In quadrilateral ABCD, triangle ADC is congruent to CBA. Show
that ABCD is a parallelogram.

Answer:

350 seconds to jog 5 laps.

Step-by-step explanation:

One lap of a running track is 350m Kyle jogs 5 complete laps at an average speed of 5 m/s. How long does it take him in seconds?

First, to run one lap:

350m / 5 meters per second = 70 seconds

Now, solve for five laps:

70 seconds * 5 laps = 350 seconds to jog 5 laps.

[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ f(-4)=1\hspace{5em}1=ab^{-4}\implies 1=\cfrac{a}{b^4}\implies b^4=a \\\\[-0.35em] ~\dotfill\\\\ f(4)=69\hspace{5em}69=ab^4\implies \stackrel{\textit{substituting from the 1st equation}}{69=(b^4)b^4\implies 69=b^8} \\\\\\ \sqrt[8]{69}=b\implies (69)^{\frac{1}{8}}=b \\\\[-0.35em] ~\dotfill[/tex]

[tex]y=\sqrt{69}\left( (69)^{\frac{1}{8}} \right)^x\implies \boxed{y=\sqrt{69}(69)^{\frac{x}{8}}} \\\\\\ \textit{when x=6.5, what is "y"?}\qquad y=\sqrt{69}(69)^{\frac{6.5}{8}}\implies y\approx 1522.73[/tex]

What is the Distribution Property?

The distribution property in math is a process that allows an equation to be simplified to help easily solve problems. Expressions that qualify to use the distributive property are usually written in the format: a(b +c)

a is then distributed to both b and c, rewriting the equation as ab +ac, where a has been multiplied to both values.

In this problem, you can distribute -15 to both 5x and 6y.

This will leave you with and equation that resembles this:

(-15×5x) + (-15×6y)

Multiply -15 to the coefficient attached to the variable to get your answer.

Your answer is -75x + -90y or -75x-90y

The product of the given matrix is  [tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]

What is a matrix?

A rectangular matrix is a set of numbers arranged into a predetermined number of rows and columns. The rows of a matrix are formed when the elements are placed in a horizontal matrix. The columns of a matrix are formed by the elements when they are stacked in the matrix vertically.

Here, we have given a matrix that is

A = [tex]\left[\begin{array}{ccc}5&5\\-2&3\end{array}\right][/tex]       B = [tex]\left[\begin{array}{ccc}-4&9\\8&7\end{array}\right][/tex]

We have to find the product of this matrix

[tex]\left[\begin{array}{ccc}5&5\\-2&3\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}-4&9\\8&7\end{array}\right][/tex]

First, we multiply the first row of matrix A with the first column of matrix B then continue in this manner, we get

[tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]

Hence, the product of the given matrix is  [tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]

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The equation that gives the value of k in terms of x and y is  k = y*x  .

In the question ,

it is given that ,

the variation is an inverse variation .

So , equation representing the inverse proportionality is

y ∝ 1/x ,

to remove the proportionality sign (∝) , we introduce

the constant k which is called as Constant of Proportionality .

So , the equation becomes

y = k * 1/x

y = k/x

Simplifying further , we get

k = y*x

Therefore , The equation that gives the value of k in terms of x and y is  k = y*x  .

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We may determine the option a) 15x - 12 by simply multiplying and adding them by the necessary terms.

A linear equation is an algebraic equation of the form y = mx + b. involving only a continuing and a first-order ( linear ) term, where m is the slope and b is the y-intercept.

5X ( 3 - 12 X) - 3 ( 4 - 20[tex]x^{2}[/tex] )

15X - 60[tex]x^{2} \\[/tex] - 3 ( 4 - 20[tex]x^{2}[/tex] )

15X - 60[tex]x^{2} \\[/tex] - 12 + 60[tex]x^{2}[/tex]

15X - 12 this is required solution .

Just by simply multiplying and adding them by required terms we can conclude 15x - 12.

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At least 10 people or guests could go to a party and the second caterer is $250 cheaper to hire.

