Find the perimeter of a rectangle whose vertices are (3,2), (13,2), (13,9), and (3,9).

Answer:

False

Step-by-step explanation:

First, you could add 16 to both sides, because the 16 is negative. 16 needs to be added to both sides to cancel it.

Then, you would divide by 6.

So, this is false because you would add 16 instead of subtracting 16.

Points (6,-11) and (-2,9)

then

a) Slope m= Y/X = (9 --11)/ (-2-6) = 20/-8= -5/2

b) equation of line y = mx + b

find b= y - mx = 9 -(-5/2)•(-2) = 9 - 5= 4

then equation is

y= (-5/2)x + 4

c) y-intercept of this line is

x= 0 , y= 4

d) graph of this line

Answer:

Wyzant

SOLVE IT

Chi Y. asked • 07/27/18

The sum of the digits of a 2-digit number is 14. If it’s digit are reversed, the original number is increased by 18. What is the number?

There is no format. I just the answer ASAP.

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Andy C. answered • 07/27/18

TUTOR 4.9 (27)

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Here is the algebraic solution:

T is the tens digit

O is the ones digit

T+O = 14

So O = 14 - T <---- this is the first equation

The original number is 10*T + O

If the digits are reversed the original number is increased by 18.

The number if the digits are reversed is:

10*O + T = 10*T + O + 18

10*(14-T) + T = 10*T + (14-T) + 18 <--- substitutes O with 14-T per first equation above in bold

140 - 10T + T = 10T + 14 - T + 18 <--- distributive left side

140 - 9T = 9T + 32

140 = 9T + 9T + 32

140 - 32 = 9T + 9T

108 = 18T

108/18 = T

T= 6

THe tens digit is 6.

The ones digit must be 8.

Reversing 86 - 68 = 18

The original number is 68.

Answer:

x=5

Step-by-step explanation:

The midsegment of a trapezoid is equal to the sum of the two bases divided by two. This means that 17 = (2x + 1 + 3x + 8)/2. To start, multiply both sides by 2 to get 34 = 2x + 1 + 3x + 8. Next, combine like terms to get 34 = 5x + 9. Subtract 9 from both sides for 25 = 5x. Finally, divide both sides by 5 to get an x-value of 5.

Ok, so

We want to simplify:

We could sum or substract the similar terms given. Remember that similar terms, are terms whose variables are the same.

This is:

Simplifying:

Answer:

Volume = 2×2×2 = 8 feet3

The Standard Normal Table is a tool that is used to calculate probabilities associated with the standard normal distribution.

When using the Standard Normal Table, we can find the area to the left of z < -2.34 by first locating the value -2.3 in the left-hand column of the table and the value -0.04 in the top row of the table.

Then, we find the intersection of the row and column to locate the corresponding value of 0.0099. This value represents the area to the left of -2.3 on the standard normal distribution.

To find the area to the left of -2.34, we need to adjust the value by subtracting the area to the left of -2.34 from the area to the left of -2.3.

The standard normal distribution is symmetric around the mean of 0. It means the area to the right of -2.3 is the same as the area to the left of 2.3.

Therefore, the area to the left of z < -2.34 is the area to the left of -2.3 (0.0099) minus the area between -2.34 and -2.3 (0.0040), which equals 0.0059. So, the area to the left of z < -2.34 is 0.0059.

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Answer:

Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 12. Many consider it to be the most important unsolved problem in pure mathematics.

Answer:The Riemann Hypothesis is a famous conjecture in mathematics that was first proposed by the German mathematician Bernhard Riemann in 1859. It concerns the distribution of prime numbers, which are the building blocks of all integers.

The hypothesis states that all non-trivial zeros of the Riemann zeta function, which is a complex function defined on the complex plane, lie on a straight line known as the "critical line" with a real part equal to 1/2. This conjecture has been shown to be true for the first several trillion zeros, but a rigorous proof has yet to be found.

The Riemann Hypothesis is considered to be one of the most important unsolved problems in mathematics and has numerous implications for the distribution of prime numbers. If the hypothesis is proven to be true, it would have far-reaching consequences for many areas of mathematics, including algebraic geometry, topology, and physics.

In addition to its theoretical importance, the Riemann Hypothesis also has practical applications in cryptography, where it is used to generate secure encryption algorithms. Despite many attempts by mathematicians over the past century and a half, the Riemann Hypothesis remains one of the most challenging and important problems in mathematics.

Answer:

  4 and 8

Step-by-step explanation:

Let 'a' represent one of the numbers. Then the other is 12-a, and their difference is ...

  a - (12-a) = -4

  2a = 8 . . . . add 12

  a = 4 . . . . . divide by 2

  12-a = 8 . . . . find the other number

The two numbers are 4 and 8.

