Write an equation that represents the line.
Use exact numbers.

[tex]a = l \times w \\ a = (10y + 4w)(10y - 4w) \\ a = 10y(10y - 4w) + 4w(10y - 4w) \\ a = 100 {y}^{2} - 40wy + 40wy - 16 {w}^{2} \\ a = 100 {y}^{2} - 16 {w}^{2} [/tex]

ATTACHED IS THE SOLUTION

When we have an x-value of 3 the corresponding y-value in the equation is 11.

It should be noted that an equation simply shows the relationship between the expression that's illustrated.

In this case, the function that is represented by the equation function that is represented by the equation y = 3x + 2. and we have an x-value of 3,

Therefore, the value of y will be:

y = 3x + 2.

y = 3(3) + 2

y = 9 + 2

y = 11

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Answer:

500 divided by 2/3 = 500 * 3/2= 750

Step-by-step explanation:

Answer:

D. 0 ≤ x ≤ 10

Step-by-step explanation:

I took the quiz.

The domain of the function is 0 ≤ x ≤ 10 if the function is f(x) = 20(2)ˣ which represnts the exponential function option (D) is correct.

It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

It is given that:

A bacteria is growing by a factor of 2 every hour from 1 p.m. to 11 p.m.

The function is:

f(x) = 20(2)ˣ

The value of x represents the domain of the exponential function.

The domain of the function is:

0 ≤ x ≤ 10

Thus, the domain of the function is 0 ≤ x ≤ 10 if the function is f(x) = 20(2)ˣ which represnts the exponential function option (D) is correct.

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The discriminant of the function will be negative.

Option C is true.

What is mean by Discriminant?

The discriminant of the function describe the roots of the function.

Which is defined as for a quadratic equation ax² + bx + c = 0;

D = b² - 4ac

Given that;

The graph of the function is shown in attached figure.

Now,

When the graph has any x - intercepts then the function has a real roots, so the discriminant must be positive.

Here, From the given graph of the function,

We have the function which have no any x - intercept, that is do not cross the x - axis at any point.

Hence, The graph of the function has no real roots.

Thus, We can say that;

The discriminant must be negative.

Therefore, The discriminant of the function is negative.

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Answer:

This is all ready written as a ratio. You could also write it as 11:18, but other than that, your good!

Step-by-step explanation:

Hope it helps! =D

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

Explanation:

Recall that [tex]i = \sqrt{-1}[/tex]

Square both sides to get [tex]i^2 = -1[/tex]

So,

[tex](i\sqrt{5})^2 = i^2*(\sqrt{5})^2 = -1*5 = -5[/tex]

We have a horizontal translation of 2 units to the right, so the correct option is B.

"The graph of y = f(x) will shift right 2 units."

For any function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

if N > 0, the translation is to the left.

if N < 0, the translation is to the right.

In this case we have the function written as:

y = f(x - 2)

So we have N = -2, which means that we have a translation of 2 units to the right.

Then the correct option is B.

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Answer:

The error is in line A. f(x), not x, is equal to 21.

f(x) = 2x - 1 = 21

2x = 20, so x = 10.

Answer:

0.87 cent

if i did this right.

Step-by-step explanation:

17.50 divided by 2 = 8.75

8.75 divided by 10 = 0.87

3x - y = -7 is the required equation of the line, which will bisect the line segment with endpoints (-7, 6) and (5,2).

the equation for the perpendicular bisector of the line  with end points [tex](x_{0},y_{0})\\[/tex] and [tex](x_{1},y_{1})[/tex] are given by:

[tex]2(x_{1} - x_{0})x+2(y_{1}-y_{0})y = x^{2} _{1}-x^{2} _{0}+y^{2}_{1}-y^{2}_{0}[/tex]

in the given case we have,

[tex](x_{0},y_{0})\\[/tex] = (-7,6)

and

[tex](x_{1},y_{1})[/tex] = (5,2)

now substituting the given values in the above equation we get,

2(5-(-7))x + 2(2-6)y = 5²- (-7)² + 2²- 6²

= 24x - 8y = 25 - 49 + 4 - 36

= 24x - 8y = -56

on simplifying by dividing the LHS and the RHS by 6 we get our equation to be,

3x - y = -7

What is a perpendicular bisector?

