5. Look at the following systems of equations.
3x – 2y = 14
6x = 4y + 28
Which of the following is a description of the solution for this system?
A. An infinite number of solutions
B. No solution
C. One solution
D. Two solutions

Answer:

Here angle B is 90°

So [tex]\triangle ABC[/tex] and [tex]\triangle ABD [/tex] Are right angled triangle

So we use Pythagoras thereon for solution

perpendicular=p=8cm

Hypontenuse =h =10cm

According to Pythagoras thereon

[tex]{\boxed{\sf b^2=h^2-p^2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf b^2=10^2-p^2[/tex]

[tex]\longrightarrow[/tex][tex]\sf b={\sqrt {10^2-8^2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf b={\sqrt{100-64}}[/tex]

[tex]\longrightarrow[/tex][tex]\bf b={\sqrt {36}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf b=6[/tex]

[tex]\therefore[/tex][tex]\overline{BC}=6cm[/tex]

[tex]\longrightarrow[/tex][tex]BD=9+6[/tex]

[tex]\longrightarrow[/tex][tex]BD=15cm [/tex]

Perpendicular=p=8cm

Base =b=15cm

According to Pythagoras thereon

[tex]{\boxed {\sf h^2=p^2+b^2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf h^2=8^2+15^2 [/tex]

[tex]\longrightarrow[/tex][tex]\sf h={\sqrt {8^2+15^2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf h={\sqrt {64+225}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf h={\sqrt {289}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf h=17cm [/tex]

[tex]\therefore[/tex][tex]{\underline{\boxed{\bf x=17cm}}}[/tex]

Answer:

67.7

Step-by-step explanation:

perimeter=15+15+6pi+6pi

=67.7

Answer:

i think B if not sorry

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a)

Suppose we came up with an ideology whereby we pick a value for the length including the length dividing the inside into 4 parts(5 parallel sides), then we can get the value for breath by using the following process.

Let assume the length of the rectangle is 50;

Then, the breath can be calculated as follows:

= 50 × 5 = 250   ( since the breath is divided into 5 parallel sides)

The fencing is said to be 950 ft

So, 950 - 250 = 700

Then divided by 2, we get:

= 700/2

= 350

So for the first diagram; the length = 50 and the breath = 350

The area = 50 × 350 = 17500 ft²

Now, let's go up a little bit.

If the length increase to 100;

Then 100 × 5 = 500

⇒ 950 - 500 = 450

⇒ 450/2 = 225

The area = 225 × 100 = 22500 ft²

Suppose the length increases to 150

Then 150 × 5 = 750

⇒ 950 - 750 = 200

⇒ 200/2 = 100

The area = 150 × 100 = 15000 ft²

The diagrams for each of the outline above can be seen in the image attached below.

(b) The diagram illustrating the general solution can be seen in the second image provided below.

(c) The expression for  the total area A in terms of both x and y is:

Area A = x×y

(d) Recall that:

The fencing is said to be 950 ft.

And the length is divided inside into 5 parallel sides;

Then:

5x + 2y = 950  (from the illustration in the second image below)

2y  = 950 - 5x

[tex]y = \dfrac{950}{2} - \dfrac{5}{2}x[/tex]

[tex]y = 475- \dfrac{5}{2}x[/tex]

(e)

From (c); replace the value of y in (d) into (c)

Then:

Area A = x×y

[tex]f(x)= x\times ( 475 -\dfrac{5}{2}x)[/tex]

Open brackets

[tex]f(x)= ( 475 x-\dfrac{5}{2}x^2)[/tex]

(f)

By differentiating what we have in (e)

[tex]f(x)= ( 475 x-\dfrac{5}{2}x^2)[/tex]

[tex]f'(x)= ( 475 (1)-\dfrac{5}{2}(2x))[/tex]

[tex]f'(x)= 475 -5x[/tex]

[tex]\implies 475 = 5x[/tex]

x = 475/5

x = 95

From (d):

[tex]y = 475- \dfrac{5}{2}x[/tex]

[tex]y = 475- \dfrac{5}{2}(95)[/tex]

[tex]y =237.5[/tex]

∴

Area A = x × y

Area A = 95 × 237.5

Area A = 22562.5 ft²

Answer:

if right triangle 10.2956 hypotenuse 7.4833 if not a right triangle then greater than 4

Step-by-step explanation:

If it’s a right triangle, and the 2 sides are 5 and 9, then the 3rd side ( the hypotenuse) will be 10.2956. If one side is 5, and the hypotenuse is 9, then the 3rd side will be 7.4833.

If it’s not a right triangle, then the 3rd side must be greater than 4.

Answer:

Tax is 9.76 total cost is 131.74

Step-by-step explanation:

40.66 x 3= 121.98

121.98 x .08= 9.76

121.98+9.76= 131.74

Answer:

Step-by-step explanation:

Answer:

6 stations

Step-by-step explanation:

24=1,2,3,4,6,8,12,24

18=1,2,3,6,9,18

Now we have to find which numbers are the same but that are the largest.

so It would be 6.

So Mrs.Davis can have every student participate in 6 stations.

