How much less is the area of a rectangular field 70 by 30 meters than that of a square field with the same perimeter?

Given:

In ΔGHI, GI is extended through point I to point J.

\(m\angle GHI=(3x+13)^\circ,m\angle IGH=(x+8)^\circ,m\angle HIJ=(6x-5)^\circ\)

To find:

The measure of angle GHI.

Step-by-step explanation:

According to exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of measure of two opposite angles.

Using exterior angle theorem, we get

\(m\angle HIJ= m\angle GHI+m\angle IGH\)

\((6x-5)^\circ=(3x+13)^\circ+(x+8)^\circ\)

\((6x-5)^\circ=(4x+21)^\circ\)

\(6x-4x=21+5\)

\(2x=26\)

Divide both sides by 2.

\(x=13\)

Now,

\(m\angle GHI=(3x+13)^\circ\)

\(m\angle GHI=(3(13)+13)^\circ\)

\(m\angle GHI=(39+13)^\circ\)

\(m\angle GHI=52^\circ\)

Therefore, the measure of angle GHI is 52 degrees.

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Total number of possible outcomes:

Number of ways to choose 3 numbers from 56 (56 choose 3): 56! / (3! * (56 - 3)!) = 22,957

Number of ways to choose 1 number from 49: 49

Total number of possible outcomes = 22,957 * 49 = 1,128,593

Number of favorable outcomes:

Number of ways to choose 1 number from 49: 1

Number of favorable outcomes = 1

Probability of winning the minimum award:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 1,128,593 ≈ 0.000000888, or approximately 0.0000888%

Answer:

x ≈ 28.7 ft

Step-by-step explanation:

Step 1: Define variables

Height (vertical leg of triangle) = 2 ft

∅ = 4°

We are trying to find the length of the hypotenuse x

Step 2: Use trig

sin∅ = opposite over hypotenuse

sin4° = 2/x

Step 3: Solve for x

xsin4° = 2

x = 2/sin4°

x = 28.6712

x ≈ 28.7 ft

Answer:

the Length of ramp is 28.7 feet.

Step-by-step explanation:

see attached image for clarity

give:

height (h) of clinic = 2 feet

angle of ramp = 4°

find:

Length (L) of ramp

using the formula : sin(Ф) =                height (h)                    

                                              Length of ramp (hypothenuse)

plugin values into the formula:

sin (4) =    2    

               L

L   =    2    

      sin(4)

L = 28.7 feet

therefore,

the Length of ramp is 28.7 feet.

ANSWER :

Z(-4, 2)

EXPLANATION :

Note that rotating an image (x, y) 180 degrees about the origin will be :

The signs of x and y coordinates will change.

From the problem, we have :

The solution is:  the rate of change is 3.

Here, we have,

Since the graph of f(x) is translated 1 unit down, we need to decrease the value of f(x) by 1 to find g(x):

g(x) = f(x) - 1

f(x) = 3|x| – 4

so, we get,

g(x) = 3|x| – 4 - 1

      = 3|x| – 5

Now, to calculate the rate of change over the interval 2 <= x <= 5, we can use the formula below:

rate = g(5) - g(2)/ 5-2

so, we get,

rate = 9/3 = 3

Therefore the rate of change is 3.

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Answer:

5/3

Step-by-step explanation:

The total distance covered by Jeremy is 1320 m

What is a line segment ?

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

For sapling 1 = No distance is covered.

For sapling 2, distance covered = 10 m

Return distance=10 m

For sapling 3, distance covered =20 m

Return distance=20 m and so on

Thus the distances covered for saplings can be represented as : 0,2(10), 2(20),...i.e. 0,20, 40,...

Therefore total distance covered by Jeremy for planting 12 saplings and coming back to original position = S 12

Total distance covered = 122 [2(0) + (12 − 1) 20 ]

Total distance covered = 6 (11)(20) = 1320 m

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Complete question:

There are 12 saplings to be planted in a straight line at an interval of 10 m between

two consecutive saplings. Jeremy can carry only one sapling at a time and he has to

come back to the original point to take the next sapling. He plants 12 saplings in this

manner, planting the first sapling at the original point. After planting all the saplings,

he comes back at the original point,

In the process, what is the total distance that Jeremy covers?

​

Answer:

  9

Step-by-step explanation:

You want the minimum value of objective function C=6x+3y, given the constraints x>1, y≥1, 4x+2y<32, and 2x+8y<56.

The objective function has positive coefficients for both x and y, so it will be minimized when x and y are at their minimum values. The constraints tell you these minimum values are x=1 and y=1, so the minimum value of C is ...

  C = 6(1) +3(1) = 9

The minimum value of C is 9.

__

Additional comment

The value of x cannot actually be 1, so the value of C cannot actually be 9. However x may be arbitrarily close to 1, so C may be arbitrarily close to 9.

  C = 6x +3y   ⇒   x = (C -3y)/6

The x-constraint requires ...

  x > 1

  (C -3y)/6 > 1

  C -3y > 6 . . . . . . multiply by 6

  C > 6 +3y . . . . . . add 3y

The minimum value of y is exactly 1, so we have ...