A line or segment that is perpendicular to another segment and passes through its midpoint is called a perpendicular bisector.

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Answer: -85/272

Step-by-step explanation:

-17/8 divided by 34/5

then opposite reciprical

-17/8 x 5/34

-85/272 (check if you can simplify)

The number that is less than a whole, in 3 decimal places and when rounded to the nearest tenth is 0.78 will be 0.775.

A fraction expressed in a particular way is called a decimal. As an alternative to expressing 1/2, you might write 0.5 instead, with the zero in the ones place and the five in the tenths position. The word decimus, which means tenth in Latin, is derived from the base word decem, or 10.

It should be noted that 0.775 is in 3 decimal places. In this case, the last 5 will be converted and this will become 0.78.

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Ans: The formula that defines the sequence is Tn = 4n - 2

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Answer:x^2*y/(4/5)

Step-by-step explanation:

That's the equation. Your question is the word form.

1. The amount donated by the people with same ratio is $40.

2. The amount greater is $40.

From the information, there's a total of $160 in donations from three people and the three donations are in the ratio 5 : 5 : 10.

It should be noted that the amount donated by the people with same ratio will be:

= 5/(5 + 5 + 10) × $160

= 5/20 × $160

= $40

The amount donated by the person with largest ratio will be;

= 10/20 × $160

= $80

Therefore, the difference will be:

= $80 - $40

= $40

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Answer:(a+1) (ba+b−5)

Step-by-step explanation:

The change in temperature was 25 F - (-8F) = 33 F.

Answer:

Explanation:

The change in temperature is the difference between the two temperatures. In our case this is 25 F - (-8F) = 33 F. Notice that the subtracting the negative number changes the sign of the operation and turns it into an addition problem25 F+ 8 F = 33 F.

Answer: N > -4

Step-by-step explanation:

Cuz It's Right

The solution for inequality  is n < -4.

The given inequality is −2(n − 3.5) > 15

An inequality will have the sign < , > , ≥ or ≤ instead of an equality in an equation. That is, an inequality compares two quantities on either sides of the inequality sign.

We are asked to solve the inequality  −2(n − 3.5) > 15. That is, to find the possible values for n.

−2(n − 3.5) > 15

Dividing throughout by 2,

-(n - 3.5) > 15/2

⇒ -n +3.5 > 7.5

Subtracting 3.5 from both sides,

⇒ -n > 7.5 - 3.5

⇒ -n > 4

Multiply -1 on both sides of the inequality and the inequality will be reversed,

⇒ n < -4 is the solution for n.

The solution is the values of n less than -4.

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The list which orders the numbers from least to greatest is π, √15, 4.1, 4. 85, √30.

To find the list which orders the numbers from smallest to largest we need to find the values of the respective numbers,

In the first list, we have the numbers √13, 2.1, 5.4, √/17, π. The value of √13 = 3.6 and the next term is 2.1. As 2.1 < 3.6, the list does not arrange numbers in increasing order.

In the second list, we have the numbers π, 3.2, 6.3, √17, √20. The value of π is 3.14 and the next terms are 3.2 and 6.3 which are more than the former. But the value of √17 is 4.1 which is less than the previous number 6.3.

In the third list,√23, 2.6, 1.3, √30, π the numbers are not arranged in increasing order as √23's value is 4.8 more than the second number.

In the fourth list, π,√15, 4.1, 4. 85, √30 the numbers are arranged in increasing order when calculated. The value of π is 3.1, of √15 is 3.8, then there are 4.1 and 4.85, and at last, is √30 whose value is 5.5.

Hence, π <√15 < 4.1 < 4. 85 <√30 is the list in the increasing order.

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If the length of a rectangle is 19 feet longer than the width. If the perimeter is 46 feet, The equation for this scenario where "x" represents the width is 2x + 2 (x +19 ) = 46  and the width is 2 feet.

Given data :

Length of a rectangle = 19 feet

Perimeter = 46 feet

Perimeter formula: 2l+2w=P

Let x represent the width

Hence,

2x + 2 (x +19 ) = 46

2x + 2 x +38 = 46

Collect like terms

4x  = 46 -38

4x = 8

Divide both side by 4x

x = 8/4

x = 2 feet

Therefore the equation that was used to find the width  is  2x + 2 (x +19 ) = 46  while the width is 2 feet.

