Compare: 2.7 x 10^3 O 27 x 10^3 A.>B.

The value of x is 10 and the length of SU is 50.

Here SU is the line and T is the mid-point of the line

So from this we have

SU = ST + TU

ST = TU

SU = 2ST = 2TU

ST = 3x - 5 and TU = 2x + 5

As ST = TU

3x - 5 = 2x + 5

x = 10

SU = 2ST

     = 2( 3x - 5)

     = 2( 3 × 10 - 5)

     = 2( 30 - 5)

     = 2× 25

     = 50

Therefore the value of x is 10 and the length of SU is 50.

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Step-by-step explanation:

Let's denote the height of the tower as "h" feet.

According to the given information, the length of the pole's shadow is 3.25 ft, and the total length of the tower's shadow (including the shadow of the pole) is 190 ft.

We can set up a proportion using the similar triangles formed by the tower, its shadow, the pole, and its shadow:

height of the tower / length of the tower's shadow = height of the pole / length of the pole's shadow

h / 190 = 10 / 3.25

Cross-multiplying:

h * 3.25 = 10 * 190

h * 3.25 = 1900

Dividing both sides by 3.25:

h = 1900 / 3.25

h ≈ 584.62

Rounding to the nearest foot, the height of the tower is approximately 585 feet.

Answer:

5.75.

Step-by-step explanation:

The mean = (8+5+7+10+3+4+31+12)/ 8

= 80/8

= 10.

Now we calculate the difference of each value from the mean We take the absolute ( positive) differences

10 - 8 = 2

10 - 5 = 5

10 - 7 = 3

10 - 10 = 0

10-3 = 7

10 = 4 = 6

10 - 31 = 21

10 - 12 = 2

Sum of the differences = 46

and the mean deviation  is 46/8 = 5.75.

Answer:

Below

Step-by-step explanation:

Line AB is of the form y = mx + b    where m is the slope = 2

 Line BC is perpendicular to this and will have slope - 1/m = - 1/2   and includes the point C (0,6)

 The point slope form of line BC will then be

     ( y-6) = - 1/2 ( x - 0)    which can be re-arranged to

       y = - 1/2x + 6     < ==== equation for line BC

Answer:

(b)

Step-by-step explanation:

graph plotting

when x = -3 ,  y = 4

when x= -2 , y = 0

when x = -1 , y = -2

when x = 0 , y = -3

when x = 1, y = -3.5

Answer:

\(h(x) = 57(0.8)^x\)

Step-by-step explanation:

Given

\(f(x) = 32(0.8)^x\)

\(g(x) = 25(0.8)^x\)

Required

A function that represents the total resale value of the two vehicles

To do this, we simply add up the functions

\(h(x) = f(x) + g(x)\)

\(h(x) = 32(0.8)^x + 25(0.8)^x\)

Factorize

\(h(x) = (32 + 25)(0.8)^x\)

\(h(x) = 57(0.8)^x\)

Answer:

(0.0147, 4.0147) and (-4.04, 0.04)

Step-by-step explanation:

Let the smaller number be x

Let the larger number be y

If a positive integer is 4 less than another, then;

x = y - 4 ...1

If 3 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer and result is -67, then;

1/y - 3(1/x) = -67

1/y   -3/x = -67 ...2

Substitute 1 into 2

1/y - 3/y-4 = -67

y-4-3y/y(y-4) = -67

-4-2y = -67(y^2-4y)

- 4-2y = -67y^2 +268y

-67y^2 +268y+2y + 4  = 0

-67y^2 +270y +  4 =0

67y^2 -270y - 4 = 0

Factorize

-270±√270² - 4(-4)(67)/2(67)

= -270±√72,900+1072/134

= -270±271.97/134

= -270 -271.97/134 and  -270 +271.97/134

= -541.97/134 and 1.97/134

x = 0.0147 and -4.04

y = x+4

y = 0.0147+4

y = 4.0147

If x = -4.04

y = -4.04 + 4

y = 0.04

Hence the pair of values are (0.0147, 4.0147) and (-4.04, 0.04)