  C > 6 +3(1)

  C > 9

An inequality is a mathematical statement that compares two expressions using an inequality symbol. In this case, we have two inequalities that involve the variables \(x\) and \(y\): \(y > -\frac{1}{2} x 2\) and \(2x y \le 8\).

To find the points that satisfy these two inequalities, we must first solve for both \(x\) and \(y\).

To find the points that satisfy the first inequality, we can solve for \(y\) and substitute it into the second inequality:

\[y > -\frac{1}{2} x 2 \implies y = -\frac{1}{2} x 2 + k \quad \text{where} \quad k > 0\]

\[2x (-\frac{1}{2} x 2 + k) \le 8 \implies x^2 - 4x + 8 \le 0\]

Solving for \(x\) yields two solutions: \(x = 2 \pm \sqrt{2}\). To find the points that satisfy both inequalities, we must test both of these solutions in the original inequalities. For \(x = 2 + \sqrt{2}\), we have:

\[y > -\frac{1}{2} \cdot (2 + \sqrt{2}) \cdot 2 \implies y > 4 - 4\sqrt{2}\]

\[2 \cdot (2 + \sqrt{2}) \cdot y \le 8 \implies 8 + 8\sqrt{2} \le 8 \quad \text{which is true}\]

Therefore, the point \((2 + \sqrt{2}, 4 - 4\sqrt{2})\) satisfies both inequalities. For \(x = 2 - \sqrt{2}\), we have:

\[y > -\frac{1}{2} \cdot (2 - \sqrt{2}) \cdot 2 \implies y > 4 + 4\sqrt{2}\]

\[2 \cdot (2 - \sqrt{2}) \cdot y \le 8 \implies 8 - 8\sqrt{2} \le 8 \quad \text{which is true}\]

Therefore, the point \((2 - \sqrt{2}, 4 + 4\sqrt{2})\) also satisfies both inequalities.

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Answer:

Expected value = $348

Step-by-step explanation:

Given the equation that modeled the total public debt D (in trillions of dollars) in the United States at the beginning of each year from 2000 through 2008 can be approximated by;

D = 0.032t^2 + 0.21t + 5.6, 0 ≤ t ≤ 8

We are to find the total public debt with the time interval;

when t = 0;

D = 0.032(0)^2 + 0.21(0) + 5.6

D = 5.6 trillion dollars

when t = 1;

D = 0.032(1)^2 + 0.21(1) + 5.6

D = 0.032+0.21+5.6

D = 5.842 trillion dollars

when t = 2;

D = 0.032(2)^2 + 0.21(2) + 5.6

D = 0.128+0.42+5.6

D =  6.148 trillion dollars

when t = 3;

D = 0.032(3)^2 + 0.21(3) + 5.6

D = 0.288+0.63+5.6

D = 6.518 trillion dollars

when t = 4;

D = 0.032(4)^2 + 0.21(4) + 5.6

D = 0.512+0.84+5.6

D = 6.952 trillion dollars

when t = 5;

D = 0.032(5)^2 + 0.21(5) + 5.6

D = 0.8+1.05+5.6

D = 7.45 trillion dollars

when t = 6;

D = 0.032(6)^2 + 0.21(6) + 5.6

D = 1.152+1.26+5.6

D = 8.012 trillion dollars

when t = 7;

D = 0.032(7)^2 + 0.21(7) + 5.6

D = 1.568+1.47+5.6

D = 8.638 trillion dollars

when t = 8;

D = 0.032(8)^2 + 0.21(8) + 5.6

D = 0.032(64)+1.68+5.6

D = 2.048+1.68+5.6

D = 9.328 trillion dollars

From the values gotten, we can see that the total public debt reached or surpassed 7 trillion dollars in 2005

To get the public debt in 2017, we can simply substitute t = 17 into the expression D = 0.032t2 + 0.21t + 5.6

D = 0.032(17)^2 + 0.21(17) + 5.6

D = 0.032(289)+3.57+5.6

D = 9.248+3.57+5.6

D(17) = 18.418 trillion dollars

Answer:

The half-life of this substance is of 569.27 days.

Step-by-step explanation:

Amount of a substance after t days:

The amount of a substance after t days is given by:

\(P(t) = P(0)e^{-kt}\)

In which P(0) is the initial amount and k is the decay rate, as a decimal.

Suppose a sample of a certain substance decayed to 69.4% of its original amount after 300 days.

This means that \(P(300) = 0.694P(0)\). We use this to find k.

\(P(t) = P(0)e^{-kt}\)

\(0.694 = P(0)e^{-300k}\)

\(e^{-300k} = 0.694\)

\(\ln{e^{-300k}} = \ln{0.694}\)

\(-300k = \ln{0.694}\)

\(k = -\frac{\ln{0.694}}{300}\)

\(k = 0.0012\)

So

\(P(t) = P(0)e^{-0.0012t}\)

What is the half-life (in days) of this substance?

This is t for which P(t) = 0.5P(0). So

\(0.5P(0) = P(0)e^{-0.0012t}\)

\(e^{-0.0012t} = 0.5\)

\(\ln{e^{-0.0012t}} = \ln{0.5}\)

\(-0.0012t = \ln{0.5}\)

\(t = -\frac{\ln{0.5}}{0.0012}\)

\(t = 569.27\)

The half-life of this substance is of 569.27 days.

