Please help me with this problem

The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

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

    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

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The square of z varies inversely as the square root of e. If z=36 when w=16, then value of z is 24 when w=81.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The square of z varies inversely as the square root of e.

If z=36 when w=16

The value of z when w is 81 we need to find

z²=k/√e

where k is a proportionality constant

36²=k/√16

36²=k/4

Apply cross multiplication

1296(4)=k

5184=k

Now let us find when k is 5184 and w is 81

z²=5184/9

z²=576

Take square root on both sides

z=24

Hence, the value of z is 24 when w is 81.

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Answer:

like 10 i think

Step-by-step explanation:

the flat line is the time it spends stopped im pretty sure so that would be 10 seconds

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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The other information required while using the intermediate value theorem to show the existence of zero for the polynomial function plotted is

f(x₁) < 0 and f(x₂) > 0

The intermediate value theorem says that if "f" is a continuous function across a closed interval [a, b] with values f(a) and f(b) at its endpoints, then the function takes any value at a point inside the interval that is between the values of f(a) and f(b).

The root of a polynomial is the value of y when x is zero. hence to show that there is a zero between the points x₁ and x₂ there is a need to show there was a change of sign in the output value

Using the graph

At the point of change of sign is the required zero

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The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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Answer:

2, 8

Step-by-step explanation:

-1/2x^2 + 5x = 8

-x^2 + 10x = 16 (Multiplying both sides of the equation by 2)

-x^2 + 10x  - 16 = 0

x^2 - 10x + 16 = 0 (changing the signs)

x^2 -2x -8x +16 = 0

x (x-2) -8 (x-2) = 0

(x-2) (x-8)

x-2 = 0

x = 2

or

x -8 = 0

x = 8

Answer from Gauthmath

The values of x are solutions to this equation that is 2, 8

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that the equation as;

-1/2x² + 5x = 8

-x² + 10x = 16

Now Multiplying both sides of the equation by 2;

-x² + 10x  - 16 = 0

Or

x² - 10x + 16 = 0

x² -2x -8x +16 = 0

x (x-2) -8 (x-2) = 0

(x-2) (x-8)

The solution are;

x-2 = 0

x = 2

or

x -8 = 0

x = 8

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Answer:

Step-by-step explanation:

To find the unit rate, we need to divide the distance traveled by the time taken.

In this case, the distance traveled is 9 miles, and the time taken is 36 minutes.

Unit rate = distance/time

Unit rate = 9 miles / 36 minutes

Simplifying the above expression by dividing both numerator and denominator by 9, we get:

Unit rate = 1 mile / 4 minutes

Therefore, the unit rate at which the go-kart is traveling is 1 mile per 4 minutes.

Answer:

34 28 37 56 34 37 28 20 43 15

The robber earned approximately $4,824.22 in interest over the 9-year period.

To calculate the interest earned by the robber, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount,

P is the principal amount (initial investment),

r is the interest rate (expressed as a decimal),

n is the number of times interest is compounded per year,

and t is the number of years.

In this case, the robber sold the stolen jewelry for $10,000 and deposited it in a bank account in London. The interest rate is 4% per year, compounded monthly (n = 12). The time period is 9 years (t = 9). Substituting these values into the formula, we get:

A = 10,000(1 + 0.04/12)^(12*9)

Calculating this expression, we find that A is approximately $14,824.22.

To find the interest earned, we subtract the initial principal from the final amount:

Interest earned = A - P

= $14,824.22 - $10,000.00

= $4,824.22.

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The value of the equation is A = ( x² + y² ) / ( x² - y² )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = x / ( x + y ) + y / ( x - y )

On simplifying the equation , we get

Multiply by the LCM , we get

x / ( x + y ) + y / ( x - y ) = [ x ( x - y ) + y ( x + y ) ] / ( x + y ) ( x - y )

where the denominator ( x + y ) ( x - y ) = ( x² - y² )

Substituting the values in the equation , we get

x / ( x + y ) + y / ( x - y ) = [ x² - xy + xy + y² ] / ( x² - y² )

On further simplification , we get

A = ( x² + y² ) / ( x² - y² )

Hence , the equation is A = ( x² + y² ) / ( x² - y² )

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Answer:

16 boxes

Step-by-step explanation:

16x5=80+150=230>15x16=240

Answer:

