Suppose you transform a square corn field by increasing one side by 2 units and decreasing the other side by 3 units. If the area of the resulting corn field equals 24, what was the length of the original corn field?

Answer:

12 ×13.5 y 13.5

Step-by-step explanation:

es igual a 400

Answer:

y=4x

Step-by-step explanation:

Answer:

[tex](-5)[/tex] and [tex]3[/tex].

Step-by-step explanation:

The [tex]x[/tex]-intercepts of a graph refer to points where the graph intersects the [tex]x\![/tex]-axis. These are [tex]x\!\![/tex] values for which [tex]f(x) = 0[/tex].

For example, since [tex]x = (-5)[/tex] is one of the [tex]x[/tex]-intercepts of [tex]y = f(x)[/tex], it must be true that [tex]f(-5) = 0[/tex]. Likewise, since [tex]3[/tex] is one of the [tex]x[/tex]-intercepts of [tex]y = f(x)\![/tex], [tex]f(3) = 0[/tex].

Since [tex]f(-5) = 0[/tex], the expression [tex]7\, f(-5)[/tex] would also evaluate to [tex]0[/tex] (that is, [tex]7\, f(-5) = (7)\, (0) = 0[/tex].) Thus, [tex]x = (-5)[/tex] would be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex].

Likewise, since [tex]f(3) = 0[/tex], [tex]7\, f(3) = (7)\, (0) = 0[/tex], such that [tex]x = 3[/tex] would also be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex].

No other points could be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex] without being an [tex]x\![/tex]-intercept of [tex]y = f(x)[/tex]. For example, assume that [tex]x = x_{0}[/tex] is an [tex]x[/tex]-intercept of [tex]y = 7\, f(x)[/tex] but not [tex]y = f(x)[/tex]. [tex]7\, f(x_{0}) = 0[/tex], such that [tex]f(x_{0}) = (1/7)\, (7\, f(x_{0})) = (1/7)\, (0) = 0[/tex]- contradiction.

Therefore, the [tex]x[/tex]-intercepts of the new graph would be [tex]x = (-5)[/tex] and [tex]x = 3[/tex].

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

Explanation:

Imagine drawing a circle and splitting it into 3 equal slices. Repeat this process to get 12 identical such circles. We have 12*3 = 36 slices so far.

Then add a 13th circle that has 2 of the 3 slices shaded, to represent 2/3. So we add 2 extra slices to the 36 original to get 36+2 = 38 total slices.

Each slice represents 1/3 of a cup. So each full circle represents 1 full cup.

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

Another approach:

Let's convert the mixed number 12 & 2/3 into an improper fraction

We use the formula

a & b/c = (a*c+b)/c

So,

12 & 2/3 = (12*3+2)/3 = (36+2)/3 = 38/3

Then rewrite the 38/3 as 38*(1/3) to show we have 38 copies of the 1/3 cup.

Answer: 38 cups

Step-by-step explanation:

       We will divide 12 2/3 cups by our measurement, 1/3 cup, to find how many 1/3 cups will be needed.

(12 + 2/3) / (1/3) = 38 cups

The required solution is 1(one) as per the given functions.

What is a function?

Every function has a(one) domain and codomain or range. A function is generally(ax) denoted by f(x) where x(ax) is the input

Given :

The function(one)

g(m)= m-4(four).

By put m is equal to 5(five) we get,

g(5)=5-4(four)

=1(one)

Hence, the required solution is 1(one) as per the given functions.

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She will spend £250 and save £400.

Ratio is an expression that indicates how many times one quantity is more than the other.

Here, we are given that Miss penny inherits £650.

Her saving to spending ratio is 9 : 4

Thus, the proportion of money she saves is 9/ (4+9) = 9/13

therefore, the amount of money saved will be-

9/13 of 650

= 9/13 * 650

= 9 * 50

= 450

Thus, Miss Penny saves £400.

The remaining amount left with her = 650 - 400 = 250.

Thus, she spends the remaining £250.

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Miss penny inherits £650. She decides to save some of the money and spend the rest. The ratio of saving to spending money is 9:4. How much does she save and how much does she spend?

Answer:

The slope of the line is -1.

We can find this by using the slope formula, where [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]. Substitute in our points; [tex]\frac{7-4}{6-9} =\frac{3}{-3}[/tex]. Remember that a negative in either the numerator or the denominator of a fraction makes the entire fraction negative, so [tex]\frac{3}{-3}=-\frac{3}{3}[/tex] Remember that an identical numerator and denominator is equal to 1. Same rule applies here, except it's negative, so the slope of the line is -1. You can see this in action if you were to use a graphing tool. I recommend checking out desmos graphing calculator.