In the question we can use the equation :

  Y = mx + b ,  which is the slope-intercept form of the equation of a straight line. Here, m is the slope of the line and b is the intercept, x and y represent the distance of the line from the x-axis and y-axis, respectively.

For caterer A, the cost per guest is $15. This is the m value. The b value is the additional fee for setting up the tables, $100.

Here, the equation will be  y = 15x + 100     -------------------------(1)

For Caterer B, the cost per guest is $20. The b value is the additional fee for setting up the tables $50.

For this the equation will be : Y = 20X + 50.  --------------------- (2)

To find the number of guests that will result in an equal cost, set the equations equal to one another. Solve for x.

                    15x + 100 = 20x + 50        ---------------------- (3)

solving the equation (3),

   15x - 20x = 50 - 100

⇒ -5x = - 50

⇒ x = 10

Putting x = 10 in equation (1),

   15 × 10 + $100 = $250

Therefore, the cost of 10 people or guest will attend the party and the second caterer is $250 cheaper then the first caterer.  

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Answer:

Divide the calories by 2 to get the amount for 1 mile the multiply that by 3 to get your answer which is 277.5 calories

Step-by-step explanation:

Answer: twenty eight-twelfths (or seven-thirds in the simplest form)

Step-by-step explanation:

The distance travelled by the car in 34 minutes is 22.667 miles.

We are given a car. The car is travelling at a steady speed. It travels 1.5 miles in 2.25 minutes. We need to find the distance travelled by the car in 34 minutes. First of all, we need to find the speed of the car. The speed of the car is the ratio of the distance travelled and the corresponding time taken.

v = s/t

v = 1.5/2.25

v = 0.667

Hence, the speed of the car is 0.667 miles per minute. The speed of the car remains constant throughout its journey. Let the distance travelled by the car be denoted by "d" . The distance travelled in 34 minutes is calculated below.

d = v*t

d = 0.667*34

d = 22.667

Hence, the distance travelled by the car in 34 minutes is 22.667 miles.

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The rate  that is the best deal for a bottle of mustard is: C: $2.42 for 12 oz.

a. $1.26 for 6 oz

Unit rate = $1.26 / 6 oz

Unit rate = $0.21

b. $1.65 for 8 oz

Unit rate = $1.65 / 8 oz

Unit rate = $0.206

Unit rate = $0.21 (Approximately)

c.  $2.42 for 12 oz

Unit rate =   $2.42 /12 oz

Unit rate =  $0.201

Unit rate = $0.20 (Approximately)

d.  $3.30 for 16 oz

Unit rate = $3.30 / 16 oz

Unit rate = $0.206

Unit rate = $0.21 (Approximately)

Therefore the correct option is C.

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Answer:

[tex]-18x+20[/tex]

Step-by-step explanation:

We can simplify to find an equivalent expression

Take a look at the attachment...

Hope this helps! :)

Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies then,

Here, given data as the first batch was 120 gingerbread cookies and the second batch consist of 150 shortbread cookies.

And, the same fractions of cookies from each batch were saved.

Let x parts of each of cookies were saved.

Then, the number of the saved gingerbread cookies = 120 x

While, the number of the saved shortbread cookies = 150 x

And, Again according to the question, the number of the saved shortbread cookies is 20 more than the number of the saved shortbread cookies.

That is equal to 150 x - 120 x = 20

⇒ 30 x = 20

⇒ x = 2/3

Hence the answer is, Mrs. Nicholas saved 2/3 part of each cookies.

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The sub contractor pays $0.94 per hour for the work .

In the question ,

it is given that ,

the amount paid by the contractor for 25 hours of work = $23.50

We need to find the amount paid by the contractor for 1 hour .

The per hour pay can be calculated using the formula ,

amount paid per hour = (amount paid for 25 hours)/( number of hours)

substituting the values ,we get

So , the amount paid by the contractor for 1 hour of work = 23.50/25

= $0.94

Therefore , The sub contractor pays $0.94  per hour for the work .

The given question is incomplete , the complete question is

A sub-contracted job pay $23. 50 for 25 hour of work. How much money does it pay per hour ?