The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

1. Given: AD is a straight line and m CBD = m DBE (Given statement) 2. Since AD is a straight line, Z ABC and Z CBD are supplementary angles (Definition of supplementary angles) 3. We can write the equation: m ABC + m CBD = 180° (Definition of supplementary angles) 4. Substitute m CBD with m DBE (Substitution) 5. We have m ABC + m DBE = 180° (Substitution)

1. Given: AD is a straight line and m CBD = m DBE (Given statement)

2. Since AD is a straight line, it forms a straight angle with any other angle on it.

3. By the definition of a straight angle, we know that a straight angle measures 180°.

4. From the given statement, we can deduce that m CBD = m DBE.

5. When two angles are equal, their measures can be substituted for each other in any equation or statement.

6. Now, consider triangle ABC and triangle DBE. The sum of the angles in a triangle is always 180°.

7. In triangle ABC, we have m ABC + m BAC + m BCA = 180°.

8. In triangle DBE, we have m DBE + m BED + m EDB = 180°.

9. Since m BAC and m BED are both part of the straight angle formed by AD, they are supplementary angles and sum up to 180°.

10. Therefore, we can rewrite the equations as m ABC + m BCA + m BAC = 180° and m DBE + m EDB + m BED = 180°.

11. By substituting m CBD with m DBE (from the given statement), we have m ABC + m BCA + m BAC = 180° and m ABC + m BCA + m BED = 180°.

12. Subtracting the common terms from both equations, we get m BAC = m BED.

13. Using the transitive property, we can deduce that m ABC + m BCA = m EDB.

14. Combining the equations, we have m ABC + m DBE = m EDB.

15. Since m EDB and m ABC are supplementary angles (as they both share the straight angle formed by AD), their sum is 180°.

16. Therefore, we can conclude that m ABC + m DBE = 180°.

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Answer:

6 yards

Step-by-step explanation:

yeah-ya........ right?

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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The discriminant of the given quadratic equation is zero, which means that it has two real solutions.

What is a quadratic equation?

The polynomial equations of degree two in one variable of type

f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x).

The discriminant's value reveals how many roots f(x) has:

- The quadratic function has two unique real roots if b² - 4ac > 0, otherwise it does not.

The quadratic function has one repeating real root if b² - 4ac = 0.

- The quadratic function has no true roots if b² - 4ac < 0.

The given quadratic equation is:

2x² - 4x = -2

2x² - 4x + 2  = 0

The general equation is :

ax² + bx + c = o

where discriminant is found using the formula b² - 4ac

Comparing the equations, we can write

a = 2

b = -4

c = 2

b² - 4ac = (-4)² - 4*2*2 = 16 - 16 = 0

Since the discriminant is equal to zero, it suggests that the quadratic equation has two equal real and rational roots.

Therefore the discriminant of the given quadratic equation is zero, which means that it has two real solutions.

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Answer:

\(P(Green\ and\ Green) = \frac{25}{144}\)

Step-by-step explanation:

Given

\(Green=5\)

\(Blue = 7\)

Required

\(P(Green\ and\ Green)\)

This is calculated as:

\(P(Green\ and\ Green) = P(Green) * P(Green)\)

Since, it is a probability with replacement, we have:

\(P(Green\ and\ Green) = \frac{Green}{Total} * \frac{Green}{Total}\)

So, we have:

\(P(Green\ and\ Green) = \frac{5}{12} * \frac{5}{12}\)

\(P(Green\ and\ Green) = \frac{25}{144}\)

Explanation:

There really is not enough information here. You have not indicated how x is related to the rectangle.Perhaps (as an alternative to the assumption I made [above]), you meant for x > 0 to be the length of one side of a square.

I have attached the answer in the picture.