The time that it will take the ball to hit the ground in 4 seconds.

To solve this problem you need the function;

h(t) = -16t² + v₀t + h₀

where;

t = time

v₀ is the initial velocity, which in our case is 0

h₀ is initial height, which in our case is 121 ft

h(t) = 0 since we want to know when the ball will hit the ground.

Thus;

0 = -16t² + 121

And we can solve for t;

If we rearrange the terms we see that this is a difference of 2 squares

0 = 121 - 16t²

0 = (11 - 4t)(11 + 4t)

Setting each factor = 0 gives;

11 - 4t = 0       11 + 4t = 0

t = 11/4       or      t = -11/44

The second solution is discarded as time cannot be negative.

Thus, the ball will hit the ground in 4 seconds.

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Answer:  27. 10 < x < 20

29. 10 < x < 20

Step-by-step explanation:

Answer:

B. 13

Step-by-step explanation:

[tex]Rule:a-\left(-b\right)=a+b\\=9-\left(-4\right)=9+4\\=9+4\\=13[/tex]

Answer:
y = x - 4

Step-by-Step Explanation:

Perpendicular lines have slopes that are negative reciprocals—multiplying their slopes result in -1.Given the slope of a line m = -1, then it means that the slope of the other line must be 1 (because multiplying the slope of line 1  (m1 = -1), and the slope of the other line (m2 = 1) results in: -1 × 1 = -1).Therefore, given the slope of line 2 (m2 = 1), and the point (2, -2), we could plug these values into the slope-intercept form and solve for the y-intercept (b):y = mx + b-2 = 1(2) + b-2 = 2 + bSubtract 2 from both sides to solve for b:-2 - 2 = 2 - 2 + b-4 = bTherefore, the y-intercept (b) = -4.Hence, the equation of the perpendicular line is: y = x - 4

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Taking into account the definition of a system of linear equations, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:

[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]

where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know:

So, the system of equations to be solved is

[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]

Among the different existing methods to solve the system of equations, it is decided to solve it using the substitution method. This method consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first one you get:

2.50×2R+4.75R=48.75

Solving:

5R+4.75R=48.75

9.75R=48.75

R= 48.75÷ 9.75

R= 5

Remembering that G=2R, you obtain that G=2×5= 10

In summary, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:

[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]

where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.

Finally, the number of games played is 10 while the number of rides she went on is 5.

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we get that Melissa is trying to solve the expression ( 3 + 4) ² - 9.

We are given that:

Melissa is simplifying an expression using the order of operations which can be addition, subtraction, multiplication or division.

She adds 3 and 4, squares the result, and subtracts 9.

We will first add 3 and 4:

3 + 4

Now we will square them:

( 3 + 4) ²

Now, we will subtract 9 from it:

( 3 + 4) ² - 9

So, the expression becomes:

( 3 + 4) ² - 9

Therefore, we get that Melissa is trying to solve the expression ( 3 + 4) ² - 9.

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Answer:

See picture below.

Step-by-step explanation:

This problem is related to the formation of a function. We need to know how an function is formed. Here it is given that there is a function which is affected by the value of t. Which means the value of t in  the function decides the value of that function.

Similarly we have to write the function as the variable r so that the value of function is related to the value of r.

h(r)=6-18r ; where 6 is the constant and 18r is the variable in the function.

Hence, the required function is  h(r)=6-18r.

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Answer:

[tex](3/4)[/tex] and [tex](2/3)[/tex].

Step-by-step explanation:

For a fraction of the form [tex](p / q)[/tex], the number in front of the division ([tex]p[/tex]) is the numerator. The number after the division ([tex]q[/tex]) is the denominator.

[tex]\begin{aligned} \frac{p}{q} \quad \genfrac{}{}{0}{}{(\text{numerator})}{(\text{denominator})}\end{aligned}[/tex].

A positive fraction [tex](p/q)[/tex] ([tex]p,\, q > 0[/tex]) is less than [tex]1[/tex] as long as the numerator [tex]p[/tex] is smaller than the denominator [tex]q[/tex] (that is, [tex]p < q[/tex].) The reason is that as long as [tex]p,\, q > 0[/tex]:

[tex]\begin{aligned} & \frac{p}{q} < 1 \\ \iff & (q)\, \left(\frac{p}{q}\right) < (q)\, (1) && (\text{given that $q > 0$}) \\ \iff & p < q\end{aligned}[/tex].

For example, in the fraction [tex](2/3)[/tex], [tex]2[/tex] is the numerator while [tex]3[/tex] is the denominator. Both the numerator and the denominator are positive, while the numerator [tex]2\![/tex] is smaller than the denominator [tex]3\![/tex]. Therefore, [tex](2/3)[/tex] would be less than [tex]1[/tex].