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Answer: Error

Step-by-step explanation: Its impossible to divide by zero.

Answer:

0

Explanation Anything divided by zero is zero

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]x-2y=6\implies -2y=-x+6\implies y=\cfrac{-x+6}{-2} \\\\\\ y-\cfrac{-x}{-2}+\cfrac{6}{-2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]

so we're really looking for the equation of a line whose slope is -2 and that it passes through (-3 , -1)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-3)}) \implies y +1= -2 (x +3) \\\\\\ y+1=-2x-6\implies {\Large \begin{array}{llll} y=-2x-7 \end{array}}[/tex]

Answer:

1/6

Step-by-step explanation:

[tex]36^{-1/2}=\frac{1}{36^{1/2}}=\frac{1}{\sqrt{36}}=\frac{1}{6}[/tex]

Answer:

what is ur questions we cant see them

Answer:

13x-12y+6xy

Step-by-step explanation:

To  make this easier, we can rearrange these terms, and get

5x+8x-12y+2xy+4xy.

x and y just represent variables, so we can combine 5x and 8x to get 13x, and we can combine 2xy and 4xy to get 6xy.

Now we have 13x-12y+6xy, and nothing else can be combined.

If the domain of the function f(x) = 2x + 1 is {-2 ≤ x ≤ 3}, an integer which is not in the range is: a) -4.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values (real numbers), which are shown on the y-axis of a graph.

When x = -2, the range of this function f(x) = 2x + 1 is given by:

f(-2) = 2(-2) + 1

f(-2) = -4 + 1

f(-2) = -3

When x = 3, the range of this function f(x) = 2x + 1 is given by:

f(3) = 2(3) + 1

f(3) = 6 + 1

f(3) = 7

Therefore, the range of this function is -3 ≤ y ≤ 7 and as such, -4 is an integer that is not within the range as shown in the number line attached below.

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Answer:

The graph gets shifted up more

Step-by-step explanation:

Calculating the values of x^2    and then adding a constant 'c' to that value shifts the graph upward by the value of 'c'

Answer:

The vertex (or minimum) would move to a higher position on the y -axis

Step-by-step explanation:

Whatever the value of C is, will be where the vertex of the quadratic sits

An equation for the curve that passes through the point (1,0) and whose slope at (x,y) is xe^y is y = -1/x -1.

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches. The slope is nothing more than the tangent to the angle formed with the x-axis measured. As a result, it is simply an angle's measurement.

Given,

The curve that passes through the point (1,0) and whose slope at (x,y) is xe^y.

Since x-2 is equal to the slope of the function f(x), we can express that as

dy/dx = x^-2

dx multiplication and integration of both sides:

y = -1/x + C

Connecting the provided point:

0 = -1/1 + C

C = -1

Consequently, the curve's equation is

y = -1/x -1

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Answer:

45

Step-by-step explanation:

At this point, b) is basically asking for how many two digits numbers have a greater digit on the right from 0-9, because we already know the other two digits in the four-digit pin.

01-09 has 9 poissibilites.

12-19 has 8 possibilites.

23-29 has 7 possibilites.

34-35 has 6 possibilites.

45-49 has 5 possibilites.

56-59 has 4 possibilities.

67-69 has 3 possibilities.

78-79 has 2 possibilities.

89 has 1 possibility.

90-99 has 0 possibilities.

9+8+7+6+5+4+3+2+1+0=45 possibilities.

Answer:

Step-by-step explanation:

Each of the digits 3 and 4 can get numbers 0 through 9, in total 10 options per each digit:

The two- digit combinations with the last digit being larger has the following cases:

Total number of possibilities:

The ordered pair that is not a solution to the inequality y ≥ 2x² - 4x + 2 is given as follows:

(-1,6).

The inequality is presented as follows:

y ≥ 2x² - 4x + 2.

Then for each pair, the numeric value is calculated, replacing x and y by it's respective coordinates, and when a false statement is generated, the ordered pair is not a solution to the inequality.