Answer:

3/6

Step-by-step explanation:

1/3 can be converted to 2/6. From the you would subtract 2/6 from 5/6 which would give you your awnser of 3/6.

Answer: 4 Rules

Step-by-step explanation:

To add integers having the same sign, keep the same sign and add the absolute value of each number. To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest. Subtract an integer by adding its opposite.

Answer:

I belive its c

Step-by-step explanation:

there are two rules for adding integers

Answer:

The answer should be -2x^2+6x

The area and perimeter of the given shaded figure are respectively 33.12 unit² and 20.56 units.

What information do we have?

Radius of semi-circle = 8 / 2 = 4 unit

Length of remain Rectangle = 8 unit

Width of remain Rectangle = 2 unit

Perimeter of shaded figure = πr + (l + 2b)

Perimeter of shaded figure = (3.14)(4) + [4 + (2)(2)]

Perimeter of shaded figure = 12.56 + 4 + 4

Perimeter of shaded figure = 20.56 units

Area of shaded figure = πr²/2 + lb/2

Area of shaded figure = (3.14)(4)²/2 + (8)(2)/2

Area of shaded figure = (3.14)(8) + 8

Area of shaded figure = 25.12 + 8

Area of shaded figure = 33.12 unit²

Find out more information about 'Area'.

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Answer:

1)27.25 feet

2)-0.2774,2.027

3)Domain = All real numbers

Range = y∈R : [tex]y \leq \frac{109}{4}[/tex]

Step-by-step explanation:

The height of the football, h, at time t seconds is modeled by the equation [tex]h(t) = -16t^2 + 28t + 15[/tex]

General quadratic equation : [tex]ax^2=bx+c=0[/tex]

1) Maximum height will be at [tex]\frac{-b}{2a}=\frac{-28}{2(-16)}=\frac{7}{8}[/tex]

To find maximum height Substitute [tex]t = \frac{7}{8}[/tex] in the given equation

[tex]h(t)=-16(\frac{7}{8})^2+28(\frac{7}{8})+15\\h(t)=27.25 feet[/tex]

2)

Substitute h(t)=6

So, [tex]-16t^2+28t+15=6[/tex]

[tex]-16t^2+28t+9=0\\t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\t=\frac{-28\pm \sqrt{28^2-4(-16)(9)}}{2(-16)}\\t=\frac{-28+ \sqrt{28^2-4(-16)(9)}}{2(-16)},\frac{-28- \sqrt{28^2-4(-16)(9)}}{2(-16)}\\t=-0.2774,2.027[/tex]

3)

Domain = All real numbers

Range = y∈R : [tex]y \leq \frac{109}{4}[/tex]

Answer:

two is the number

Step-by-step explanation:

i think that

The required number is 1.786.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let the number is x,

According to given condition,

3×x²= 2×x+6

⇒3x²= 2x+6

⇒3x²-2x-6=0

There are two values of x, -1.12 and 1.786

Neglect negative value,

By solving the equation, the value of x is 1.786.

To know more about Equation on:

https://brainly.com/question/187506

Answer:

36.598 - 0.001 = 36.597

Answer:

x - 2y - 8 = 0

Step-by-step explanation:

y + 2 = 1/2x - 2

y + 2 + 2 - 1/2x = 0

-1/2x + 4 + y = 0

-2[-1/2x + y + 4] = 0(-2)

x - 2y - 8 = 0

Answer:

18/2 is 9

Step-by-step explanation:

2*9 is 18

Answer: None of these answers are correct.

Explanation: 2÷18 is 1/9 (one ninth).

Answer:

x+y=5

Step-by-step explanation:

Answer:

56/100 or 14/25 simplified

Answer:

2:6

Step-by-step explanation:

2 banana nut, to, 6 chocolate chip

Answer:

Step-by-step explanation:

slope is -3/2. rise/run. There's already a graph there so I'm assuming no need to show one

Answer:

slope: -3/2

y intercept: -1

equation: y = -3/2x-1

Answer:

118

Step-by-step explanation:

27x+2=118[being alternate angles ]

27x=116

x=4.29

one angle =27×4.29+2

117.83

118

10x+5+118=180[sum of angles of triangle is 180]

10x+5+118=180

X=62

Answer:

radius : 29.99 feet

Area : 2824.57 square feet

Step-by-step explanation:

The graph that shows the solution of the system of inequalities is A y> -3  and y≤ -x

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

We have been given graph,

we can see that shaded portion lies above the dotted line which shows open interval (y >-3 ).  

Here the graph lies below the line y= -x ,

Thus, the solution region will be y ≤ -x ,

hence, the solution region is given by system of inequalities ;

y> -3  and y≤ -x

Learn more about inequalities here:

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Answer:

What terms?

Step-by-step explanation:

Answer:

x=

2

f

2

−8f+4

​

​

−

2

f

​

+1

x=−

2

f

2

−8f+4

​

​

−

2

f

​

+1, (f



=0 and f≤4−2

3

​

) or f≥2

3

​

+4

Step-by-step explanation:

im srry if this is wrong

Answer:

.7881

Step-by-step explanation:

Answer:

65 degrees

Step-by-step explanation:

115*2=230

360-230=130

130/2=65

65 degrees is the answer.