Using Gaussian elimination, the solution to the given system of equations is given as follows:

x = 5, y = -11, z = 3.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are x, y and z, and the system is given as follows:

There are multiple ways in which a system can be solved, and for this one, Gaussian elimination will be used.

The first step is writing the augmented matrix of the system, as follows:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]

Then, the first column, which is equivalent to be coefficient of y, has to be of zero on the second and on the third row, hence:

The updated matrix will be given by:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]

Then, the second column, equivalent to the coefficient of y, on the third row has to be zero, hence:

R3 -> 11R2 + 5R3.

Then the matrix is:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]

From each row of the system, from bottom up, we find the variables, as follows:

40z = 120

z = 120/40

z = 3.

5y - 10z = -85

5y - 30 = -85

5y = -55

y = -11.

2x - y + 4z = 33

2x + 11 + 12 = 33

2x = 10

x = 5.

Hence the solution for the system is:

x = 5, y = -11, z = 3.

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Answer:

{2,3,5,6,8}

Step-by-step explanation:

U={1,2,3,4,5,6,7,8}

A{3,4,5,6}

B{1,4,8}

C{2,3,4,5,6}

We are to find

{A' n B} U {A' n C'}

={3,5,6,8}. U. {2}

= {2,3,5,6,8}

The distance between the two points rounding to the nearest tenth is

9.2 units.

Given that the two points are (-1,4) and (8,2).

We are required to find the distance between two given points.

Distance is basically a numerical or occasionally qualitative measurement of how far apart objects or points are.

The points are (-1,4) and (8,2).

The formula to calculate the distance between two points (x,y),(,a,b) is as under:

Distance=[tex]\sqrt{(a-x)^{2} +(b-y)^{2} }[/tex]

Distance=[tex]\sqrt{(8+1)^{2} +(2-4)^{2} }[/tex]

=[tex]\sqrt{(9)^{2} +(-2)^{2} }[/tex]

=[tex]\sqrt{81+4}[/tex]

=[tex]\sqrt{85}[/tex]

=9.2195

After rounding off to nearest tenth we will get 9.2.

Hence the distance between the two points rounding to the nearest tenth is 9.2 units.

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Answer:

Step-by-step explanation:

From the question above, there are two zeros after the decimal point, so it will be ignored because it is not a significant figure.

0.007349 to 3 significant figure=0.00735

The solution interval for x is x ∈ (-1/4 , ∞)

An inequality shows the relationship of a non-equal comparison between two numbers or mathematical expressions.

Here, we are given two inequalities

x/4 > -1 and -4x - 4 < -3

Let us take the first equation

x/4 > -1

⇒ x > 4(-1)

x > -4

Now, the second equation

-4x - 4 < -3

-4x < -3 + 4

-4x < 1

Now since we are dividing both sides by a negative number, that is 4, the sign of the inequality will be reversed,

x > 1/-4

x > -1/4

Thus, we get x > -4 and x > -1/4

This means that all values of x greater than -1/4 will satisfy.

Thus, x ∈ (-1/4 , ∞)

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This range defines that the babies delivered weigh between 6.9 and 9.5 pounds.

Part 1.

Given inequality is  | x − 8.1 |  ≤ 1.3

Simplifying this inequality as

x - 8.2 ≤ 1.3 or x - 8.2 ≥ -1.3

Solving x - 8.2 ≤ 1.3  we get, x ≤ 9.5

And

Solving x - 8.2 ≥ -1.3 we have, x ≥ 6.9

Now combining the ranges we get,

6.9 ≤ x ≤ 9.5

Part 2.

This range defines that the babies delivered weigh between 6.9 and 9.5 pounds.

Hence, This range indicates that the babies' weights fall within the range of 6.9 to 9.5 pounds.

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The value for the given question is x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.

Given iteration formula as xₙ ₊ ₁ = ∛ 10 - 2xₙ

Given x₀ = 2

We have to find the values of x₁, x₂, and x₃ as

For finding the value of x₁ we need to substitute n = 0 as

xₙ ₊ ₁ = ∛ 10 - 2xₙ

x₀ ₊ ₁ = ∛ 10 - 2x₀

x₁ = ∛ 10 - 2(2)    (∵ x₀ = 2)

x₁ = ∛ 10 - 4

x₁ = ∛ 6

x₁ = 1.8

For finding the value of x₂ we need to substitute n = 1 as

xₙ ₊ ₁ = ∛ 10 - 2xₙ

x₁ ₊ ₁ = ∛ 10 - 2x₁

x₂ = ∛ 10 - 2(1.8)    (∵ x₁ = 1.8)

x₂ = ∛ 10 - 3.6

x₂ = ∛ 6.4

x₂ = 1.85

For finding the value of x₃ we need to substitute n = 2 as

x₂ ₊ ₁ = ∛ 10 - 2xₙ

x₂ ₊ ₁ = ∛ 10 - 2x₂

x₃ = ∛ 10 - 2(1.85)    (∵ x₀ = 1.85)

x₃ = ∛ 10 - 3.7

x₃ = ∛ 6.3

x₃ = 1.846

Therefore, the value of x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.