For the first ordered pair, (-1, 6), the numeric value of the inequality is given as follows:

6 ≥ 2(-1)² - 4(-1) + 2

6 ≥ 8.

Which is a contradiction, hence it is not a solution to the inequality.

For the pair (1,0), we have that:

0 ≥ 2(1)² - 4(1) + 2

0 ≥ 0.

Which is true, hence it is a solution.

For the pair (0,3), we have that:

3 ≥ 2(0)² - 4(0) + 2

3 ≥ 2

Hence it is also a solution.

For the pair (2,5), we have that:

5 ≥ 2(2)² - 4(2) + 2

5 ≥ 2

Hence it is also a solution.

The problem is given by the image shown at the end of the answer.

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Answer:

Step-by-step explanation:

OB = 10 cm

OA = OC = Radius = 4 cm

COS <AB = OA/OB = 4/10 = 2/5 =

COS< COB = OC/OB = 4/10 = 2/5

=> <AOC = <AOB + <COB

=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)

=> <AOC = 2 Cos-¹(2/5)

=> <AOC = 2 * 66.42

=> <AOC = 132.84°

if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm

if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm

Answer:

W = 35/4 aka 8 3/4 or 8.75

Step-by-step explanation:

Answer: w = 35/4

Step-by-step explanation: w−

2

1

​

=8

4

1

​

Multiply both sides of the equation by 4, the least common multiple of 2,4.

4w−2=8×4+1

Multiply 8 and 4 to get 32.

4w−2=32+1

Add 32 and 1 to get 33.

4w−2=33

Add 2 to both sides.

4w=33+2

Add 33 and 2 to get 35.

4w=35

Divide both sides by 4.

w= 35/4

​

Answer:

Let r be the rate at which he travels and t be the time.

Then, rt = 60

If he travels 8 mph faster, he arrives 10 hours sooner, so

(r+8)(t - 10) = 60

Multiplying, rt - 10r + 8t - 80 = 60

Substituting rt = 60, we get

60 - 10r + 8t - 80 = 60

Then, 8t = 10r + 80

t = 5/4r + 10

Substitute this into rt = 60

r(5/4r + 10) = 60

5/4r^2 + 10r - 60 = 0

Multipling by 4/5

r^2 + 8r - 48 = 0

(r + 12)(r - 4) = 0

r = -12, 4

A negative solution does not make sense

Thus, r = 4 4 mph is the solution.

Checking, rt = 60, so 4t = 60, and t = 15

Showing that this meets the other condition,

(r+8)(t - 10) = (4+8)(15-10) = 12 * 5 = 60

It checks.

The function (f-g)(x) = x²+3x+5

A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable

Given: f(x) = √16x⁴ = 4x² and g(x) = 3x²-3x-5

To evaluate (f-g)(x) such g(x) from f(x). Thus:

(f-g)(x) = 4x²-(3x²-3x-5)

          = 4x²-3x²+3x+5

          = x²+3x+5

Therefore, (f-g)(x) is x²+3x+5. The 4th option is the answer

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Answer:

m<M = 76°

m<N = 76°

LN = 18 in

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180.

triangle LMN is an isosceles triangle and the measure of M is equal to N and LM = LN.

Now the measure of missing angle:

m<M + m<N + 28 = 180 subtract 28 from both sides

m<M + m<N = 152 since the measure of M is equal to N divide 152 by 2

152 ÷ 2 = 76 each angle is 76°

The probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].

Given:

mean = 1/100

Let X = the number of components that fail before 200 hours . The X has a binomial distribution n = 3 and p = 1 – e^-2.

probability p = 3/2[tex]p^{2} (1-p)[/tex] + 3/3 [tex]p^{3}[/tex].

= 3([tex]1-e^-2)^2[/tex][tex]e^-2[/tex] + ([tex]1-e^-2)^3[/tex]

= [tex](1-e^-^2)^2[3e^-^2 - e^-^2+1][/tex]

= [tex](1-e^{-2} )^2[2e^-2+1][/tex]

Therefore the probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].

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