Answer:

9.92 feet or 9 feet 11 1/16 inches

Step-by-step explanation:

1.24X8 feet=9.92 feet or 9 feet 11 1/16 inches

Answer:

26, 28, and 30

...............

Answer:

In the first movie, Elsa is 21, Anna is 18, and Kristoff is 23.

So after 3 years, Elsa would be 23, Anna would be 21, and Kristoff would be 26.

Step-by-step explanation:

I didn't fully understand the question, so I tried my best.

Forgive me if I am wrong.

Answer:

456

Step-by-step explanation:

Product means an answer derived from multiplication.  Therefore, if the product is 155952, and one value is 342, then the following equation is true:

342x = 155952, or 342 * x = 155952

Divide 155952 by 342 to get: 456.

Check the work in the equation:

342(456) = 155952

155952 = 155952, which is true, so the answer is 456.

If I helped, please make this answer brainliest! ;)

Answer:

90units²

Step-by-step explanation:

area of a triangle= ½base *height

area = ½*12*15

area= 90units²

Answer:

Umm is it division or what I’m confused but I want to help.

Step-by-step explanation:

Answer:

if it is 46-2004 then the answer is  -1958

Step-by-step explanation:

Answer:

  35 cm

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr²h

We want to find h for the given volume and diameter. First, we must convert the given values to compatible units.

  1 L = 1000 cm³, so 99 L = 99,000 cm³

  60 cm diameter = 2 × 30 cm radius

So, we have ...

  99,000 cm³ = π(30 cm)²h

  99,000/(900π) cm = h ≈ 35.01 cm

The oil is 35 cm deep in the drum.

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

The correct alternative that, matches the correct value of this expression is the letter A. That is, the answer will be 35.

To find the value of this expression, let's eliminate the parentheses, and add the numbers, where the signs are equal.

_ When the signs are the same: just add them up.

_ When the signs are different: just subtract.

\(\large \sf =27-(-8)\)

\(\large \sf =27+8\)

\(\boxed{\boxed{\large \sf \ 35 \ }}\)

So, the numeric value of this numeric expression will be 35.

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:   The Answer Is NOT Letter A

C. y = (x – 2)^2  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 2 , 0 )  =Already in vertex form.   y = ( x − 2 ) ^2

Step-by-step explanation:  I used math.way

A. y = (x – 2)^2 + 4  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 2 , 4 )  =Already in vertex form.   y = ( x − 2 ) ^2 + 4

B. y = x^2 – 4  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 0 , − 4 )  =Find the vertex form.   y = ( x + 0 ) ^2 − 4

C. y = (x – 2)^2  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 2 , 0 )  =Already in vertex form.   y = ( x − 2 ) ^2

D. y = (x – 4)^2 – 4  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 4 , − 4 )  =Already in vertex form.   y = ( x − 4 ) 2 − 4

Answer:

Step-by-step explanation:

AC=BD

8x-4=6x+10

2x=14

x=7

AC=8x-4=52

BD=6x+10=52

Option A and B : This statements is generally false in probability theory.

A. P(A ∪ B) = P(A) + P(B) - This statement is generally false in probability theory. This is known as the inclusion-exclusion principle, which states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.

B. P(A | B) = P(A) - This statement is generally false in probability theory. In general, P(A | B) is not equal to P(A) because the occurrence of event B affects the probability of event A.

C. P(A ∩ B) = P(A)P(B) - This statement is generally true in probability theory. This is known as the independent events rule, which states that the probability of the intersection of two independent events is equal to the product of their individual probabilities.

D. P(A | B) + P(A' | B) = 1 - This statement is generally true in probability theory.

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Let A and B be any two events. Which of the following statements, in general, are false? P(A∣B)+P(A∣B)=1                                                                                                                                    

A. P(A ∪ B) = P(A) + P(B)

B. P(A | B) = P(A)

C. P(A ∩ B) = P(A)P(B)

D. P(A | B) + P(A' | B) = 1

The value of x in the triangle is 18.59 units.

The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.

In order to find the missing side just find the ratio of the known corresponding sides of the triangles. Thus:

scale factor = (18 1/2 + 4 5/8)/ (18 1/2) = 5/4

For the smaller triangle:

3rd side = √(18.5² - 11²) = 14.87  (Pythagoras)

scale factor = x / 14.87

5/4 = x / 14.87

x  = 5/4 * 14.87

x = 18.59 units

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The correct option for the expression (5 + 9) + 10 showing the associative property is  5+ (9 + 10) = 5 + 19 = 24

The associative property of addition states that the sum of three or more numbers remains the same regardless of how the numbers are grouped.

Given that, an expression, (5 + 9) + 10

According to associative property of addition, (a+b)+c = a+(b+c)

Therefore,

(5 + 9) + 10 = 5+(9+10)

= 5+19

= 24

Hence, the correct option for the expression (5 + 9) + 10 showing the associative property is  5+ (9 + 10) = 5 + 19 = 24

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