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Answer:

Number of 12$ Shares? 25

Number of 14$ Shares? 57

Step-by-step explanation:

Let x = number of $12 shares.

Let y = number of $14 shares.

"Ivan has $1098 worth of $12 and $14 stock shares."
12x + 14y = 1098

The number of $14 shares is seven more than twice the number of $12 shares.

y = 2x + 7

We have a system of equations.

12x + 14y = 1098

y = 2x + 7

We can use the substitution method since the second equation is already solved for y. Substitute 2x + 7 for y in the first equation.

12x + 14(2x + 7) = 1098

12x + 28x + 98 = 1098

40x = 1000

x = 25

There are 25 $12 shares.

y = 2x + 7 = 2(25) + 7 = 57

There are 57 $14 shares.

Check:

25 × $12 + 57 × $1`4 = $300 + $798 = $1098

The total value is correct, so the answer is correct.

Answer:

  30 mL/h

Step-by-step explanation:

You want the rate 336 ml in 11.2 h as a rate in simplest form.

The rate can be expressed in simplest form in a number of ways. We usually want rates involving time to be expressed with time units in the denominator:

  (336 mL) / (11.2 h) = 30 mL/h

__

Additional comment

Medicine is often prescribed on a "per day" basis. In 24 hours, this rate would be ...

  (30 mL/h)×(24 h/day) = 720 mL/day

The machine setup to dispense this medicine might use time units of minutes:

  (30 mL/h) / (60 min/h) = (1/2) mL/min

Answer:

40°

Step-by-step explanation:

At point C, the angle is shown as 110°.
Since a line is 180°, you now know that the other side of point C is 70°.
Line A-B and A-C are equal (shown by the short lines), meaning the angle at point B is also 70°,
A triangle is 180° in total, so the equation would be 180° - 2(70°) = 180° - 140° = 40°

The ordered pair for each letter on the graph would be A at (2, 4), B at (-1, 2), C at (-3, -2), D at (2, 0), E at (0, 4), and F at (5, -5).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

As per the given graph,

The coordinates of point A would be (2, 4)

The coordinates of point B would be (-1, 2)

The coordinates of point C would be (-3, -2)

The coordinates of point D would be (2, 0)

The coordinates of point E would be (0, 4)

The coordinates of point F would be (5, -5)

Therefore, the ordered pair for each letter on the graph would be A at (2, 4), B at (-1, 2), C at (-3, -2), D at (2, 0), E at (0, 4), and F at (5, -5).

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Answer:

[tex]\frac{11}{12}[/tex]

Step-by-step explanation:

[tex]Rule: \frac{x}{y} \pm \frac{a}{b} = \frac{x \pm y}{z}\\\frac{1}{4}+\frac{2}{3} = \frac{3}{12}+\frac{8}{12} (LCM)\\=\frac{3+8}{12}\\=\frac{11}{12}\\[/tex]

The 48 inches allowable minimum height of a rider and the 52 and 2.5 mean and standard deviation of the height of the children in the camp of 140 campers, by the Z–Score gives the number of campers allowed as approximately 132 campers.

The required height of riders is at least 48 inches.

The mean height of the children = 52 inches

The standard deviation of the children's height = 2.5 inches

The number of campers at the camp, n = 140

Required: The number of the 140 campers that will be allowed on the ride

Solution:

The Z–Score of the allowable campers is found using the equation;

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

Which gives;

[tex]z = \frac{48 - 52}{2.5} = - 1.6[/tex]

From the Z–Score table, the probability (proportion) of a camper's height to be less than 48 inches is P(x < 48) = 0.05480

Therefore;

The probability that the height of a camper is more than 48 inches is given by the equation;

P(x > 48) = 1 - P(x < 48) = 1 - 0.05480

Which gives;

P(x > 48) = 1 - 0.05480 = 0.9452

Which gives;

The number of campers allowed, c, is given by the equation;

c = n × P(x > 48)

c = 140 × 0.9452 = 132.328 ≈ 132

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