Answer: x = 4, y = 8

Step-by-step explanation:

Let the two numbers be x and y

sum of the two numbers will be

x + y =  12 ------------------------------1

Difference of the two numbers

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

Now, to find the two numbers , we solve equation 1 & 2 together

  x + y =  12

  x - y  =  -4

we now add the two equations to eliminate y

   2x =  8

      x = 4.  Now to find the value of y, we substitute for x in any of the equation above

 x + y  = 12

 4  + y = 12

        y =  12 - 4

        y  =  8

The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

We have,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l

where:

a and b are the lengths of the two parallel sides (the bases) of the trapezoid

h is the height of the trapezoid (the perpendicular distance between the two bases)

l is the length of the prism (the distance between the two trapezoidal faces)

Now,

a = 9

b = 12

l = 15

Height h can be calculated using the Pythagorean theorem.

15² = (12 - 9)² + h²

h² = 225 + 9

h² = 234

h = √234

h = 15

Now,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l
V = ((9 + 12) / 2) x 15 x 15

V = 2362.5

And,

The surface area (A) of a trapezoidal prism can be calculated using the formula:

A = ph + 2B

where p is the perimeter of the trapezoidal base, h is the height of the prism, and B is the area of one of the bases.

So,

p = 12 + 8 + 12 + 8 = 44

h = 15

B = 12 x 8 = 96

Now,

Total surface area​.
= 44 x 15 + 2 x 96

= 660 + 192

= 852

Thus,

The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

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The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.

The probability of missing all 4 shots is (0.75)^4 = 0.3164.

Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:

1 - 0.3164 = 0.6836 or 68.36%.

So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.

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Answer:

57°F

Step-by-step explanation:

The absolute value of -9 plus 48 equals 57.

The matrix A of T

a. \(A = [ 0 -1 ]\)

b. \(A = [ 0 -1 ]\)

c. \(A = [ 1/sqrt(2) 1/sqrt(2) ]\)

d. \(A = [ -1/sqrt(2) 1/sqrt(2) ]\)

To find the matrix A of the reflection transformation T in the line \(y = -x\), we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [-1 0]\) and \(T(e2) = [0 -1]\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ -1 0 ]\)

\([ 0 -1 ]\)

To find the matrix A of the transformation \(T(x) = -x\) for each x in R2, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [-1 0]\) and \(T(e2) = [0 -1]\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ -1 0 ]\)

\([ 0 -1 ]\)

To find the matrix A, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [1 1] / sqrt(2)\)  and \(T(e2) = [-1 1] / sqrt(2)\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ 1/sqrt(2) -1/sqrt(2) ]\)

\([ 1/sqrt(2) 1/sqrt(2) ]\)

d. To find the matrix A, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [1 -1] / sqrt(2)\) and \(T(e2) = [1 1] / sqrt(2)\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ 1/sqrt(2) 1/sqrt(2) ]\)

\([ -1/sqrt(2) 1/sqrt(2) ]\)

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Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

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The first one is Add/Subtract the same quantity to/from both sides and the second one is Yes

The letter E would be drawn roughly 40 times, but probably not exactly 20 times.

The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

P(A) = f / N determines probability, which quantifies the possibility of an event happening. Probability and odds are connected, but probability is necessary for odds to exist.

Statistical formula

P(A) stands for the likelihood that event A will occur.

f = Number of possible outcomes of an event (frequency)

N stands for the total number of outcomes.

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Answer:

x=–4, y=1

Step-by-step explanation:

adding the 2 equations, we see the X's go away and we are left with: 10y=10. we can simplify and solve for y by dividing both sides by 10 and we are left with y=1

plugging 'y=1' into the fist equation we get: -7x+6=34. we can now solve for x by subtracting 6 from both sides and dividing both side by –7, so we are left with: x=–4

we can check by plugging both x and y into one of the original equations:

-7(-4)+6(1)=34

28+6=34

34=34✓

Answer:

x=67

y=113

z=50

Step-by-step explanation:

x=180-28-85=67

y=180-67=113

z=17+113=50

The solution to the expression 7 x 6 - 3(22 - 1) using BODMAS is -21.

BODMAS is an acronym that stands for "Brackets, Orders, Division and Multiplication, and Addition and Subtraction." It is a rule used to determine the order of operations when evaluating mathematical expressions.

Using BODMAS, we can simplify the given expression as follows:

7 x 6 - 3(22 - 1)

= 7 x 6 - 3(21)   [since 22 - 1 = 21]

= 42 - 63         [since 3(21) = 63]

= -21             [since 42 - 63 = -21]

Therefore, the solution to the expression 7 x 6 - 3(22 - 1) using BODMAS is -21.

