Given that these simultaneous equations
x-y=k
2x²+y²-15
have exactly one pair of solutions, find k.

The answer is supposedly (±3√10)/2, but I don't know how to get to the answer

Answer:

last one is the answer brother

Answer:

Approx. 1343 feet

Step-by-step explanation:

Building A is 71 stories at 875 feet tall. Since the two buildings have the same number of feet per floor, we can divide building A's stories to find the height of 1 story, and then multiply by the stories of building B.

Building A
71 ÷ 71 = 1 story
875 ÷ 71 = 12.32 feet
Each story is approximately 12.32 feet tall

Building B
1 story × 109 = 109 stories
12.32 feet × 109 = 1343.31 feet

Rounded to the nearest foot is 1343 feet.

the equation of f(x) which is "x" terms is the equation of a vertical parabola that is opening upwards like a bowl, the minimum will be at its vertex

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 4}{2(1)}~~~~ ,~~~~ 12-\cfrac{ (4)^2}{4(1)}\right) \implies \left( - \cfrac{ 4 }{ 2 }~~,~~12 - \cfrac{ 16 }{ 4 } \right) \\\\\\ (-2~~,~~12-4)\implies \stackrel{minimum}{(-2~~,~~\stackrel{\downarrow }{8})}[/tex]

Answer:

[tex]1.25332[/tex]

Step-by-step explanation:

[tex] tan(30 times tan(60 ) \div \tan(60 \div + 30) [/tex]

Using the Charles law, the following are the solutions to the problems;

1) 16 dm3

2) 170 K

3) 2.4 L

Charles law states that, the volume of a given mass of gas is directly proportional to the temperature at constant pressure.

For problem 1;

T1 = 20 + 273 = 293 K

V1 = 15 dm3

T2 = 318 K

V2 = ?

V1/T1 = V2/T2

V1T2 =V2T1

V2 = V1T2/T1

V2 = 15 dm3 * 318 K/293 K

V2 = 16 dm3

Problem 2

V1 = 250cm3

T1 = 10 + 273 = 283 K

V2 = 150cm3

T2= ?

T2 = V2T1/ V1

T2 =  150cm3 *  283 K/250cm3

T2 = 170 K

Problem 3

V1 = 2.3 L

T1 = 25 + 273 = 298K

V2 = ?

T2 = 40 + 273 = 313 K

V2 = V1T2/T1

V2 = 2.3 L * 313 K/298K

V2 = 2.4 L

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Answer:

y - 2 = -5 (x - 1)

Step-by-step explanation:

Formula for point-slope equation :

y - y₁ = m (x - x₁)

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

Given :

⇒ Point (x₁, y₁) = (1, 2)

⇒ Slope (m) = -5

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

Solving :

⇒ y - 2 = -5 (x - 1)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Equation of line can be written in point - slope form as :

[tex]\qquad \sf  \dashrightarrow \:y - y_1 = m(x - x_1)[/tex]

So, required equation is ~

[tex]\qquad \sf  \dashrightarrow \:y - 2 = - 5(x - 1)[/tex]

Answer:

6x-2

Step-by-step explanation:

-4x(1-3)-(2x+2)

= 4x+12x-2x-2

6x-2

(simplify)

Answer:

6x - 2

Step-by-step explanation:

Edge

Answer:

Step-by-step explanation:

Je calcule la facture totale

11x4=44

La facture totale d'Eugène et ses trois amis était de 11$

Answer: 5 is the mode

Step-by-step explanation: The mode is the number that is appeared most often in the data, so the mode in this case (4, 5, 5, 6, 10, 11, 12, 13) is 5.

Answer:

x = 2

Step-by-step explanation:

x/5 + 1 = 11
    x/5 = 10
        x = 50

The expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

Complex numbers are square root of negative numbers. They are expressed as a + bi

Using the expression

(4+7i)-2i(2+3i)

Expand

4 + 7i - 4i -2i(3i)

4 + 3i - 2(-3)

4 + 6 + 3i

10 + 3i

Hence the expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

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The price of the stock after the change in price on Thursday is  $16.76.

