex]

[tex]\Rightarrow k =3[/tex]

Equation (1) becomes

y= 3x

So, when x=10

y=3×10

⇒y=30

Answer: 15/24

Step-by-step explanation: 6x4=24 which is the denominator and 5x3=15 which is the numerator

Answer:

15/24

Step-by-step explanation:

The answer for the above mentioned problem is JL = 12.5

Step by step explanation:

Given:

JM = 8

KM = 6

To Find:

JL = ?

Formula to be used:

[tex]KM^2[/tex] = JM x ML

In order to find " JL" we must first find "ML",

[tex]KM^2[/tex] = JM x ML

         [tex]6^2[/tex] = 8 x ML

         36 = 8 x ML

         36/8 = ML

         ML = 4.5

Now JL = 4.5+8

             = 12.5

Thus the value of JL = 12.5

Answer:

4

Step-by-step explanation:

2x-7=-2x+9

2x-(-2x)-7=9

2x+2x-7=9

4x-7=9

4x=9+7

4x=16

x=16/4

x=4

Answer: y= 40

Step-by-step explanation:

1. The lowest point of the cable is 40 feet above the surface of the bridge.

2. The towers are 450 feet apart.

3. The vertical distance from the surface of the bridge to the top of each tower is 500 feet.

We’ll use the general form of a parabolic equation:

[ y = a(x - h)^2 + k ]

Where:

(y) represents the vertical position (height) of the cable.

(x) represents the horizontal position along the bridge.

(h) represents the horizontal position of the vertex (lowest point) of the parabola.

(k) represents the vertical position of the vertex.

Given that the lowest point of the cable is at (y = 40) feet, we have:

[ k = 40 ]

Now let’s find the vertex position ((h)). Since the towers are 450 feet apart, the midpoint between the towers corresponds to the vertex. Therefore:

[ h = \frac{{450}}{2} = 225 ]

Now we can express the equation as:

[ y = a(x - h)^2 + k ]  

Next, let’s find the value of (a). At the top of each tower, the cable is at a height of 500 feet. So, when (x = 0) (left tower) or (x = 450) (right tower), we have:

At the left tower (left end of the span): [ y = 500 = a(0 - 225)^2 + 40 ] Solving for (a): [ a = \frac{{500 - 40}}{{225^2}} = \frac{{460}}{{50625}} ]

At the right tower (right end of the span): [ y = 500 = a(450 - 225)^2 + 40 ] Solving for (a): [ a = \frac{{500 - 40}}{{225^2}} = \frac{{460}}{{50625}} ]

Since the value of (a) is the same at both ends, we can use either tower to find the equation of the parabolic curve:

[ y = \frac{{460}}{{50625}}(x - 225)^2 + 40 ]

Answer:

Total amount of saving = $212.5

Step-by-step explanation:

Let x be the amount of saving to begin with.

Given:

Maya spent = 40%

Bicycle cost = $85

We need to find the amount of savings Maya began with.

Solution:

From the statement, Maya spent 40% of her savings to pay for a bicycle that costs $85.

So, 40% of total amount = $85

[tex]40\%\times Total\ amount = \$85[/tex]

Substitute [tex]40\% = \frac{40}{100}[/tex] and total amount = x in above equation.

[tex]\frac{40}{100}\ties x = 85[/tex]

Using cross multiplication rule.

[tex]x=\frac{85\times 100}{40}[/tex]

[tex]x=\frac{8500}{40}[/tex]

x = $212.5

Therefore, amount of savings Maya began with (x) = $212.5

Check the picture below.

The measure of arc CD of circle A will be 90°. Then the correct option is A.

Let r be the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

In circle A, arc CD is congruent to arc BD. And we know that the Line segment CAD is the diameter of the circle. Then the equation is given as,

arc CD = arc BD                           ....1

arc CD + arc BD = 180°                ....2

From equations 1 and 2, then we have

arc CD + arc CD = 180°

2 arc CD = 180°

arc CD = 90°

The measure of arc CD of circle A will be 90°. Then the correct option is A.

More about the arc length of the sector link is given below.

https://brainly.com/question/15955580

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Answer:

[tex]2(x - 3)\: >\: \frac{1}{14}[/tex]

Step-by-step explanation:

The difference of x and 3 is given as:

x-3

Twice the difference of x and 3 becomes:

2(x-3)

The reciprocal of 14 is

[tex] \frac{1}{14} [/tex]

Twice the difference of x and 3 is greater than the reciprocal of 14 then becomes

[tex]2(x - 3)\: >\: \frac{1}{14} [/tex]

We found the volume of water by finding the volume of fish tank from given dimensions and dividing it by 2.

Step-by-step explanation:

Given,

Height of tank = 3 feet

Width of tank = 1.5 feet

Length of tank = 2 feet

We will first find the volume of tank;

Volume = Length * Width * Height

Volume = 3 * 1.5 * 2

Volume = 9 feet cubed

As we know the water is 1/2; therefore we will divide the volume of tank by 2.