\(m = 1\) -- Slope

\(y = x + 3\) --- Equation

Step-by-step explanation:

Given

\((x_1,y_1) = (0,3)\)

\((x_2,y_2) = (-4,-1)\)

Required

The slope and the equation

The slope (m) is calculated using:

\(m=\frac{y_2 - y_1}{x_2 - x_1}\)

\(m=\frac{-1-3}{-4- 0}\)

\(m=\frac{-4}{-4}\)

\(m = 1\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = 1(x - 0) + 3\)

\(y = 1(x) + 3\)

\(y = x + 3\)

Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

The value of m ∠ABD will be;

⇒ ∠ ABD = 50°

Parallel lines are those lines that are equidistance from each other and never intersect each other.

Given that;

In the diagram, the parallel lines are cut by transversal BC.

And,  BD bisects ∠ABC and m∠3 = 80.

Now,

Since, The parallel lines are cut by transversal BC.

Hence, We get;

⇒ ∠ 3 + ∠ 2 = 180°

⇒ 80° + ∠ 2 = 180°

⇒ ∠ 2 = 180 - 80

⇒ ∠ 2 = 100

And, We have;

⇒ ∠ 2 = ∠ ABC

⇒ ∠ ABC = 100°

Since, BD bisects ∠ABC.

Hence, We get;

⇒ ∠ ABD = 100 / 2

⇒ ∠ ABD = 50°

Thus, The value of m ∠ABD = 50°

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

The correct answer is:

a = 43%

b = 88%

To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.

From the Venn diagram, we can gather the following information:

The circle labeled "satellite" has a value of 55.

The circle labeled "cable" has a value of 75.

The overlap between the two circles is labeled as 12.

Using this information, we can complete the table:

First column - "Satellite":

Entries: Satellite, Not satellite, Total

Total: 55 (as given in the Venn diagram)

Second column - "Cable":

Entries: Blank, 51%, Blank

To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).

Cable: 75 - 12 = 63

Therefore, the entry becomes: Blank, 51%, Blank

Third column - "Not Cable":

Entries: a, b, Blank

To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).

a: 55 - 12 = 43

To find the value for "b," we subtract the overlap (12) from the total number of households (100).

b: 100 - 12 = 88

Therefore, the entries become: 43, 88, Blank

Fourth column - "Total":

Entries: Blank, Blank, 100%

The total number of households is given as 100% (as stated in the question).

Therefore, the values of a and b in the relative frequency table are:

a = 43% (rounded to the nearest percent)

b = 88% (rounded to the nearest percent)

Hence, the correct answer is:

a = 43%

b = 88%

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The region \(D\) is essentially parameterized in three dimensions by

\(\Phi(u,v) = (u^2, u+v, 0)\)

with \(1\le u\le8\) and \(0\le v\le6\).

The normal vector to \(D\) is

\(\vec n = \dfrac{\partial\Phi}{\partial u} \times \dfrac{\partial\Phi}{\partial v} = (0,0,2u)\)

with norm \(\|\vec n\| = 2u\).

Then the surface integral is

\(\displaystyle \iint_D y \, dA = 2 \int_0^6 \int_1^8 (u+v)u \, du \, dv \\\\ = 2 \int_0^6 \left(\frac{1022}3 + 63 v\right) \, dv = \boxed{3178}\)

Answer: y <= x^(2) - 3x - 1

How to: Graph the inequality by finding the boundary line, then shading the appropriate area.

Have a great day and stay safe !

A circle has the following equation

Answer:

on what

Step-by-step explanation:

(a) 0.5, (b) f_Y(y) = 12y(1-y), (c) 9/128, (d) 7/36 - Probability calculations using joint density function.

(a) To find the Probability that the Turkish tobacco represents over a portion of the mix, we want to incorporate the joint thickness capability over the district where x > 0.5 and y < 1 - x. This gives:

P(X > 0.5) = ∫[0.5,1]∫[0,1-x] 24xy dy dx = 0.5

Consequently, the Probability that the Turkish tobacco represents over around 50% of the mix is 0.5.

(b) To find the negligible thickness capability for the extent of homegrown tobacco, we really want to incorporate the joint thickness capability over all potential upsides of Turkish tobacco:

f_Y(y) = ∫[0,1-y] 24xy dx = 12y(1-y) ; 0 < y < 1

Thusly, the peripheral thickness capability for the extent of homegrown tobacco is f_Y(y) = 12y(1-y).