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Answer:

31

Step-by-step explanation:

9+10

19

4+8

12

19+12= 31

As per the given question;

The coordinates of the original triangle ABC with vertices is ;

A(-4, 1), B(-1, 1), and C(-1, 3)

For the first reflection along y-axis, the coordinates of y will remain same and x will reverse to positive.

Y-axis reflection: A(4, 1), B(1, 1), and C(1, 3)

Now, the triangle is again reflected along x-axis.

Thus, for the first reflection along x-axis, the coordinates of x will remain same and y will reverse to positive.

x-axis reflection: A(4, -1), B(1, -1), and C(1, -3)

Rotation: The circular motion of an item around a center is referred to as rotation.

The rotation of triangle ABC 180° about the origin.

Rule for Rotation 180° (Clockwise and Counterclockwise);

(x, y)   ----- > (-x, -y)

A(4, -1)  ------> A(-4, 1)

B(1, -1) ------>  B(-1, 1)

C(1, -3) ------>  C(-1, 3)

Rotation 180° = A(-4, 1), B(-1, 1) and C(-1, 3)

Thus, the result of the coordinates of the new triangle with vertices are found.

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A line with slope m then the slope of a line perpendicular to it is ;M = -2/3

A straight line of the form  y = mx + c has its slope as 'm'

It is constant for a line. The more the slope is, the steeper the line is.

Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.

To find the slope m of the given line using the slope formula

[tex]m = \dfrac{y-q}{x-p}[/tex]

with (p, q ) = (1, 0) and (x₂, y₂ ) = (x, y)  2 points on the line

m =  (3 -0)/(3-1)

m = 3/2

ALso it is given that a line with slope m then the slope of a line perpendicular to it is ;

M = -2/3

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Given,

No. of photos Marcus took on his cell phone = 18

Ratio of photos took by Marcus and Maribel = 3:4

Let the no. of photos took by Maribel be [tex]x[/tex].

∴ [tex]\frac{18}{x} = \frac{3}{4}[/tex]

⇒[tex]3x = 72[/tex]

⇒ [tex]x = \frac{72}{3} = 24[/tex]

Hence, Maribel took 24 photos.

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Answer: y=9 when x=-2

y=5 when x=0

y=-3 when x=4

Step-by-step explanation:

y+2x=5

y=5-2x

y=5-2(-2)

y=5-(-4)

y=5+4

y=9 when x=-2

y=5-2(0)

y=5 when x=0

y=5-2(4)

y=5-8

y=-3 when x=4

Answer:

C (50, - 40 )

Step-by-step explanation:

C is the midpoint of AB

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = A (0, - 80 ) and (x₂, y₂ ) = B (100, 0 ) , then

C = ( [tex]\frac{0+100}{2}[/tex] , [tex]\frac{-80+0}{2}[/tex] ) = ( [tex]\frac{100}{2}[/tex] , [tex]\frac{-80}{2}[/tex] ) = (50, - 40 )

First, we will find the weight of each oranges and grape fruit

Let x be the unit weight of orange

Let y be the unit weight of grape fruit

If "10 oranges and 20 grapefruits weigh 35 pounds total"

Then this implies;

10x + 20 y = 35 -----------------(1)

And

If " 16 oranges and 10 grapefruits weigh 23 pounds total"

This implies;

16x + 10y = 23 ---------------------(2)

We can solve the two equations simultaneously.

Using elimination method;

we eliminate y and to do that, the y variables in the two equations must be same, Hence we can achieve that by multiply equation (1) by 10 and then multiply equation (2) by 20

100x + 200y = 350 ----------------------------(3)

320x + 200y = 460 ------------------------------(4)

subtract equation (3) from equation (4)

220x = 110

divide both-side of the equation by 220

x = 0.5

substitute x=0.5 into equation(1) and then solve for y

10(0.5) + 20y = 35

5 + 20y = 35

subtract 20 from both-side of the equation

20y = 35 - 5

20y = 30

divide both-side of the equation by 20

y = 1.5

"13 oranges and 15 grape fruits" = 13 x + 15y

substituting x = 0.5 and y= 1.5 in the above;

13(0.5) + 15(1.5)

=6.5 + 22.5

=29

Hence;

13 oranges and 15 grapefruits will weigh 29 pounds