Can Σx² be negative? Why or why not

Answer:

center:(0,0)

Radius:7

Step-by-step explanation:

the equation of circle:

(x-h)^2+(y-k)^2=r^2

the point h and k are the center of the circle
(h,k)  ———-> (0,0)

since r^2 =49

So, the radius will be the square root of that number
\(r^{2} =49\)

\(\sqrt{r^{2} } =\sqrt{49}\)

\(r=7\)

The solution of the system of equations is (2, 4, 5)

The given equations are :

3x+10y-12z = 40    equation(1)

x-5y = 0     equation (2)

x-4z = 0      equation(3)

From 2nd equation, x -5y = 0, 5y = x, y = x/5

From 3rd equation, x -4z = 0, 4z = x, z = x/4

Putting the values of y and z in equation (1), we get :

\(3x +10y -12z = 40\\\\3x +10*\frac{x}{5} -12*\frac{x}{4} = 40\\\\3x +2x -3x =40\\\\2x = 40\\\\x = \frac{40}{2} = 20\)

Now, putting the value of x = 20 to evaluate y and z, we have,

y = 20/5 = 4

and z = 20/4 = 5

Hence, the solution of the system of equations is (2, 4, 5)

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Answer:

A

Step-by-step explanation:

Find cross-sectional area first:

Area of triangle = 6x4/2

Multiply the cross-sectional area by height which in this case is 9ft so

(6x4/2) x 9

Answer:

$56,226

Step-by-step explanation:

x = investment

Earning interest of 3.57% is the equivalent of multiplying the initial balance (investment) by 1.0357;

Over 20 years, the new balance can be found by multiplying the initial balance by (1.0357)²⁰;

We can formulate an equation to solve to get the initial investment:

x(1.0357)²⁰ = 113400

(2.01687752)x = 113400

x = ¹¹³⁴⁰⁰/₍₂.₀₁₆...₎

x = 56225.5263 → 56226

Answer:

slope = - \(\frac{8}{5}\)

Step-by-step explanation:

calculate the slope m using the slope- formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line

m = \(\frac{-4-4}{4-(-1)}\) = \(\frac{-8}{4+1}\) = \(\frac{-8}{5}\) = - \(\frac{8}{5}\)

Conditional probability: p(A|B) is the probability of event A occurring, given that event B occurs.

Example: the probability that a card drawn is red (p(red) = 0.5).

Another example: the probability that a card drawn is a 4 (p(four)=1/13).

Joint probability: p(A and B). The probability of event A and event B occurring.

Answer:

-22

Step-by-step explanation:

x-3y

(-4)-3(-6)

(-4)-(-18)

(-22)

Answer:

\(a^{12} b^{4}\)

Step-by-step explanation:

To simplify we will have to use the negative exponent rule and the power rule along with some algebra.

Negative Exponent Rule

\(a^{-b} =\frac{1}{a^b}\)

Power Rule

\((a^b)^{c} =a^{bc}\)

Given

\((a^{-4}b^{-1}c )^{2} (a^2bc)^{2}\)

Rewrite \(a^{-4}\) using negative exponent rule.

\((\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}\)

Rewrite \(b^{-1}\) using negative exponent rule.

\((\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}\)

Simplify

\((\frac{c}{a^4b} )^{2} (a^2bc)^{2}\)

Rewrite the base as its reciprocal.

\((\frac{a^4b}{c} )^{2} (a^2bc)^{2}\)

Apply the power rule.

\(\frac{a^8b^2}{c^2} *(a^2bc)^{2}\)

Apply the power rule.

\(\frac{a^8b^2}{c^2} *a^4b^2c^2\)

Cancel the common factor of \(c^2\).

\(a^8b^2 a^4b^2\)

Apply the power rule.

\(a^{12} b^{4}\)

Answer:

\(a^{12}\:b^{4}\)

Step-by-step explanation:

Given expression:

\(\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2\)

Simplify:

\(\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2\)

Collect like terms:

\(\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)

\(\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}\)

Simplify:

\(\implies a^{12}\:b^{4}\:c^{0}\)

\(\textsf{Apply exponent rule} \quad a^0=1:\)

\(\implies a^{12}\:b^{4}(1)\)

\(\implies a^{12}\:b^{4}\)

Answer:

The decrease of the decimal rate -1.05 mm/year can be rounded to -1. You don’t need to round 2.48 because you’re multiplying by -1. Since -1.05 is negative and rounded to a greater value, the estimate could be adjusted to a slightly lesser value, maybe -2.5 or -2.6.

