from the chapter Rational Numbers​some body please answer fast

Answer:

1.

Equation: y = -4x + 7

Slope: -4

y-intercept = 7

2.

Equation: y = 2/3x - 3

Slope: 2/3

y - intercept: -3

3.

Equation: y = 5/4x - 3/2

Slope: 5/4

y - intercept: -3/2

4.

Equation: y = -1/2x + 4

Slope: -1/2x

y - intercept: 4

Answer:

It will take approximately 68.2 years for the Caribou population to reach 21,000.

Step-by-step explanation:

The population P of Caribou in the Yukon is modeled by P=6x²-120x+1250 where x is the number of years from today.

If the population P of Caribou in the Yukon is 21000, then, replacing you get:

21000= 6x²-120x+1250

So:

0= 6x²-120x+1250 -21000

0= 6x²-120x - 19750

This is a quadratic function of the form: 0= ax²+ bx +c, where: a=6, b= -120 and c=-19750

To solve a quadratic function and determine the value of x you can use the expression:

[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]

Replacing the values ​​of a, b and c and solving you get:

[tex]x1,x2=\frac{-(-120)+-\sqrt{(-120)^{2}-4*6*(-19750) } }{2*6}[/tex]

[tex]x1,x2=\frac{120+-\sqrt{14400+474000 } }{12}[/tex]

[tex]x1,x2=\frac{120+-\sqrt{488400 } }{12}[/tex]

[tex]x1,x2=\frac{120+-698.86 }{12}[/tex]

So:

[tex]x1=\frac{120+698.86 }{12}[/tex]

x1= 68.24 ≅ 68.2

and

[tex]x2=\frac{120-698.86 }{12}[/tex]

x2= -48. 24 ≅ -48.2

As time cannot be negative, it will take approximately 68.2 years for the Caribou population to reach 21,000.

Answer:

5x^2−10x−2

Step-by-step explanation:

I hope this is what you are looking for I just added (5x^2 – 9) + (-10x + 7)

Answer:

Step-by-step explanation:

Inscribed angle = 130°/2 = 65°

Answer:

57

Step-by-step explanation:

<=1/2(AP-BN)

12=1/2(x-33)

(2) 12=1/2(x-33) (2)

24=x-33     24+33

57=x

57=AP

Answer:

672

Step-by-step explanation:

Answer:

<AEB = 51.2

Step-by-step explanation:

Remark

A straight line has a degree value of 180. There are 3 angles. One of them is 90. The other two must add to 90

Equation

2.7x + 8 + 3.8x - 22 = 90      combine like terms on the left.

6.5x - 14 = 90                        add 14 to both sides

6.5x = 90 + 14

6.5x = 104                              Divide by 6.5

x = 104/6.5

x = 16

<AEB = 2.7*16 + 8

<AEB = 51.2

Answer:

b

Step-by-step explanation:

Answer:

supplementary means angles that add up to 180°

one angle = 155°

other angle = 180° - 155° = 25°

A) 25°

hope this answer helps you......

Answer:

[tex]Volume=288in^{3}[/tex]

Step-by-step explanation:

Given

Base Cubes =36

Layers = 8

The number of base cubes represents the base area and the number of layers represents the height of the prism.

So, the volume is calculated as:

Volume = Base Cubes * Layers, i.e Base Area * Heights

Volume = [tex]36*8[/tex]

Volume = [tex]36in^{2} * 8 in[/tex]

Volume = [tex]288in^{2}[/tex]

Answer:

Step-by-step explanation:

Answer:

Black socks pairs = 7

Brown socks pairs = 3

White socks pairs = 8

P(not black) = ?