The price of the stock at the beginning of the week is $16.81.

The price at the end of the week is a function of the total changes in price and the price at the beginning of the week.

$17.17 = beginning price + 0.21 + 0.09 - 0.03 -  0.02 + 0.11

$17.17 = beginning price + 0.36

Beginning price = $17.17 - 0.36 = $16.81

Price on Thursday = $16.81 + 0.21 + 0.09 - 0.03 -  0.02 = $16.76

Here are the questions:

What was the price of the stock after the change in price on Thursday?

What was the price of the stock at the beginning of the week?

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Answer:

V≈314

Step-by-step explanation:

* means times

volume of a cone

it's a right circular cone

formula

volume =

π * radius squared * (height ÷ 3)

π * 5 squared * (12 ÷ 3)

π * 25 * (4)

π * 100

3.14 * 100 = 314

factoid

pi or π in fraction form is 22/7

5 and 12 means the length of that

cone is 13

because it's a right circular cone

that means there's a right triangle

one of the special triangles is a

5,12,13 right triangle where

13 is the hypotenuse

moomoomath

Answer:

8 million insect species

Step-by-step explanation:

Solving :

⇒ Number of species = Total organisms × % of the species

⇒ Number of species = 12.4 × 64%

⇒ Number of species = 0.124 × 64

⇒ Number of species = 7.936 million ≈ 8 million insect species

The value of x is 14 because the sum of all angles in kite is 360 degree option first 14 is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The question is in the picture please refer to the attached picture.

We know the sum of all angles in a kite is 360 degree

110 + (5x) + 110 + 70 = 360

290 + 5x = 360

5x = 70

x = 14

Thus, the value of x is 14 because the sum of all angles in kite is 360 degree option first 14 is correct.

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Answer:

T10=108

Step-by-step explanation:

TN=bn+c

27,36,81=constant difference is 9

Tn=bn+c

Tn=9n+18

T10=9(10)+18

T10=90+18

T10=108.

hope it helps.

Answer: 2.703

Step-by-step explanation:

The area of the wooden part of the frame is 4x² +20x +17 sq.cm , Area of a Rectangle is 4x² +2x-2 sq.cm .

A rectangle is a polygon with four sides . The opposite sides are parallel and equal.

It is given that the outside length and breadth is 4x + 5 centimeters and width 2x + 3 centimeters.

inside the frame has length and breadth 4x - 2 centimeters long and x + 1 centimeters wide.

The polynomial to describe the area of the picture window

The dimension of the inner picture frame is the dimension of the picture window

Area of a Rectangle = Length *  Breadth

Area of a Rectangle = (4x-2) (x+1) = 4x² +4x -2x-2 = 4x² +2x-2 sq.cm

The picture frame area without the window =

Area of the total picture frame - Area of the inner picture frame

= (4x+5)(2x+3) - (4x-2)(x+1)

= 8x² + 12x +10x+15 -4x²-2x +2

= 4x² +20x +17

The area of the wooden part of the frame is 4x² +20x +17 .

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Answer:

131

Step-by-step explanation:

The expression represents the volume of the can is 2x³ + 35x² + 176x + 192.

Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. The measurement for volume is in cubic units, such m3.

Expression: (Math Operator, Number/Variable, Math Operator)

We have,

radius = (x + 8) and, height = (2x + 3)

So, Volume of can

= πr²h

= π(x+8)² (2x+3)

= π (x² + 16x + 64) (2x+3)

= π (2x³ + 3x² + 32x² + 48x + 128x + 192)

= π (2x³ + 35x² + 176x + 192)

So, the Expression for volume is 2x³ + 35x² + 176x + 192.

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A triangle is a three-edged polygon with three vertices. The correct option is C.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The sides of the triangle PQR are PQ, QR, and PR. Thus, the correct option is C.