Volume of water = [tex]\frac{9}{2} = 4.5\ ft^3[/tex]

We know that;

1 cubic feet = 7.481 gallons

4.5 cubic feet = 7.481*4.5 = 33.66 gallons

Keywords: volume, division

Learn more about volume at:

#LearnwithBrainly

To calculate a 20% tip and round up, multiply the bill by 0.2, then round to the nearest 10 cents.

To calculate a 20% tip, first, determine the total bill amount. Then, multiply the bill amount by 0.2 to find 20% of the bill. Finally, round up to the nearest multiple of 5 or 10 cents. Since Kadisha always rounds up, she should round up to the nearest 10 cents.

If the total bill is $50, to calculate a 20% tip, we multiply $50 by 0.2 to get $10, which is 20% of the bill. Then, we round up to the nearest 10 cents, making the tip $10.00.

https://brainly.com/question/33172213

#SPJ12

Final answer:

Min will need a total of 700 bookmarks for the pages where the digits in the thousands and units places add up to 7, since there are 700 four-digit page numbers meeting the criteria.

Explanation:

To determine the number of bookmarks Min needs for the pages where the digits in the thousands and units place add up to 7, we will consider all four-digit numbers that meet this criterion. This involves taking the sum of the thousands and units digits, which can equal 7 in the following ways: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, and 7+0. Considering that for every combination of thousands and units digits, there are 10 possibilities for the hundreds digit and 10 possibilities for the tens digit, we can calculate the total number of eligible page numbers.

For 1+6 or 6+1, the number of possibilities is 2 (the two combinations) multiplied by 100 (since there are 10 choices for each of the two remaining digits), giving us 200 options.

For 2+5 or 5+2, we have another 200 options.

For 3+4 or 4+3, we get another 200 options.

For 7+0, we would only have 100 options, as there is only one combination.

Summing these up, we find Min will need 700 bookmarks: 200 + 200 + 200 + 100 = 700.

Answer:-2+5

Step-by-step explanation:

So basically you do simple math and you need to know that the highest number goes on the right

So basically for each one there is

3-1 that makes 2

-2+5 creates 3 because it’s a negative so you must cancel the negative out and your left with three after

And with that mind set in mind with having to cancel the negative out with the positive

4+(-2) is basically 4-2 and that makes 2

And the last one is a little bit tricky because of all the negatives involved and with this one you need to know that to negatives make a positive

So it’s -4-(-2) so because of the minus and the negative two being negatives right next to each other they cancel each other out to make the equation basically -4+2 which would ultimately make -2

So all the answers are

3-1=2

-2+5=3

4+(-2)=2

-4-(-2)=-2

And out of all those we know 3 is the highest number there so therefore it would make it the one farthest to the right on a number line when solved.

Answer:

[tex]2.5\ \frac{people}{book}[/tex]

Step-by-step explanation:

The correct question is

The ratio of people to books in a classroom is 10:4 what is the unit rate of people per book?

Let

x ----> the number of people

y ----> the number of books

we know that

To find out the unit rate of people per book , divide the total number of people by the total number of books

we have

[tex]x=10\ people\\y=4\ books[/tex]

so

[tex]\frac{x}{y}=\frac{10}{4}=2.5\ \frac{people}{book}[/tex]

Answer:

.97 cents

Step-by-step explanation:

3.88 divided by 4 = .97

Answer:

97¢

Step-by-step explanation:

If 4 liters cost $3.88, then divide 4 into 3.88

Answer:

C) Consistent and Dependent.

Step-by-step explanation:

As the system has at least ONE solution. Both lines lie over each other, which makes them dependent.

The system, therefore, is consistent and dependent.

Answer: It's negative! Dude, could I please have brainiest!?!

Final answer:

The sign of the expression 3x * y^3 is negative when x is positive and y is negative because a negative number raised to an odd power remains negative.

Explanation:

The question asks about the sign of a mathematical expression where the variables have specified signs based on their values. Given that x is positive (x > 0) and y is negative (y < 0), the expression 3x * y^3 encompasses multiplying a positive number by a negative number raised to an odd power. Multiplying a positive number by a negative number results in a negative number, and raising a negative number to an odd power preserves the negative sign. Therefore, the product 3x * y^3 will be negative because y^3 maintains its negative sign while 3x is positive.

Final answer:

The negative solution to the equation x² - 3x - 4 = 0 is x = -1.

Explanation:

The difference of the square of a number and 4 is equal to 3 times that number. To find the negative solution, let's represent the number as x.

The equation becomes x2 - 4 = 3x.

Rearranging the equation, we get x2 - 3x - 4 = 0.

To find the negative solution, we can use the quadratic formula: x = (-b - √(b2 - 4ac)) / (2a).

For our equation, a = 1, b = -3, and c = -4. Plugging these values into the quadratic formula, we get x = (-(-3) - √((-3)2 - 4(1)(-4))) / (2(1)).

Simplifying further, we get x = (3 - √(9 + 16)) / 2, which simplifies to x = (3 - √25) / 2.

The square root of 25 is 5, so x = (3 - 5) / 2, which equals -1.

Therefore, the negative solution to the equation is x = -1.