(c) To find the Probability that the extent of Turkish tobacco is under 1/8 given that the mix contains 3/4 homegrown tobacco, we really want to utilize Bayes' standard:

P(X < 1/8 | Y = 3/4) = P(X < 1/8 ∩ Y = 3/4)/P(Y = 3/4)

We can find the numerator by coordinating the joint thickness capability over the district where x < 1/8 and y = 3/4:

∫[0,1/8] 24xy dx = 27/128

To find the denominator, we coordinate the joint thickness capability over all potential upsides of Turkish tobacco when y = 3/4:

∫[0,1/4] 24xy dx = 3

Thusly, the contingent Probability is:

P(X < 1/8 | Y = 3/4) = (27/128)/3 = 9/128

(d) To find the likelihood that the extent of homegrown tobacco is over two times the extent of the Turkish tobacco, we want to incorporate the joint thickness capability over the area where y > 2x and x + y < 1. This gives:

P(Y > 2X) = ∫[0,1/3]∫[2x,1-x] 24xy dy dx + ∫[1/3,1/2]∫[2x,1-x] 24xy dy dx

= 7/36

Accordingly, the likelihood that the extent of homegrown tobacco is over two times the extent of the Turkish tobacco is 7/36

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The complete question is:

A tobacco company produces blends of tobacco, with each blend containing various proportions of Turkish, domestic, and other tobaccos. The proportions of Turkish and domestic in a blend are random variables with joint density function (X = Turkish and Y = domestic) 24xy ;0< x, y < 1, x +y<1 fx.y(1,7) (2) ; otherwise (a) (1 point) Find the probability that in a given box the Turkish tobacco accounts for over half the blend. Page 2 (b) (1 point) Find the marginal density function for the proportion of the domestic tobacco. (c) (1 point) Find the probability that the proportion of Turkish tobacco is less than 1/8 if it is known that the blend contains 3/4 domestic tobacco. (d) (2 points) Find the probability that the proportion of domestic tobacco is more than twice the proportion of the Turkish tobacco.

Answer:

the constant term in this problem is 8

The Volume of the box is 12 cubic unit.

We have,

Height = 1 unit

Width = 2 unit

Length = 6 unit

So, Volume of box

= l w h

= 1 x 2 x 6

= 12 cubic unit

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Answer:

911.20

Step-by-step explanation:

Adults that have a cell phone = 85% of 1072

= 0.85 x 1072

= 911.20

When substituting y = 11 into the equation y = 1/2(x) - 25, we find that x = 72, confirming that (23.5, 11) is a valid point of intersection.

Given that x is 23.5, it is required to prove that it is an intersection point for the equation y = 1/2(x) - 25 when y is equal to 11.

The equation is given as y = 1/2(x) - 25

When y = 11, we can substitute the value of y in the equation to obtain 11 = 1/2(x) - 25

This can be simplified as 11 + 25 = 1/2(x)36 = 1/2(x)

On solving, x = 72Thus, when y is equal to 11 and x is equal to 72, the given point of intersection is valid.

Therefore, it can be concluded that x = 23.5 is a point of intersection for the equation y = 1/2(x) - 25 when y is equal to 11.

In summary, when given an equation with two variables, we can find the point of intersection by setting one of the variables to a given value and solving for the other variable. In this case, when y is equal to 11, we can solve for x and obtain the point of intersection as (72,11).

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The graph of the given absolute function is attached below and the end points (-5,0) (0, 5) of the rays are marked in it.

Absolute value function:

The  function that contains an algebraic expression within absolute value symbols is called as absolute value function.

Given,

Here we have the absolute value function f(x) = |-x - 5|

Now, we have to plot the graph for this function and we have to mark the end point of the rays.

Here the given function is written as,

=> f(x) = | -x - 5|

In order to plot the graph for the function we need the table of values to point it on the graph,

For that we have to take following sample values,

When x = -5, then f(-5) = |-5 -5| = 0

When x = 0,  then f(0) = |0 - 5| = 5

Therefore, the end points of the rays are (-5,0) and (0,5)

Now, we have to plot these values on the graph.

Then we get the graph like the following.

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