On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction
The number b varies directly with the number a. For example b= 2 when a = -2
-2. Which equation represents this
direct variation between a and b?
Obra
O b = a
Ob-a= 0
Ob(-a) = 0

Answer:

y = (-1/2)x + 21/2

Step-by-step explanation:

Given equation:

y - 2x + 7

Coordinates = (5,8)

Find:

Perpendicular equation

Computation:

y = mx + c

y - 2x + 7

y = 2x - 7

So,

m = 2

The negative reciprocal of 2 is -1/2

So,

For,

Coordinates = (5,8)

y = mx + c

8 = (-1/2)(5) + c

8 = -5/2 + c

c = 8 + 5/2

c = 21 /2

So,

y = mx + c

y = (-1/2)x + 21/2

Answer:

y = 150

Step-by-step explanation:

y varies inversely as x²

yx² = k

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

y = 6 when x = 30

6(30²) = k

6(900) = 5400

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

what is y when x = 6

y(6²) = 5400

y(36) = 5400

y = 5400/36

y = 150

Answer:

     y= 150

Step-by-step explanation:

[tex]y\ \alpha \ \frac{1}{x^2}\\\\y = k \times \frac{1}{x^2}\\\\[/tex]

Given y = 6, and x = 30. Find k.

[tex]6 = k \times \frac{1}{30^2}\\\\6 \times 900 = k\\\\5400 = k[/tex]

Given  x = 6 and k = 180. Find y

[tex]y = 5400\times \frac{1}{6^2}\\\\[/tex]

 [tex]=5400 \times \frac{1}{36}\\\\=150[/tex]

Answer:

480,700

Step-by-step explanation:

C(25,7)

25!/(7!*(25-7)!)

15511210043330985984000000/(6402373705728000*5040)

480700

Answer:

$882.75

Step-by-step explanation:

In order to calculate tax, you need to multiply the percentage by the purchase costs. First, start by finding the decimal value of the percentage.

7 ÷ 100 = 0.07 — Percentage converted to a decimal.

[tex]825 \times 0.07 = 57.75[/tex]

— The tax. Now, in order to find the whole price, the tax and retail price must be added together.

[tex]825 + 57.75 = 882.75[/tex]

As per linear equation, the amount I have to pay in total is $645.

The simplified value of the given expression is (8 - 17x).

"A linear equation is an equation in which the highest power of the variable is always 1."

1. Given, the cost of television is $825.

The sales tax rate is 7%.

Therefore, total price of the television is

= $[tex][825 + (\frac{825(7)}{100})][/tex]

= $[tex](825+57.75)[/tex]

= $[tex]882.75[/tex]

2. The given expression is:

[tex]-4(3x - 2)- 5x\\= -12x + 8-5x\\= 8-17x[/tex]

Learn more about a linear equation here:

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Answer:

468.75 Cubic meters

Step-by-step explanation:

15 x 12.5 x 2.5 = volume

187.5 x 2.5 = volume

468.75 = volume

Answer:

its 393.75 cubic meters

Step-by-step explanation:

I hope this helps

Answer:

9km

Step-by-step explanation:

30-(13+8)=9km

I hope you understand

Answer:

369

Step-by-step explanation:

g(f(x)) simply means to put the whole expression of function f(x) into the place of "x" in g(x).

and to find the functional value for a specific x we just need to calculate functional value for f(x) and use that result as input for g(x).

f(6) = 8×6 + 5 = 48 + 5 = 53

and now

g(53) = 7×53 - 2 = 371 - 2 = 369

to check we do the general functional substitution :

g(f(x)) = 7×(8x+5) - 2 = 56x + 35 - 2 = 56x + 33

g(f(6)) = 56×6 + 33 = 336 + 33 = 369

correct

Answer:

3

Step-by-step explanation:

Pythagorean rule

[tex]hyp = opp + adj \\ therefore. \\ opp = hyp - adj \\ and \\ adj = hyp - opp[/tex]

opp=13-10

opp=3

Answer:

x = 50 degree

Step-by-step explanation:

x + 10 + x + x + 20 = 180 degree (being linear pair)

3x + 30 = 180

3x = 180 - 30

x = 150/3

x = 50 degree

Answer:

x = 260

Step-by-step explanation:

Add the two angles together.  They will sum to 180

x/2+ 50 = 180

Subtract 50 from each side

x/2+50-50 = 180-50

x/2 = 130

Multiply by 2

x/2*2 = 130*2

x = 260

Answer:

260°

Step-by-step explanation:

x / 2 + 50° = 180°

Subtract 50° from each side

x/2 + 50° - 50° = 180° - 50°

x / 2 = 130°

Multiply each side by 2

2 × x/2 = 130° × 2

x = 260°

Answer: 10.3 s

Step-by-step explanation:

Given

The height of the arrow is given by [tex]h=-16t^2+v_ot+h_o[/tex]

At  [tex]t=0, h=19\ ft[/tex]and [tex]v_o=163\ ft/s[/tex]

When arrow hits ground, h becomes 0 i.e.