First, you need to add the brown & white socks pairs,

[tex]3 + 8 = 11[/tex]

Then you need to add the total number of socks pairs,

[tex]7 + 3 + 8 \\ = 7 + 11 \\ = 18[/tex]

P(not black)

[tex] = \frac{11}{18} [/tex]

Step-by-step explanation:

solution given:

total pair of socks[S]=(7+3+8)=18

total pair of black socks[B]=7

total pair of brown socks [C]=3

total pair of white socks[W]=8

total no of orange marbles[O]=2

now

the P( not black) =?

we have

P( not black) =1-[tex] \frac{n[B]}{n[S]} [/tex]

P( not black) =1-[tex] \frac{7}{18} [/tex]

P( not black) =[tex] \frac{18-7}{18} [/tex]

P( not black) =[tex] \frac{11}{18} [/tex]

so 11/18 is a required probabilty.

Answer:

y=3,000(0.985)^x

y=1,500(1.012)^x

Step-by-step explanation:

System of equations  Brandon can use for  two location are y= 3000[tex](0.985)^{x}[/tex] and y =[tex]1500(1.012)^{x}[/tex]

Profit and loss percentage are used to refer to the amount of profit or loss that has been incurred in terms of percentage.

According to question

Brandon is analyzing the profits from two of his restaurant locations.

where

x = number of week

y = the profit

1st restaurant : showed a profit of $3,000 in the first week of the year but

has a showed a steady decrease in profits of 1.5% each week since then

So in equation we can write it as

y= [tex]3000(1 - 0.015)^{x\\}[/tex]

y= 3000[tex](0.985)^{x}[/tex]

2nd restaurant : showed a profit of $1,500 in the first week of the year and has showed a steady increase in profits of 1.2% each week since then.

So in equation we can write it as

y = [tex]1500(1+0.012)^{x}[/tex]

y =[tex]1500(1.012)^{x}[/tex]

Hence, system of equations can Brandon use to determine the x and y form the two location are y= 3000[tex](0.985)^{x}[/tex] and y =[tex]1500(1.012)^{x}[/tex]

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Answer: BC = 5.83

Step-by-step explanation:

Luckily, the triangle is placed on the graph nicely so we can count the legs of the triangle:

AB = 5

AC = 3

BC = ?

To find BC, we can simply use the Pythagorean Theorem:

[tex]a^{2}+b^{2}=c^{2}[/tex]

5^2 + 3^2 = c^2

25 + 9 = c^2

34 = c^2

Now square root to find c, or BC.

[tex]\sqrt{34}=\sqrt{c^{2} }[/tex]

c = 5.83 (rounded by nearest hundredth)

Answer: for C it is that 1/2 is half of an whole therefore 1/2 is  half is less than the rest

for D you will have to add more 1/2 for it to be greater than but for now, it is less than.

for E you will have to add more 1/2 for it to be greater than

Answer:

4x^2 - 14x + 19

Step-by-step explanation:  

A = LW

A = (2x-3) (2x-3)

4x^2 - 6x - 6x + 9

Combine like terms:

4x^2 - 12x + 9

-2(x - 5) (for both ovals)

(4x^2 - 12x + 9) -2(x - 5)

4x^2 - 12x + 9 - 2x + 10

Group then combine like terms:

4x^2 - 12x - 2x + 10 + 9

4x^2 - 14x + 19

Sorry for being 10 days late but here is the answer for anybody that needs this! :D

Given:

The base of a prism is a right triangle with legs measuring 16 feet and 4 feet.

Height of the prism is 14 feet.

To find:

The volume of the triangular prism.

Solution:

The area of a triangle is:

[tex]Area=\dfrac{1}{2}\times b\times h[/tex]

Where, b is base and h is height of the triangle.

The base of a prism is a right triangle with legs measuring 16 feet and 4 feet. It means the base of the triangle is 16 feet and height is 4 feet. So, the area of the base of the prism is:

[tex]B=\dfrac{1}{2}\times 16\times 4[/tex]

[tex]B=32[/tex]

Now, the volume of a triangular prism is:

[tex]V=Bh[/tex]

Where, B is base area and h is the height.

Putting [tex]B=32,h=14[/tex] in the above formula, we get

[tex]V=32\times 14[/tex]

[tex]V=448[/tex]

Therefore, the volume of the triangular prism is 448 cubic feet.