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Answer:

[tex]y = 3x - 6[/tex]

Step-by-step explanation:

Hello!

With an x - intercept of 2, the coordinate is (2, 0). With a y - intercept of -6, the coordinate is (0, -6).

We have to find the equation of the line that goes through these points.

The equation of a line is written in slope-intercept format: [tex]y = mx + b[/tex]

First let's find the slope using the slope formula: [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]. Remember that a coordinate is written in (x, y) format.

So, we have the slope and the y - intercept. We can plug those into the equation.

The equation of the line is [tex]y = 3x - 6[/tex]

The linear regression equation that represents this data set is equal to y = 11.7x + 48.2 and an estimate of the calendar year is 2022.

First of all, we would determine the slope of the given data set by using this formula:

[tex]Slope = \frac{\sum (x-\bar x)(y-\bar y)}{\sum (x-\bar x)^2}[/tex]

For the sample mean (years), we have:

∑x = 0 + 1 + 2 + 3

∑x = 6.

∑x² = 0² + 1² + 2² + 3²

∑x² = 14.

For the sample mean (profits), we have:

∑y = 46 + 57 + 84 + 76

∑y = 263.

∑xy = (0 × 46) + (1 × 57) + (2 × 84) + (3 × 76)

∑xy = 453.

Now, we can determine the slope:

[tex]Slope = \frac{4(453) - 6(263)}{4(14) - 6^2} \\\\Slope = \frac{234}{20}[/tex]

Slope, m = 11.7.

For the intercept, we have:

[tex]Intercept = \frac{14(263) - 6(453)}{4(14) - 6^2} \\\\Intercept = \frac{964}{20}[/tex]

Intercept, c = 48.2.

Therefore, the linear regression equation is given by:

y = 11.7x + 48.2.

Since the profit would reach 144,000 dollars, the calendar year would be calculated as follows:

144 = 11.7x + 48.2

11.7x = 144 - 48.2

11.7x = 95.8

x = 95.8/11.7

x = 8.2.

For the calendar year, we have:

Year = 2014 + 8.2

Year = 2022.2 ≈ 2022.

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Given the FDIC insurance limit, the amount that Gordon would get back is $200,000.

The Federal Deposit  Insurance Corporation (FDIC) was established after the great depression with the aim of insuring the deposits of customers in banks.

If the limit on insurance is $250,000, depositors with $250,000 or less would get the full amount of their deposits in case of bank failure. If the deposit is greater than $250,000, they would get $250,000.

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Answer:

120

Step-by-step explanation:

Corresponding angles of similar figures are congruent.

The measure for w is 120 degree.

We have ABCD ~ FECG

If two quadrilaterals are similar, it means that their corresponding angles are congruent, and their corresponding sides are proportional.

Then, we can write as

AB/ FE = CB/ EC = CD/ CD = AD/ FG

and, <A= <F,          

<B = <E,

<C= <C,

<D= <G

So, the measure for w is same as angle G.

Thus, the measure for w is 120 degree.

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If there was a nuclear plant disaster, then GDP would be a false beacon because it would account for government spending but not for the pollution caused.

Two of the components of GDP are government spending and private investment.

If there is a nuclear plant disaster, either the government will spend a lot to clean it up, or a private company will depending on if the plant is public or private.

GDP would therefore increase.

This would be a false beacon however, because this increase would not take into account the nuclear pollution that would have occurred that would negatively impact future production.

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Answer:

7,654

Step-by-step explanation:

Arrange the digits in order to create the highest possible number.

7000 + 600 + 50 + 4 = 7654

The probability that an animal has stripes will be 0.86.

The probability that an animal has stripes will be:

= Orange stripes + Brown stripes + Grey stripes

= 0.16 + 0.3 + 0.4

= 0.86

The probability that an animal doesn't have stripes will be:

= 1 - 0.86

= 0.14

Therefore, the probability that an animal doesn't have stripes is 0.14.

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Answer:

the answer is D

hope it will help