[tex]\Rightarrow 0=-16t^2+163t+19\\\Rightarrow 16t^2-163t-19=0\\\\\Rightarrow t=\dfrac{163\pm \sqrt{(-163)^2+4(16)(19)}}{2(16)}\\\\\Rightarrow t=-0.115,10.30\ s[/tex]

Neglecting the negative value of t

So, the arrow hits the ground after 10.30 s

Answer:

si sumas 9+4×5 te da la respuesta

Answer:

81

Step-by-step explanation:

90+25= 115

115 - 34 = 81

Answer:

B is the right answer and if you want learn this, than learn algebric expression

Answer:

part a-24 questions

part b-2 or 3 more questions

Step-by-step explanation:

part a-to find the number, change the percent into a decimal (.75) and multiply (24)

part b-first find how many questions need to be right to get 80% (.80 times 32=25.6). then subtract by how many he would get with a 75% (25.6-24=about 2 to 3 more questions, rounded 2)

Answer:

the answer is 113.398 grams

Answer:

(v - 6)(v + 4)

Step-by-step explanation:

v² - 2v - 24

v² + 4v - 6v - 24

v(v + 4) - 6(v + 4)

(v - 6)(v + 4)

Answer:

Step-by-step explanation:

This is only my guess, as I haven’t done this topic in a few months

A. 398/427

0.93

B. 123/1192

0.10

C. 339/403

0.84

Answer:

g = 3 + b

b + 3 = g

3 + b = g

Step-by-step explanation:

Answer:

[see below]

Step-by-step explanation:

Rewriting the rule so 'b' would be the subject:

[tex]g = b + 3\\\\g - 3 = b + 3-3\\\\g-3=b\\\\\boxed{b=g-3}[/tex]

Hope this helps.

Answer:

7.22

Step-by-step explanation:

solved in the diagram

Answer:

90 or -270

Step-by-step explanation:

Answer: 1/6

Step-by-step explanation:

This is a question that has to do with the addition of a fraction. Since we are given the information that of the teacups in Bonnie's Tea Shop, 1/12 are blue and another 1/12 are orange.

Then, the fraction of the teacups that are either blue or orange will be calculated as:

= 1/12 + 1/12

= 2/12

= 1/6

Therefore, the fraction of the teacups that are either blue or orange is 1/6.

Answer:

x=2

HPT 3x+5y=6 (1) và 2x+y=4 (2)

Nhân phương trình (2) với 5 để hệ số y của 2 phương trình bằng nhau. Ta có:

(2)⇔ 10x+5y=20(3)

Trừ (3) cho (1), có: 7x+0y=14⇒x=2

Answer:

3x+5y=6.....eqn 1

2x+y=4.......eqn 2

y=4-2x.....eqn 3

Step-by-step explanation:

substitute eqn 3 into eqn 1

3x+5(4-2x)=6

3x+20-10x=6

-7x = -14

x=2

Answer:

A.

Step-by-step explanation:

we are going from a large shape to a smaller shape. the proof is that the side lengths go down from 7m to 0.5m. so, it is a reduction.

and the scaling factor s ? what do we need to multiply the original side lengths with to get the new ones ?

7 × s = 0.5 = 1/2

s = (1/2)/7 = (1/2)/(7/1) = (1×1)/(2×7) = 1/14

=> answer A is correct

The dilation from the figure on the left to the figure on the right is a reduction.  

Reduction scale factor 1/14.

The correct option is A.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

We have given that two figures.

The dilation from the figure on the left to the figure on the right is a reduction.

And the scale factor is,

= actual / scale

= 1/(7 / 0.5)

= 1/14

Therefore, the scale factor is 1/14.

To learn more about the scale factor;

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When multiplying the same number raised to different powers add the powers together.

3 + 2 + 5 = 10

Because you are also multiplying a value without a power you need to add 1 to the sum of the powers:

10 + 1 = 11

Answer: 6^11

Step-by-step explanation:

first number=x

second number=x+2

third number=x+4

(x+2)(x+4)=3x+26

x(x+4)+2(x+4)=3x+26

x²+4x+2x+8=3x+26

x²+6x+8=3x+26

x²+6x-3x=26-8

x²+3x=18

x²+3x-18=0

you can use that to find the numbers

Answer:

6, 8 and 10

Step-by-step explanation:

Let the 3 consecutive odd numbers be x, x+2, x+4

product of the second and the third integer

(x+2)(x+4)

twenty-six more than three times the first integer is expressed as;

3x + 26

Equate

(x+2)(x+4) = 3x + 26

x²+4x+2x+8 = 3x + 26

x²+6x +8= 3x+26

x²+3x +8-26 = 0

x²+3x-18 = 0

Factorize

x²-6x+3x-18 = 0

x(x-6)+3(x-6) = 0

x+3 = 0 and x-6 = 0

x = -3 and 6

The first 3 number is are 6, 8 and 10

Answer:

x is greater than or equal to 3

Step-by-step explanation:

x ≥ 3

x is greater than or equal to 3

so you got the plot right

Answer:

x = 2 and x = 3

Step-by-step explanation:

Formulas used :

[tex]log_5 \ 5 = 1[/tex]

[tex]log_5 \ x + log_5 \ y = log_5 \ (xy)[/tex]

[tex]log_5 \ x = log_5 \ y => x = y[/tex]

Steps :

[tex]2 \ log_5 \ x = 1 + log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ 5+ log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ ( 5(x - \frac{6}{5} ))\\\\x^2 = 5(x - \frac{6}{5})\\\\x^2 = 5x - 6\\\\x^2 - 5x + 6 = 0\\\\x^2 - 2x - 3x + 6 = 0\\\\x(x - 2 ) - 3 (x - 2) = 0\\\\(x - 3)(x-2) = 0\\\\x = 3 , x = 2[/tex]