Answer:

The sequence is increasing by 5 at each step. So, we can write:

a1 = 30

a2 = 30 + 5 = 35

a3 = 30 + 25 = 40

a4 = 30 + 35 = 45

a5 = 30 + 4*5 = 50

We notice that the nth term is given by:

an = 30 + (n-1)5

So, the explicit formula for the nth term is:

an = 25n + 5

Answer:

\((3 {}^{x} + 2)(3 {}^{x} + 2)\)

hope it is helpful to you

Answer:636

Step-by-step explanation: I just kno

Answer:

(3 / 7) * 497 = 213 liters of natural oil

************************************************************

As a double check:

(4 / 7) * 497 = 284 liters of synthetic oil needed

213 + 284 = 491 liters

Step-by-step explanation:

The number of different passwords, considering 2 digits and 2 letters, is given as follows:

A. 6,760,000.

B. 3,276,000.

The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.

This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

The password is composed by:

With repetition, we have that:

Hence the number of passwords is given as follows:

10^4 x 26² = 6,760,000.

Without repetition, we have that:

Hence the number of passwords is given as follows:

10 x 9 x 8 x 7 x 26 x 25 = 3,276,000.

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Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

It will take 12 weeks for Praisys corn to be ready for picking.

We have been given that,

 Maya plants corns In = 4 rows

 Praisy plants corns in  = 6 rows

Maya corns ready to be picked in = 8 weeks

We have to find the number of weeks will it take Praisys corn to be ready for picking.

To find we will use the unitary method that is,

            4 rows = 8weeks

            6 rows = 8/4*6 weeks

                         = 12 weeks

Thus 12 weeks will it take Praisys corn to be ready for picking.

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Hi Student!

Looking at the question provided we are asked to find two integers.  It further specifies that those two integers should be the boundaries around the number that is produced from the square root of 11.  

Now that we know what the question is asking for, we can move onto answering the question.  We know that \(1^2\) is equal to \(1\), \(2^2\) is equal to \(4\), \(3^2\) is equal to \(9\), and \(4^2\) is equal to \(16\).  The number that was provided to us inside of the square root was 11.  That means that it would be between the number 9 and 16 which is given using \(3^2\) and \(4^2\).  

Therefore, the square root of 11 would be between the numbers 3 and 4.  The final answer is option E, 3 and 4

Therefore , coordinate problem solution is A) 3140 pulses per minute , B) 2915 beats per minute , C) heartbeat of 2915 beats per minute (D) or 2915.5 beats per minute .

When locating points or other mathematical objects precisely on a region, such as Euclidean space, a coordinate system is a technique that uses one or more numbers or coordinates. Locating a point or item on a the double plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y vectors are used to define a point's location on a 2D plane. a collection of numbers that indicate specific locations.

Here,

The slope method can be used to calculate the patient's heart rhythm after 42 minutes that use the secant line connecting the points with the specified values of t:

Heartbeat change / time change is the trend.

The heart rate can then be estimated using this slope value along with the number for heartbeats at t = 42 minutes.

A)Using coordinates 36, 2510, and 42, 2915 as examples:

Cardiac rate at 42 minutes = 2510 + (42 - 36) * 75 = 3140 Slope = (2915 - 2510) / (42 - 36) = 75

b) Using coordinates (38, 2647) and (42, 2915), respectively:

Cardiac rate at 42 minutes = 2647 + (42 - 38) * 67 = 2915 Slope = (2915 - 2647) / (42 - 38) = 67

c) Applying the values (40, 2784) and (42, 2915):

Heart rate at 42 minutes = 2784 + (42 - 40) * 65.5 = 2915.5 Slope = (2915 - 2784) / (42 - 40) = 65.5

Using coordinates (42, 2915), and (44, 3048), respectively:

Cardiac rate at 42 minutes = 2915 + (42 - 42) * 66.5 = 2915 Slope: (3048 - 2915) / (44 - 42) = 66.5

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Answer:

408.2sq inches

Step-by-step explanation:

Area of the cylindrical box = 2πr(r+h)

r is the radius  = diameter/2

r = 10/2 = 5in

h is the height = 8in

Substitute

Area of the cylindrical box  = 2(3.14)(5)(5+8)

Area of the cylindrical box = 2 * 3.14 * 5 * 13

Area of the cylindrical box  = 408.2sq inches