If shown, AB and CD are straight lines. Find x in each case.
NEED HELP ASAP

The coordinates of the point will be (5 , 5).

Section formula is used to find coordinates of a point when a point divides the line segment externally or internally.

For a line segment A ([tex]x_{1} , y_{1}[/tex]) and B ([tex]x_{2} , y_{2}[/tex]) getting divided by point C (x , y) in ratio m : n the formula is given as

x = [tex]\frac{mx_{2} + nx_{1} }{m + n}[/tex]             y = [tex]\frac{my_{2} + ny_{1} }{m + n}[/tex]

Now in the question it is given that C from point A is twice the distance from point B which means ratio of A:B IS 2:1

A = (1 , 3)

B = (7 , 6)

by applying the formula

x = (2*7 + 1*1) / 2+1

x = 15/3

x = 5

y = (2*6 + 1*3) / 2+1

y = 15/3

y = 5

Therefore the coordinates of C will be (5 , 5)

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Answer:

a number x times by 3

Step-by-step explanation:

yw I hope that helps

Answer: 422.39

Step-by-step explanation:

To find the shaded region (I'm assuming it's the area inside the circle but outside the rectangle), subtract the area of the rectangle from the area of the circle.

The formula for circle area: πr^2

r is the radius, and it is given that r = 12, so the area of the circle is:

π * 12^2    --->    144π    is the area of the circle

Next, find the area of the rectangle: 3 * 10 = 30

Finally, find subtract the area of the rectangle from the area of the circle to find the shaded region:

144π - 30 ≈ 422.39

Answer:

x=-4 or x=2

Step-by-step explanation:

2(x+4)(x-2)=0

Subtract 4 from both sides:

(x+4)=0

Simplify:

x=-4

Expression equivalent to log 9⁵ is 5 log9.

Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is equivalent to 2, even if 2 is said to be equal to 2. Equivalent value or dated value refers to the value of an original sum at any given moment. The original amount and interest accrued up to the dated value date are combined to create the comparable payment. Money amounts are not directly comparable if they are payable or due at separate times.

Given,

Expression equivalent to log 9⁵

a) 5 log9

Expression equivalent to log 9⁵ is 5 log9.

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The equation representing the sum of three consecutive integers as 42 are x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]+[/tex] (x + 2) [tex]=[/tex] 42   and (x - 1) [tex]+[/tex] x + (x [tex]+[/tex] 1) [tex]=[/tex] 42   , the correct option are (a) and (c) .

In the question ,

it is given that ,

the sum of the three consecutive integers = 42

the equations that shows the relationship is only option (a) and option(c) , because

option (a)

x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]+[/tex] (x + 2) [tex]=[/tex] 42

3x + 3 = 42

3x = 39

x = 13

yes , the terms are consecutive and are  13 , 14 , 15 .

option(c)

(x - 1) [tex]+[/tex] x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]=[/tex] 42

3x = 42

x = 14

putting in equation we get 14-1 = 13 , 14 , 14+1 = 15

yes , the terms are consecutive and are  13 , 14 , 15 .

Therefore , The equation representing the sum of three consecutive integers as 42 are x + (x + 1) + (x + 2) = 42   and (x - 1) + x + (x + 1) = 42 .

The given question is incomplete , the complete question is

The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.

(a) x + (x + 1) + (x + 2) = 42

(b) x + (x + 2) + (x + 4) = 42

(c) (x - 1) + x + (x + 1) = 42

(d) (x - 2) + x + (x + 2) = 42

(e) x + 2 x + 3 x = 42

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Answer:

458.7 cm

Step-by-step explanation:

to find circumference we multiply diameter by pi

146(pi)

458.673

And we round to 1 d.p.

458.7

Hopes this helps please mark brainliest

a) The bearing of Wellington from Gisborne is 232°

b) The bearing of Wellington from Auckland is  175.37°

We are given that AW = 410 km and GW = 400 km.

a) AG  is a transversal intersecting two parallel lines N₁A and N₂B and ∠N₁AG = 115°.

Thus;

∠AGN₂ = 180 − 115 = 65°  

since the sum of the interior angles on the same sides of the transversal intersecting two parallel lines are supplementary.

Thus;

∠N₂GW = 65 + 63 = 128°.

The reflex angle;

∠N₂GWW = 360 − 128° = 232°

b) In  △AGW, we can say that by the sine rule;

(sin∠WAG)/WG = (sin∠AGW)/AG  

Plugging in the relevant values;

(sin∠WAG)/400 = (sin∠63°)/410

Solving for ∠WAG gives; ∠WAG = 60.37°

Then;

∠N₁AW = 115 + 60.37

∠N₁AW = 175.37°

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Answer: B

Step-by-step explanation:

Answer:

The perpendicular slope is the negative reciprocal of the original slope:

For example: the perpendicular slope for y/x is -x/y

In this case, we want the slope from x +4y = 28

x +4y = 28

4y = 28 - x

y = 7 -x/4

so the answer is: 4/x

Answer:

9x-4

Step-by-step explanation:

The expression that represents the amount of sodium per serving in the new soup is 0.67x milligrams.