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

The blueprints say that 1 inch represents 10 feet. This means we can form the equation below

1 inch = 10 feet

Of course 10 feet is much larger than 1 inch, so they cannot be actually equal to one another, but it helps tie together the two quantities. And it also allows us to multiply both sides by 3 to get

3 inches = 30 feet

So 3 inches on paper means we have 30 feet in real life.

Similarly,

1 inch = 10 feet

5.5 inches = 55 feet (multiply both sides by 5.5)

The 3 inch by 5.5 inch rectangle on paper corresponds to a 30 feet by 55 feet rectangle in real life.

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

In short, you multiply each given dimension by 10

3 inches goes to 3*30 = 30 feet

5.5 inches goes to 5.5*10 = 55 feet

The correct options are (a) and (b). The graph of f(x) will intersect the x-axis at x = 9 - 3 = 6 or x = 9 - 4 = 5.

Given that f(9) = 7, f'(9) = 6, and f''(9) = 2.

Now, we can use the second derivative test to determine whether the graph of the function intersects the x-axis or not at point (9, 7).

Second Derivative Test: Let f be a function whose second derivative is continuous near c. If f'(c) = 0 and f''(c) > 0, then f has a relative minimum at (c, f(c)).

If f'(c) = 0 and f''(c) < 0, then f has a relative maximum at (c, f(c)).

If f'(c) = 0 and f''(c) = 0, then the test fails and we cannot say whether c is a relative maximum, relative minimum, or neither.

Let's see if there is an x-intercept of the graph of f.

To do this, we need to look for values of x such that f(x) = 0.

Using Taylor's formula, we can write:

f(9+h) = f(9) + f'(9)h + f''(c)/2!h²

where c is between 9 and 9 + h.

Therefore, we have

f(9+h) = 7 + 6h + ½(2)h² = 7 + 6h + h².

So, to find the possible values of h, we must find the roots of the quadratic equation:

f(9+h) = 7 + 6h + h² = 0.

By solving the quadratic equation, we get the roots as h = -3 and h = -4.

Therefore, the graph of f(x) will intersect the x-axis at x = 9 - 3 = 6 or x = 9 - 4 = 5.

Thus, the answer is the options (a) and (b) are both correct.

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Answer:

1/2 x 7= 3.5

Step-by-step explanation:

The bottom left graph is the line of best fit for the graph in this problem.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence the graph of the line of best fit should have the smallest possible residual values, meaning that the points on the scatter plot are the closest possible to the line.

For this problem, we have that the bottom left graph has the smaller residuals, hence it shows the line of best fit for the data.

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The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)

f(x) = x^2 -2x +3 and f(x) = -2x + 12

which means

x^2 -2x +3  = -2x + 12

x^2 -2x +3  + 2x - 12 = 0

x^2 -9 = 0

by factorizing we have

(x-3)(x+3) = 0

x = 3 or -3

when x = 3

f(x) = -2x + 12

f(3) = -2(3) + 12 which is 6

when x = -3

f(-3) = -2(-3) + 12 which is 18

ordered pairs are (3, 6) and (-3, 18)

In conclusion, (3, 6) and (-3, 18) are the ordered pairs

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Answer:

1,-3

Step-by-step explanation:

Answer:

-3/1

Step-by-step explanation:

take the two points

(-2,10) and (-1,7)

plug it in into y2-y1/x2-x1

and you get -3/1

Answer:

30

Step-by-step explanation:

Answer:

Depends...

Step-by-step explanation:

If 2in and 14 in are diameter

C=2pi in.

C=14pi in.

If 2in and 14in are radii

C=4(pi).

C=28(pi)

The thickness of the tharsan thir is approximately 0.06 mm when expressed in two decimal places.

To convert micrometers (μm) to millimeters (mm), we need to divide the value in micrometers by 1000 since there are 1000 micrometers in a millimeter.

Given that the thickness is 60 μm, we can perform the conversion as follows:

60 μm / 1000 = 0.06 mm

Therefore, the thickness of the tharsan thir is approximately 0.06 mm when expressed in two decimal places.

Millimeters and micrometers are both units of length, with millimeters being the larger unit. Micrometers are often used to represent very small measurements, such as the thickness of thin materials or microscopic objects. In this case, the tharsan thir has a thickness of 60 micrometers, which is equivalent to 0.06 millimeters.

Converting between micrometers and millimeters is a simple process involving the division by 1000. This conversion is necessary when dealing with different scales or when using units that are more convenient for a specific application.

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A tharsan thir has a thicknoss of about 60μm. What is this in millimeters? Express your answer in two decimal places

Answer:

I think it is 3

Step-by-step explanation:

3,

Answer:

Its three.

Step-by-step explanation:

When you see a sequence such as this one, it is called an arithmetic sequence. You must add to get to the next term. So, the amount of numbers that you need to get from 3 to 6, 6 to 9, and 9 to 12 would be the common difference, so the common difference in this specific sequence would be 3.