Step-by-step explanation: I'm taking the test

Answer:

Sample response: The decrease of the decimal rate -1.05 mm/year can be rounded to -1. You don’t need to round 2.48 because you’re multiplying by -1. Since -1.05 is negative and rounded to a greater value, the estimate could be adjusted to a slightly lesser value, maybe -2.5 or -2.6.

Step-by-step explanation:

The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.

Let's assume the volume of water in Jug B is x.

According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.

Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].

To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:

(x) / [(3/5) * (6/7) * x]

Simplifying the expression, we get:

x / (18/35 * x)

The x values cancel out, leaving us with:

1 / (18/35)

To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:

1 * (35/18)

The final ratio is:

35/18

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Answer:1/40

Step-by-step explanation: If the Smiths bought 25 raffle tickets, and there were 1000 sold in total, it would mean they have a 25/1000 chance. we can simplify 25/1000 into 1/40. Therefore, the answer is (3)

The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

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Answer: -4/3 < x< 1/2

Step-by-step explanation: inequality form

In order for three sides to make a triangle, if any two sides are added together, their sum should be greater than the third side:

→ 5 + 7 = 12 < 13 (DOES NOT check off the rule)

→ 7 + 13 = 20 > 5 (Checks off the rule)

→ 5 + 13 = 18 > 7 (Checks off the rule)

As shown, even though 2 of the statements check off the rule the third one does not, this means that the sides don't make a triangle.

Answer:

$6,722.63

Step-by-step explanation:

Now: $10,200

In 1 year: 0.92 × $10,200 = $9,384

In 2 years: 0.92 × $9,384 = $8,633.28

In 3 years: 0.92 × $8,633.28 = $7,942.6176

In 4 years: 0.92 × $7,942.6176 = $7,307.208192

In 5 years: 0.92 × $7,307.208192 = $6,722.63

Answer: $6,722.63

Answer:

$6,722.63

Step-by-step explanation:

Using this formula A=P(1-d/100)^n where

A = Amount

P = Principal

d = percent

n = number of year

A=P(1-d/100)^n

A = 10,200(1-8/100)⁵

A = 10,200(1-0.08)⁵

A = 10,200(0.92)⁵

A = 10,200(0.6591)

A= $6,722.63

For a rotation of 180° clockwise or counterclockwise, the x and y will always be the opposite. For instance, if coordinates (4, 7) are being 180° rotated, the new set of coordinates will be (-4, -7).

Remembering the rule, the final answer to your question is A, 180° clockwise rotation about the origin.

Answer:

2/-5

Step-by-step explanation:

This function represents a downward-opening parabola with a vertical shift of 6 units upward.

The given function is Ƒ(t) = –1/(2t²) + 2t + 6.

This is a quadratic function in terms of t. The general form of a quadratic function is f(t) = at² + bt + c, where a, b, and c are constants.

Comparing the given function Ƒ(t) = –1/(2t²) + 2t + 6 with the general form, we can see that a = -1/2, b = 2, and c = 6.

So, the function Ƒ(t) can be written as:

Ƒ(t) = (-1/2)t² + 2t + 6

This function represents a downward-opening parabola with a vertical shift of 6 units upward.

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Answer:

12

Step-by-step explanation:

If Alicia has 2 pets Fatima has 4 since 2 x 2 = 4. Izzy has 3 times as many as Fatima then she has 12 since 3 × 4 = 12

Lamar is taller than Kenny.

There are twelve inches in a foot. Sixty-seven divided by twelve equals five with a remainder of seven. Lamar is five feet and seven inches tall, two inches taller than Kenny.