The new soup recipe contains 33%, percent less sodium per serving than the old soup recipe. The old soup recipe contained x milligrams of sodium per serving.

The expression that can be used to represent the amount of sodium per serving in milligrams in the new soup can be computed as follows;

Old soup amount of sodium = x milligram

The new soup contains 33% less sodium per serving than the old soup recipe.

Therefore,

amount of sodium per serving in the new soup = x - 33% of x

amount of sodium per serving in the new soup = x - 33 / 100 x

amount of sodium per serving in the new soup = x - 0.33x

Therefore,

amount of sodium per serving in the new soup = x(1 - 0.33)

amount of sodium per serving in the new soup = x(0.67)

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Box 1 = 8

Box 2 = 2

If he earned $64 in 8 hours then dividing by 64 by 8 will tell us how much he earned in 1 hour. That gives $8

Using that we can then divide the number of dollars by the amount he receives in 1 hour to see how many hours it was.

So $16 / $8 per hour gives 2 hours

The value of 5.37 divided by 3 will be 1.79.

The necessary steps include:

It should be noted that it's important to bring down the next digit of the dividend. For long division problems, always follow the divide, multiply, subtract, and drop down process until each digit in the dividend has been divided.

Therefore, 5.37 ÷ 3 = 1.79.

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Answer:

Step-by-step explanation:

Answer:

length = 13 cm and width = 14 cm

Step-by-step explanation:

let n be the length then n + 1 is the width

the perimeter (P) of a rectangle is calculated as

P 2(l + w) ← l is length and w is width

given P = 54 , then

2(n + n + 1) = 54 ( divide both sides by 2 )

2n + 1 = 27 ( subtract 1 from both sides )

2n = 26 ( divide both sides by 2 )

n = 13

n + 1 = 13 + 1 = 14

length = 13 cm and width = 14 cm

The recursive formula for sequence starting with 12, 6 is, [tex]a_1=a_0-\frac{a_0}{2}[/tex].

What is recursive formula?

Any term of a series can be defined by its preceding term in a recursive formula (s).

For instance: An arithmetic series has the recursive formula [tex]a=a_n_-_1+d[/tex] . [tex]a_n=a_n_-_1r[/tex] is the recursive formula for a geometric sequence.

Given two terms are, 12, 6.

The first term is 12, so [tex]a_0=12[/tex].

The second term is 6, which is half of the first term.

So, [tex]a_1=a_0-\frac{a_0}{2}[/tex]

Therefore, the recursive formula for the sequence starting with 12, 6 is

[tex]a_1=a_0-\frac{a_0}{2}[/tex].

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Answer:

j = 0.4

Step-by-step explanation:

hope it helps

To answer this question, you should combine like terms:

Like terms are two or more terms that share the same variable.

J is the variable in this question so add 0.9j to both sides of the equation to get j on one side:

-0.1j + 0.8 = 0.76

Now subtract 0.8 from both sides to isolate j on one side of the equation:

-0.1j = -0.04

Divide both sides by -0.1 to isolate j and your answer should be:

Answer: j = 0.4

1  is the value of cat in linear equation.

What is an explanation of a linear equation?

number of cats  =  n

number of fleas per cat  =  2n

total number  of fleas  =  (number  of fleas per cat) * (number of cats)   =   2n * n   =   2n2

If we take the total number of fleas, subtract the fleas of two cats, then subtract  3  for every remaining cat, we get half the total number of fleas.

(total number of fleas) - 2(number of fleas per cat) - 3(n - 2)  =  (total number  of fleas)/2

2n2  -  2(2n)  -  3(n - 2)   =   (2n2)/2

2n2 - 4n - 3n + 6   =   n2

                                               Subtract  n2  from both sides and combine like terms.

n2 - 7n + 6  =  0

                                                Factor the left side

(n - 6)(n - 1)  =  0

n = 6      or      n = 1

n  must be  6  because we can't remove  2  cats if there is only  1  cat to begin with.

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The complete question is -

Each of n cats has 2n fleas. If two cats (and their fleas) are removed, and three fleas are removed from each remaining cat, the total number of fleas remaining would be half the original total number of fleas. What is the value of n?

Step-by-step explanation:

both roots are square roots.

if we write the 2 or leave the base of the root blank, it both means square root.

so, we have

sqrt(15) / sqrt(3)

we can combine them into

sqrt(15/3) = sqrt(5) = 2.236067977...

