бx - 6 = 24х +6
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Answer:

don't give up try and you will find the answers

Answer:

Step-by-step explanation:

Given the vectors based on the number line as RS = 7y +3, ST = 5y +8, and RT = 83, the equation RS+ST = RT will be used to get the unknown.

Substituting the given equation into the expression we will have;

7y +3+5y +8 = 83

collect like terms'

7y+5y+3+8 = 83

12y + 11 = 83

12y = 83-11

12y = 72

y = 72/12

y = 6

b) Substitute y = 6 into RS and ST

Given RS = 7y+3

RS = 7(6)+3

RS = 42+3

RS = 45

For ST;

ST = 5y+8

ST = 5(6)+8

ST = 30+8

ST = 38

Answer:

x = 0

y = 3

Step-by-step explanation:

Step 1: Write systems of equations

9x - 2y = -6

5x + 4y = 12

Step 2: Rewrite 1st equation

9x = 2y - 6

x = 2/9y - 2/3

Step 3: Substitute

5(2/9y - 2/3) + 4y = 12

Step 4: Solve for y

10/9y - 10/3 + 4y = 12

46/9y - 10/3 = 12

46/9y = 46/3

y = 3

Step 5: Plug in y to find x

5x + 4(3) = 12

5x + 12 = 12

5x = 0

x = 0

Answer:

AB = 38.6metres

Step-by-step explanation:

Given the right angled triangle ABC with hypotenuse AB and ∠CAB to be 75°, the opposite side of the triangle will be the side facing the angle ∠CAB directly and this is side BC. The adjacent side of the triangle will be side CA.

To get the length of the hypotenuse AB, we will use the trigonometry identity SOH, CAH, TOA.

According to CAH;

Cos∠CAB = adjacent/hypotenuse = CA/AB

Substituting CA = 10 metres and ∠CAB = 75° into the equation;

Cos75° = 10/AB

AB = 10/cos75°

AB = 10/0.2588

AB = 38.6metres

Hence the length of the hypotenuse AB is 38.6metres.

Answer:

38.6 m

Step-by-step explanation:

Answer:

The equation that represents the perimeter of the rectangle is:

[tex]\text{Perimeter} = \frac{2}{3} \times [4l-27][/tex]

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

Perimeter = 2 × [l + w]

It is provided that the width of a rectangle is 9 less than one-third it's length.

That is:

[tex]w = \frac{1}{3}l-9[/tex]

The perimeter is given as 45.

The equation that represents the perimeter of the rectangle is:

[tex]\text{Perimeter} = 2 \times [l + \frac{1}{3}l-9]\\\\\text{Perimeter} = 2 \times [\frac{3l+l-27}{3}]\\\\\text{Perimeter} = 2 \times [\frac{4l-27}{3}]\\\\\text{Perimeter} = \frac{2}{3} \times [4l-27][/tex]

Thus, the equation that represents the perimeter of the rectangle is:

[tex]\text{Perimeter} = \frac{2}{3} \times [4l-27][/tex]

Answer:

z = -5

y = 1

x = 4

Step-by-step explanation:

2z = -10 ➡ z = -5

4y -(-5) = 9 ➡ 4y = 4 and y = 1

2x + 3 + (-5) = 6 ➡ 2x = 8 and x = 4

==============================================

Work Shown:

F = future value

P = present value = 280

r = rate of inflation in decimal form = 0.08

t = elapsed time in years = 2

---------

F = P*(1+r)^t

F = 280*(1+0.08)^2

F = 326.592

F = 326.59

Answer:

$1.50 per card

Step-by-step explanation:

Knowns:

$10 to spends, Wants to buy $7 book and two equal priced cards.

10 = 7 + 2x

Subtract 7 from both sides to find out how much money Dave has after he buys his book.

3 = 2x

Divide each side by 2 to find out how much he cana spend on each card

x = 1.50

i hope this helps!

-TheBusinessMan

Prime factorization of 100 is 2 * 2 * 5 * 5

100 as a product of prime factors will be 2 ×2×5×5 .