Answer:

i think kenny is taller

Step-by-step explanation:

hope this helps have a nice day :)

Given dimensions of the room:

Length: \(\displaystyle\sf 12.5 \,m\)

Width: \(\displaystyle\sf 9 \,m\)

Height: \(\displaystyle\sf 7 \,m\)

Area of each wall:

\(\displaystyle\sf Area_1 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_2 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_3 = 9 \times 7 = 63 \,m^2\)

\(\displaystyle\sf Area_4 = 9 \times 7 = 63 \,m^2\)

Area of each door:

\(\displaystyle\sf Area_{\text{door}} = 2.5 \times 1.2 = 3 \,m^2\)

Area of each window:

\(\displaystyle\sf Area_{\text{window}} = 1.5 \times 1 = 1.5 \,m^2\)

Total area occupied by doors:

\(\displaystyle\sf Total_{\text{doors}} = 2 \times Area_{\text{door}} = 2 \times 3 = 6 \,m^2\)

Total area occupied by windows:

\(\displaystyle\sf Total_{\text{windows}} = 4 \times Area_{\text{window}} = 4 \times 1.5 = 6 \,m^2\)

Total wall area excluding doors and windows:

\(\displaystyle\sf Total_{\text{wall\,area}} = (Area_1 + Area_2 + Area_3 + Area_4) - Total_{\text{doors}} - Total_{\text{windows}}\)

\(\displaystyle\sf = (87.5 + 87.5 + 63 + 63) - 6 - 6\)

\(\displaystyle\sf = 275 - 6 - 6\)

\(\displaystyle\sf = 263 \,m^2\)

Cost of painting the walls:

\(\displaystyle\sf Cost_{\text{painting}} = Total_{\text{wall\,area}} \times 3.50\)

\(\displaystyle\sf = 263 \times 3.50\)

\(\displaystyle\sf = 920.50 \,Rs\)

Therefore, the cost of painting the walls of the room at Rs. 3.50 per square meter is Rs. 920.50.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The way to solve the equation for the width, w, is to divide both sides by l. The correct option is A. We want to get w by itself, so we would divide both sides by l

From the question, we are to determine how we can solve the given formula for area of rectangle for the width, w

The given formula is

A = lw

To solve the given equation for w, we will divide both sides of the equation by l

That is,

A/l = lw/l

So that

A/l = w

and

w = A/l

Hence, the way to solve the equation for the width, w, is to divide both sides by l. The correct option is A. We want to get w by itself, so we would divide both sides by l

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(4) y = (3 - 2x)³ + 24x

Use the power and chain rules:

dy/dx = 3 (3 - 2x)² d/dx [3 - 2x] + 24

dy/dx = 3 (3 - 2x)² (-2) + 24

dy/dx = -24x ² + 72x - 30

(5) y = 54x - (2x - 7)³

Same basic procedure:

dy/dx = 54 - 3 (2x - 7)² d/dx [2x - 7]

dy/dx = 54 - 3 (2x - 7)² (2)

dy/dx = -24x ² + 168x - 240

Answer:

y=3x+9 would be the equation

Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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Number of car sold are 98.

Number of trucks sold are 66.

Given,

Dealer 1 sold 164 cars and trucks and dealer 2 sold 229 cars and trucks .

Let number of cars sold are x.

Let number of cars sold of y .

Now,

For dealership 1 equation will be,

x + y = 164  ......(1)

For dealership 2 equation will be,

As the cars are sold twice and trucks are sold half .

2x + y/2 = 229......(2)

Solving 1 and 2,

y = 66

x = 98

Thus number of car sold are 98.

Thus number of trucks sold are 66.

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Answer:

\(x + 3y > 9 \\ 3y > - x + 9 \\ y > - \frac{1}{3} x + 3 \\ y - intercept \: is \: 3 \\ first \: point = 3 \\ second \: point \: = 9\)

Answer:

20

Step-by-step explanation:

3³ - 3² + 3 - 1

27 - 9 + 3 - 1

30 - 9 - 1

30 - 10

= 20

Answer:

\(\tt{}20\)

Step-by-step explanation:

\(\tt{} {3}^{3} - {3}^{2} + 3 - 1\)

\(\tt{}(3 \times 3 \times 3) - (3 \times 3) + 3 - 1\)

\(\tt{}27 - 9 + 3 - 1\)

\(\tt{}20 \\ \)

Answer:

a = 28, b = -35 and c =7

Step-by-step explanation:

Given expression is :

28x-35y=-7

We need to express it in the form of ax+by+c=0 and then find the value of a,b and .

Adding 7 to both sides.

28x-35y+7=-7+7

28x-35y+7=0

or

28x+(-35y) +7=0

It is in the form of ax+by+c=0.

On comparing,

a = 28, b = -35 and c =7