Answer:

BANK A

I=5700.825

T.P=25190.83

BANK B

I=3274.32

P=22764.32

The area of the circle is 153.86 inches square.

What is a circle?

Every point in a plane that is at a specific distance from the centre, or the circle's centre, forms a shape. To put it another way, it is the curve that a moving point in a plane draws to keep a constant distance from another point.

Main Body:

given:

diameter = 14 in

[tex]\pi[/tex] = 3.14

radius = diameter/ 2

          = 14/2

        r = 7 in

Area of circle is given by = [tex]\pi r^{2}[/tex]

Inserting the value of [tex]\pi[/tex] and r ,

area of circle = 3.14* [tex]7^{2}[/tex]

HENCE, Area of circle = 153.86 inches square

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Answer:

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

It has a variable x and its coefficient (-1), the 3 is the constant.

[tex]\Large \boxed{\sf -1}\\\\\\\displaystyle \sf A\ coefficient\ in\ an\ expression\ is\ the\ integer\\ value\ multiplied\ by\ the\ variable.\\\\(-1) \times x + 3[/tex]

If a washer and dryer cost $750 and the cost of the washer is two times the cost of the dryer, then the cost of the dryer $250

The total cost of a washer and dryer combined = $750

The cost of the dryer = x

The cost of the washer is two times the cost of the dryer.

The cost of the washer = 2x

Then the equation will be

x + 2x = 750

Add the like terms of the equation

3x = 750

Move 3 to the right hand side of the equation

x = 750/3

x = $250

Hence, if a washer and dryer cost $750 and the cost of the washer is two times the cost of the dryer, then the cost of the dryer $250

The complete question is:

A washer and dryer cost $750 combined the cost of the washer is two times the cost of the dryer what is the cost of the dryer?

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The equation of the line is - 175 x + 2 y = - 500

From the question, we have

Point 1 :

x-coordinate, x1 = 6

y-coordinate, y1 = 275

Point 2 :

x-coordinate, x2 = 8

y-coordinate, y2 = 450

We know that,

y-275 = (275-450)/(6-8)*(x-6)

y-275 = 175/2*(x-6)

- 175 x + 2 y = - 500

Slope of a Line :

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.

where "m" represents a line's slope.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

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The cost of materials for the least expensive such container is $327.081  .

In the question ,

it is given that

the volume of the container = 10 m³ .

let the width of the container = x

so , the length of the container = 2x

So , base area = 2x*x = 2x²

cost for base = $20

cost for the sides = $12

Since the volume is 10 m³

Volume = base area *  height

10 = 2x² * h

h = 10/2x²

h = 5/x²

The cost of making the container

cost of base = 2x² * (20) = 40x²

cost of sides = [2*2x*(5/x²) + 2*x*(5/x²)](12)

= 360/x

the total cost of the container [tex]=[/tex] cost of base [tex]+[/tex] cost of sides

= 40x² + 360/x

= 40( x² + 9/x)

to get the minimum cost , we differentiate with respect to x and equate to 0

= 40 ( 2x - 9/x²)

2x - 9/x² = 0

2x³ = 9

x³ = 9/2

x³ = 4.5

x = 1.651

Substituting x in the cost equation ,

we get

Cost = 40x² + 360/x

= 40(1.651)² + 360/(1.651)

= 109.032 + 218.049

= 327.081

Therefore , The cost of materials for the least expensive such container is $327.081  .

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The system of equation for the given condition is: 5+0.03x = 0.10x, where x is the number of texts.

There is no certain number of texts for which two plans are equal.

Let the number of texts for which two plans amount to same number be = x

Plan A: $5.00 per month charge along with a charge of $0.03 per text.

So, Plan A: 5+0.03x

Plan B: No per month charge but a charge of 0.10 per text.

Plan B: 0.10x

Since the plans amounted to same for x texts. So, the suitable system of equation is,

5+0.03x = 0.10x

Solving the equation we get,

0.10x - 0.03x = 5

0.07x = 5

x = 5/0.07 = 71.42 (approximately)

Since the number of texts cannot be decimal number so there is no such number of texts for which plans are equal.

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a = -2 is the value of linear equation .

What are examples of linear equations?

Step 1 - Write the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 2 - rewrite the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 3 - Take the LCM.

3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4

Step 4 - Further simplify the above expression

3a - 6 - a - 2/a² - 4 = 6a/a² - 4

Step 5 - Cancel out the denominator of both sides and then further simplify.

2a - 8 = 6a

a = -2

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The complete question is -

A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.

3/a + 2 − 6a/a2 − 4 = 1/a − 2