Given,

Number = 100

Now,

To write 100 as prime factor product ,

Take LCM of 100

LCM 100 = 2 ×2×5×5

Thus the factors obtained in the LCM is prime factors only .

So we can write 100 as the product of prime factors:

100 = 2 ×2×5×5

Know more about prime factors,

https://brainly.com/question/29763746

#SPJ6

Answer:

Linear

Step-by-step explanation:

Answer:

the answer is Linear

Step-by-step explanation:

Answer:

x=23, y=14

Step-by-step explanation:

The triangles are indeed simular

Answer:

Midpoint is (-6,-34)

Step-by-step explanation:

(6+(-18))/2. (-41+(-27))/2

-12/2. (-68)/2

-6. , - 34

Distance =(6--18)^2 +(-14--27)^2

23^2. +13^2

529 +169

= 698

So u will find the square root of 698

The ans u get is the distance

Answer:

-320000

Step-by-step explanation:

Given

Lost Land = 80,000 acres yearly

Duration 4 years

Required

The total change

Represent the total change with y;

y is calculated as thus;

[tex]y = Lost\ Land * Duration[/tex]

[tex]y = -80,000 acres * 4[/tex]

[tex]y = -320000\ acres[/tex]

Hence, a total of 320000 acres were lost during the period

1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².

a = 51 m, b = 37 m, c = 20 m

semiperimeter:  p = (51+37+20):2 = 54 m

Area of triangle:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2[/tex]

Rate:  ₹ 3 per m².

Cost:  ₹ 3•306 = ₹ 918

2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.

a = 5 cm

a+2b = 11 cm  ⇒  2b = 6 cm   ⇒  b = 3 cm

p = 11:2 = 5.5

[tex]A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2[/tex]

3. Find the area of the equilateral triangle whose each side is 8 cm.

a = b = c = 8 cm

p = (8•3):2 = 12 cm

[tex]A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2[/tex]

4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

a = 2x

b = 3x

2x + 2•3x = 32 cm  ⇒ 8x = 32 cm   ⇒  x = 4 cm  ⇒ a = 8 cm, b = 12 cm

p = 32:2 = 16 cm

[tex]A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2[/tex]

Answer:

X = 6

Step-by-step explanation:

Subtract 1 x from both sides so the equation will be 3x = 18.  Then divide 3x by 3 and 18 by 3 to get 6

Answer: [tex]x=6[/tex]

Subtract x from both sides

[tex]4x-x=x+18-x\\3x=18[/tex]

Divide both sides by 3

[tex]3x=3=18/3\\x=6[/tex]

Answer:

53°, 127°, 127°

Step-by-step explanation:

Two intersecting lines form two pairs of angles:

So if one of the angles is measured 53°, then the other angles are:

Answer:

18

Step-by-step explanation:

We can create a ratio of the amount of students who picked green over the total amount of students.

9 students picked the green pattern, and a total of 50 students were surveyed. This means the ratio is [tex]\frac{9}{50}[/tex].

To turn [tex]\frac{9}{50}[/tex] into a percentage, we must divide it's numerator by it's denominator and multiply by 100.

[tex]8\div50=0.18\\\\0.18\cdot100=18[/tex]

So the green bar's height will be 18.

Hope this helped!

Answer:

[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]

Step-by-step explanation:

Let be [tex]f(x,y) = \log_{4}(2\cdot x^{2}-20\cdot x +12\cdot y)[/tex], this expression is simplified by algebraic and trascendental means. As first step, the second order polynomial is simplified. Its roots are determined by the Quadratic Formula, that is to say:

[tex]r_{1,2} = \frac{20\pm \sqrt{(-20)^{2}-4\cdot (2)\cdot (12\cdot y)}}{2\cdot (2)}[/tex]

[tex]r_{1,2} = 5\pm \sqrt{25-6\cdot y}[/tex]

The polynomial in factorized form is:

[tex](x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})[/tex]

The function can be rewritten and simplified as follows:

[tex]f(x,y) = \log_{4} [(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})][/tex]

[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]

Answer:

The inequality is

88<x<93

Step-by-step explanation:

The average of Shondra's test scores in physics is between 88 and 93.

