The plan for a city park shows that the park is a quadrilateral with straight paths along the diagonals. For what values of the variables is the park a parallelogram? In this case, what are the lengths of the paths?

Answer:

y = -2x + 5

Step-by-step explanation:

The slope is -2/1 and the y intercept is 5.  

Answer:

Felicia needs 3.17 minutes to run once around the track

Step-by-step explanation:

Subtraction

Shaq is known to run once around the track in 8.07 minutes. Felicia runs once around the track in 4.90 less than Shaq.

We don't know how long does it take Felicia to run once around the track, but we can find it by subtracting the time done by Shaq with the difference between their relative times.

Felicia takes 8.07 min - 4.90 min = 3.17 min.

Felicia needs 3.17 minutes to run once around the track

Answer:

27.4%

Step-by-step explanation:

Step one:

given

original cost $69

seling price $52

Required

The percent reduction

Step two:

% reduction= change in price/original price*100

% reduction= 69-52/62*100

% reduction=17/62*100

% reduction= 0.274*100

% reduction= 27.4%

Answer:

[tex]\dfrac{31}{2}+\dfrac{27}{2}i[/tex]

Step-by-step explanation:

The given complex number is:

[tex]z=\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}[/tex]

Firstly we can solve (2+3i)(4-7i)(1+i)

= 2(8)+2(-7i)+4(3i)+3i(-7i²)× (1+i)

= (16-14i+12i-21i²i)× (1+i)

Since, i² = -1

= (16-14i+12i-21(-1)i)× (1+i)

= (16-14i+12i+21)× (1+i)

= (29-2i)(1+i)

= 31+27i

Denominator : (1-i²)

= (1-(-1))

= 2

[tex]\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}=\dfrac{31+27i}{2}\\\\=\dfrac{31}{2}+\dfrac{27}{2}i[/tex]

Hence, the correct answer is [tex]\dfrac{31}{2}+\dfrac{27}{2}i[/tex].

Answer:

x=-3

Step-by-step explanation:

x+8=5

subtract 8 from 5 to get x on its own

x=-3

Answer:

2cos(330º)

Step-by-step explanation:

both equal to √3

Expressing 4cos2(165°) – 2 as a single trignometric function, it will be written as : 2cos(330º)

Trigonometric function can be defined as real functions in mathematics that forms a relationship between an angle of a right-angled triangle to the ratio of the length of two sides.

Trigonometric function is very important as it is mostly concerned with functions of angles and their application in calculation

In conclusion, to express 4cos2(165°) – 2 as a single trignometric function, it will be written as : 2cos(330º)

Learn more about  trigonometric  function: https://brainly.com/question/24349828

#SPJ2

Answer:

5p+4>14 (A)

Step-by-step explanation:

Open dot means that the value is not included.

Answer:

No solutions

Step-by-step explanation:

As it's parallel line

Answer:

42:14

42 cats and 14 fish

Answer:

3:1

Step-by-step explanation:

42 : 14 ---> 42/14 = 21/7 = 3/1 ---> 3 : 1

Answer:

using a scale of 2", is another way to say, "is going to grab the original, and blow it up to 2 times as large".

so, the resulting copy is twice as large as the original.

Step-by-step explanation:

Answer: A picture is photocopied by using a scale factor of 2. Each side of the photocopy of the picture is

enlarged by a factor of 2.

enlarged by a factor of One-half.

reduced by a factor of 2.

reduced by a factor of One-half

Step-by-step explanation:

Answer:

$11.80

Step-by-step explanation:

3*$1.10 = $3.30

price without tax,

= 38.70-3.30

= 35.40

Cost of each CD,

= 35.40/3

= 11.80

Answer:

11.80 dollars

Step-by-step explanation:

Well, first I would multiply 1.10 by 3 which is 3.30 then subtract 38.70 - 3.30 and get 35.40, and finally divide 35.40 by 3 to get 11.80

Answer:

$23.75

Step-by-step explanation:

5.50*2=11

4.25*3=12.75

11.00+12.75=23.75

Denominators= 4 and 6

LCM of 4 and 6 => 12

So, the least common denominator of the given fractions is 12.

Hope it helps!

Answer:

12

Step-by-step explanation:

1/4 and 5/6

4, 8, 12

6, 12

Answer:

a) (i) 1200

b) (ii) 3750

c) (i) [tex]\frac{3}{20}[/tex]

Step-by-step explanation:

a) Total number of students = 5000

Ratio of teachers to students = 6 : 25

i) Number of teachers = ?

By the given ratio, we can let the number of teachers = 6[tex]x[/tex]

and we can let the number of students = 25[tex]x[/tex]

[tex]25x = 5000\\\Rightarrow x = 200[/tex]

Therefore, number of teachers = 6 [tex]\times[/tex] 200 = 1200

b) A Quarter of the students own i-phone classic 20.

ii) Number of students who do not own an i-phone classic?

As per question statement,

Number of students who own i-phone classic 20 = [tex]\frac{1}{4}\times 5000[/tex] = 1250

Number of students who do not own i-phone classic 20 = 5000 - 1250 = 3750

c) Number of students who own samsung galaxy a80s = 60% of students who own i-phone classic 20 = [tex]\frac{60}{100}\times 1250[/tex] = 750

Fraction of students who own samsung galaxy a80s = Number of students having samsung a80s divided by total number of students

[tex]\dfrac{750}{5000} = \dfrac{3}{20}[/tex]

Answer:

a)

x      -3         -2         -1         0          1            2         3

y       0          8          6         0         -4           0        18

b)

see in the table, at x = {-3; 0; 2}, y = 0

=> x = {-3; 0; 2} is the solutions of the equation x³ + x² - 6x = 0

Step-by-step explanation:

a) 0 and 6  will be written in the given blank spaces.

b) The value of x for the given equation is 0, -3 and 2.