Answer:

6.63 pounds

Step-by-step explanation:

Total pounds of mixture = 20

The contents of the mixture are; peanuts and almonds. Of which;

Peanuts cost = $2.95 per pound

Almonds cost = $5.95 per pound

The mixture cost = $4.00 per pound

Total cost of contents of the mixture = $8.90

The pounds of peanuts = [tex]\frac{2.95}{8.90}[/tex] x 20

                     = 6.63

Therefore, 6.63 pounds of peanuts was used in producing 20 pounds of the mixture.

Answer:

18

Step-by-step explanation:

The key of this leaf stem-leaf plot is:

4 | 5 = 45

Therefore, the data points that represents children with weight that is less than 50 pounds would be as follows:

First row => 12, 13, 15, 15 15, 16, 16, 19

Second row => 23, 25

Third row => 33, 35, 37, 38, 39

Fourth row => 44, 45, 45

Therefore, the number of children that weigh less than 50 pounds = 18

Answer:

Substitute the value of the variable into the expression and simplify.

− 18

Step-by-step explanation:

I'm sorry if it's not what you are looking for.

Answer:

Don't have them

lol

Answer:

4,140 degrees

Step-by-step explanation:

Mathematically, the sum of interior angles of a polygon is;

(n-2)180

where n is the number of sides the polygon has

Mathematically;

we will be replacing n by 25 here

So, we have;

(25-2)180

= 23 * 180 = 4,140 degrees

Answer:

answer b

Step-by-step explanation:

lol  points ig

Answer:

V= 2* L*B*H

Step-by-step explanation:

Although we are not given the dimension of the rectangular prisms in this question

The volume of a rectangular prism is

V= L*B*H

Since the number of the prism is two

Hence the volume of the two prisms

V= 2* L*B*H

Therefore, when the plugin the dimensions of the prism into the expression above, you will get the volume of the two prisms combined

Answer:

addition property of equality

Step-by-step explanation:

9514 1404 393

Answer:

  B, C, E

Step-by-step explanation:

When the central angles are congruent, the corresponding triangles are congruent:

  ΔJHK ≅ ΔLHM . . . . selection E

and the base chords are congruent:

  ML ≅ JK . . . . selection B

The subtended arcs are also congruent, so adding arc LK to each will result in congruent arc measures:

  arc MLK ≅ arc LKJ . . . . selection C

Answer:

The correct anser for delta math is 68%

Step-by-step explanation:

I gave up on delta math

Given:

The graph of the system of inequalities.

To find:

The system of inequalities.

Solution:

From the given graph it is clear that the first line passes through the points (0,2) and (1,-1). So, the equation of the boundary line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-2=\dfrac{-1-2}{1-0}(x-0)[/tex]

[tex]y-2=-3x[/tex]

[tex]y=-3x+2[/tex]

The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.

[tex]y\geq -3x+2[/tex]

The second line passes through the points (0,-2) and (3,0). So, the equation of the boundary line is:

[tex]y-(-2)=\dfrac{0-(-2)}{3-0}(x-0)[/tex]

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

[tex]y=\dfrac{2}{3}x-2[/tex]

The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.

[tex]y\geq \dfrac{2}{3}x-2[/tex]

Therefore, the system of inequalities contains two linear inequalities [tex]y\geq -3x+2[/tex] and [tex]y\geq \dfrac{2}{3}x-2[/tex].

Answer:

Step-by-step explanation:

g(x) =(1/4 x)²

g(x)  = 4x² will be the equation of the parabola.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, two parabolas f(x) and g(x),

From the general equation of the parabola,

y = a(x – h)² + k or x = a(y – k)² +h.

Here (h, k) denotes the vertex.

As we can see in our case, the vertex is (0, 0)

Thus, the equation of the parabola will be

y = ax²

Since the given parabola passes through the point (1, 4)

Substitute the values,

4 = a(1)²

a = 4

therefore, the equation of the parabola g(x) will be,

g(x)  = 4x²

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