Let me give out the meaning of some inequality symbols

<= Less than or equal to

>= Greater than or equal to

< Less than

> Greater than

Let the average score be x

In this case , the average score is between 88 and 93

The inequality is

88<x<93

Answer:

9x - 24 ÷ 6

Step-by-step explanation:

Quotient means that one number will be divided by another, so the division sign will be involved in the expression.

9 times x minus 24 translates to 9x - 24.

Now, put it all together.

9x - 24 ÷ 6 will be the expression.

Hope that helps.

Answer:

0 Is Integer ,

rational and a

whole number.

Hope it helps.

Answer: The digit in the thousand place is '9'.

Step-by-step explanation: The given number is 5_278.

The difference between the values of the digits in the thousandth place and the tenth place is 8930.

The digits in the tenth place is already given, which is 7

Let's assume the digits in the thousandth place is x,

Answer:

the answer is 28

Step-by-step explanation:

This is simple

if 5 people need 2 gallons we can use that to figure out how many gallons 75 people need.

75 divided by 5 is 15. so if 5 fits into 75 15 times that means that 75 people need 15 times 2 gallons or 30 gallons of fruit punch.

But the problem ask how much "additional" fruit punch so we subtract 2 from 30 to get 28 additional gallons of fruit punch

Answer:

The eight in the first number is ten times larger than the eight in the second number.

Answer:

(−∞,−7/2)∪(−7/2,3)∪(3,∞)

Step-by-step explanation:

(x-3)

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

2x^2 +x -21

First factor the denominator

(x-3)

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

( 2x +7) (x-3)

The domain is restricted when the denominator goes to zero

2x+7 =0    x-3 =0

2x = -7     x-3=0

x = -7/2    x =3

This two points are not in the domain

(−∞,−7/2)∪(−7/2,3)∪(3,∞)

Answer:

m = slope= 5/3

Step-by-step explanation:

[tex](-6, -2) = (x_1,y_1) \\ (-1.5, 5.5) (x_2 ,y_2) \\ \frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 -x _1} [/tex]

[tex] \frac{y - ( - 2)}{x - ( - 6)} = \frac{5.5 - ( -2 )}{ - 1.5 - ( - 6)} \\ \frac{y + 2}{x + 6} = \frac{5.5 + 2}{ - 1.5 + 6} [/tex]

[tex] \frac{y + 2}{x + 6} = \frac{7.5}{4.5} \\ 4.5(y + 2) = 7.5(x + 6)[/tex]

[tex]4.5y + 9 = 7.5x + 45 \\ 4.5y = 7.5x + 45 - 9 \\ 4.5y = 7.5x + 36[/tex]

Divide through by 4.5

[tex] \frac{4.5y}{4.5} = \frac{7.5x}{4.5} + \frac{36}{4.5} \\ y = \frac{5}{3} x + 8 \\ [/tex]

Answer:

6:1

Step-by-step explanation:

48:( 4+4 )

= 48:8

= 6:1

Answer:

[tex]=\left(\frac{15}{2},\:\frac{5}{2}\right)[/tex]

Step-by-step explanation:

[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(6,\:4\right),\:\left(x_2,\:y_2\right)=\left(9,\:1\right)\\\\=\left(\frac{9+6}{2},\:\frac{1+4}{2}\right)\\\\=(\frac{15}{2} , \frac{5}{2} )\\\\[/tex]

Answer:

Lulu's money = £81

Ruby's money= £108

Emma's money= £72

Step-by-step explanation:

Let

Lulu's money = x

Ruby's money= y

Emma's money= z

x+y+z= 261

Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.

2/3x = 1/2y= 3/4z

2/3x= 1/2y

4/3x= y

2/3x= 3/4z

8/9x= z

x+y+z= 261

x+4/3x+8/9x= 261

9x+12x+8x= 2349

29x= 2349

X= 81

4/3x= y

4/3(81) =y

108= y

8/9x= z

8/9(81)= z

72= z

Answer:

Step-by-step explanation:

Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.

1 answer

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Top answer:

Answer:Lulu= £81Ruby=£108Emma=£ 72