It is a method for finding the values of variable, by substituting the value of one variable to get the another.

To solve a polynomial equation, first write it in standard form. Once it is equal to zero, factor it and then set each variable factor equal to zero.

a). We have, an equation

[tex]y = x^{3}+x^{2} -6x[/tex]

so, at x = -3

[tex]y = -3^{3} +(-3)^{2} -6(-3)[/tex] =  -27+9+18 = 0   (substitute x = -3 in the given equation)

at x = -1

y = [tex]-1^{3} +(-1)^{2} -6(-1) = -1+1+6 = 6[/tex]

Hence, 0 and 6 will we written the blank spaces of the given table.

b). We have an equation

[tex]x^{3} +x^{2}-6x = 0[/tex]

⇒ [tex]x(x^{2} +x-6)=0[/tex]

⇒ [tex]x (x^{2} +3x-2x-6)=0[/tex]

⇒ [tex]x(x(x+3)-2(x+3))=0[/tex]

⇒ [tex]x(x+3)(x-2)=0[/tex]

⇒ [tex]x = 0,-3 and 2[/tex]

Hence, 0, -3 and 2 are the solutions of the given equation.

Learn more about substitution method  here:

https://brainly.com/question/14619835

#SPJ2

Answer:

A. The slope is  [tex]\frac{3}{2}[/tex]

B.  the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point.

Step-by-step explanation:

PART A: Slope

Given tangent line;

[tex]y = \frac{3x}{2} + \frac{9}{2}[/tex]

The slope of the tangent line is equal to the derivative of the function;

[tex]\frac{dy}{dx} =\frac{3}{2}[/tex]

the slope = [tex]\frac{3}{2}[/tex]

PART B: Correct statement that describe the slope of a tangent line:

A secant line is a straight line joining two points on a function and the slope of the function is equal to average rate of change of the function between the two points.

A tangent line is a straight line that touches a function at only one point, and the slope of the function is equal to the instantaneous rate of change of the function at that one point.

Thus, the correct statement is " the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point".

Answer: See explanation

Step-by-step explanation:

You didn't really say what you want to know but let me explain.

The gross domestic product of an economy is the value of the goods and.d services that are being produced in such an economy. The gross domestic Product is used to know how well an economy is doing

Per capita gross domestic product (GDP) is a used to know the economic output of a particular country per person. It is calculated by dividing the GDP of such an economy by the population.

For example, let us say the GDP of a country is $800,000,000 and the population is 3,500,254. Therefore, the per capita GDP would be:

= $800,000,000 / 3,500,254

= $228.56 per person

Answer:total market value of goods and services produced within a year divided by total population

Step-by-step explanation:

basic defenition

Answer:

$40 and $72, see below :)

Step-by-step explanation:

One way we can do this is to add the total ratios and then divide that from 112.

10x + 18x = 28x = 112

28x = 112

x = 4

That means, for every ratio, you just have to multiply the amount by 4.

so for example, 10 is just 10 * 4 = 40

So, your answer would be you share the money into $40 and $72

Answer:

y=36

Step-by-step explanation:

using that 63° angle there on the right, we know that the other angle for a 180° total is 117°.

Now we have to figure out y using that total of 117

(4y-27)=117

4y-27=117

4y=144

y=36

Now if we substitute y...

(4y-27)=117

(4(36)-27)=117

(144-27)=117

(117)=117

Step-by-step explanation:

The angle at B is the same as the angle at E so equate them to each other to find x

2x+4=40°

2x=40-4

2x=36

x=36/2=18

Answer:

To write 65/100 as a decimal you to divide numerator by the denominator of the fraction.

We divide now 65 by 100 what we write down as 65/100 and we get 0.65.

And finally we have:

65/100 as a decimal equals 0.65

Step-by-step explanation:

Answer: Choice A) The value of s(x) depends on the value of x, since s is a function of x.

The outer letter s tells us what the function's name is. It's the dependent variable and it might be handy to tie it to the y variable. The x is the independent variable. It changes freely without relying on what s happens to be.

Answer:  A. The value of s(x) depends on the value of x, since s is a function of x.

Step-by-step explanation: s(x) is the output of the function when a given value of x is calculated according the operations in the function.

Answer:

16. this would be "base" but that isn't an option...

17.  R, exponent

24. F, term

4x and –3(–x) are negative.

Answer:

Step-by-step explanation:

here you go mate'

step 1

X / 2 + 1 > 3  equation

step 2

X / 2 + 1 > 3  simplify the equation

step 3

1/ 2 + 1 > 3  subtract the number at the front

1 / 2 + 1 (-1)> 3(-1)

step 4

1/2x>2  multiply

answer

x>4

Answer:

wHaT?

Step-by-step explanation:

Answer:

y=−3

Step-by-step explanation:

(−2)(5)−7y=11

−10+−7y=11

−7y−10=11

Step 2: Add 10 to both sides.

−7y−10+10=11+10

−7y=21

Step 3: Divide both sides by -7.

−7y

−7

=

21

−7

Answer:

slope = - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 5x + 9 ← is in slope- intercept form

with slope m = - 5