Solve the system by finding the determinants and using Cramer's Rule:
2x - y = 4
3x + y = 1

Answer:

30.625 m

Step-by-step explanation:

Maximum Height :

(u²sin²θ) / 2g

u = 49 m/s

θ = 30°

g = 9.8m/s

(49² * 0.5²) / 2 * 9.8

600.25 / 19.6

= 30.625 m

Surface area overall of a cone is A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

Volume of a cone:

V = (1/3)πr2h

Cone's slant height:

s = √(r2 + h2)

Lateral surface area of a cone:

L = πrs = πr√(r2 + h2)

Cone (circle) base surface area:

B = πr2

Total surface area of a cone:

A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

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why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Answer:

2x+3

f(-2)=:2x+3

2(-2)+3

-4+3

= -1

The percent increase is 8%.

The ratio of the increased value to the original value, multiplied by 100, is the percentage increase formula. It is outlined as a percentage. Anything's value will increase if it is valued more, so will its proportion.

As follows is the percentage increase formula:

Percentage Increase = (Increased Value ⁄ Original Value) × 100

Given:

The number varies from $6.25/h to $6.75/h.

So, change in amount = 6.75- 6.25 = 0.50

Now, percent increase

= change in amount / original amount x 100

= 0.50/ 6.25 x 100

= 0.08 x 100

= 8%

Hence, the percent increase is 8%.

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I don't know if you mean rounding to the HUNDRED place or the HUNDREDTHS place, but I will give you both answers.

8.162 rounded to the hundreds place - 0

8.162 rounded to the HUNDREDTHS place- 8.16

There will be no change in the price of the car.

A number line is a representation of a graduated straight line used to abstract real numbers in elementary mathematics. Its points are considered to correspond to real numbers and vice versa.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Let the sticker price = x, Price reduced by $300

Hence the new price is,

N= x-$300

The cost of additional features = $900

Hence the new price for selling will be.

=x-$300+$900

=x+$600

Dealer also provides a discount of $600

Hence Final  selling price will be

=x+$600-$600

Hence there seems to be no change in the sticker price as the sticker price and the final selling price are the same.

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The expanded form of the expression is 10 + 9 + 0.3 + 0.00 + 0.005

He runs the 100 meters dash in 19.305 seconds.

Therefore, the seconds he runs the race can be represented in expanded form as follows:

Expanded form is a way to write a number by adding the value of its digits.

We can use a place value chart to think of the value of a number's digits.

Therefore,

19.305 in expanded form is as follows:

19.305 = 10 + 9 + 0.3 + 0.00 + 0.005

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Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.

9514 1404 393

Answer:

  A, C, E

Step-by-step explanation:

A. 0.6 • 25 = x . . . . . a direct translation of 60% of 25 (yes)

B. x • 1.6 = 25 . . . no (means 160% of x is 25)

C. 6/10=x/25 . . . . . . the ratio of x to 25 is 60% (yes)

D.60/100 = 25/x . . . no (means 25 is 60% of x)

E. x/25 = 60/100 . . . . . the ratio of x to 25 is 60% (yes)

F.6.0 • 25 = x . . . no (no means 600% of 25)

Answer:

A, C, E

Step-by-step explanation:

The complex number in standard form is written as:

Z =  1.99 + i*0.201, so the correct option is a

Remember that a complex number can be written in standard form as:

Z = a + b*i

And in polar form the notation is (R, θ):

\(Z = R*e^{i*\theta} = R*cos(\theta) + i*R*sin(\theta)\)

Here we have the complex number:

Z = 2(cos(11pi/6) + i*sin(11pi/6))?

So here we just need to solve these expressions, we will get:

Z = 2*(0.995 + i*0.100)

Z =  1.99 + i*0.201

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Complete question:

"Convert the polar representation of this complex number into its standard form: z = 2(cos 11pi/6+ i sin 11pi/6)? "

Equaling both equations, it is found that the correct option that states the number of solutions you will have for the system is:

The equations are:

\(4y + x = 16 \rightarrow x = 16 - 4y\)

\(y = 4 - x \rightarrow x = 4 - y\)

Equaling both equations for x, we have that:

\(16 - 4y = 4 - y\)

\(3y = 12\)

\(y = \frac{12}{3}\)

\(y = 4\)

\(x = 4 - y = 4 - y = 0\)

Hence, the system has one solution, which is (0,4), and option d is correct.

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let x be the capital invested in the 9% account

let y be the capital invested in the 8% account

let j be the interest earned from the 9% account

let k be the interest earned from the 8% account

\(j = xi_{1}n \: \: \: (n = 1 \: year)\\ j = x( \frac{9}{100})(1) = 0.09x\)

\(k =yi_{2}n \: \: \: \: (n = 1 \: year) \\ k = y( \frac{8}{100} )(1) = 0.08y\)

But the total interest made is 2100 $, hence:

\( \: \: \: \: \: \: \: j + k = 2100 \\ 0.09x + 0.08y = 2100\)

And the total capital invested is 25000 $

\(x + y = 25000\)

System of 2 equations and two unknowns:

\(0.09x + 0.08y = 2100 \\ x + y = 25000 \\ \\ \: \: \: \: (x,y)=(10000,15000)\)

The sequence that represents the number of customers is arithmetic, and the recursive formula is \(T_n = T_{n-1} + 8\)

The number of customers on the first day is represented as:

\(T_1 = 3\)

The number of customers on the second day is represented as:

\(T_2 = 11\)

The number of customers on the third day is represented as:

\(T_3 = 19\)

So, we have:

\(T_1 = 3\)

\(T_2 = 11\)

\(T_3 = 19\)

Rewrite the above sequence as:

\(T_1 = 3\)

\(T_2 =3 + 8\)

\(T_3 =11 + 8\)

So, we have:

\(T_1 = 3\)

\(T_2 = T_1 + 8\)

\(T_3 = T_2 + 8\)

Express 2 as 3 - 1

\(T_3 = T_{3-1} + 8\)

Substitute n for 3

\(T_n = T_{n-1} + 8\)

Hence, the sequence represents an arithmetic pattern, and the recursive formula is \(T_n = T_{n-1} + 8\)

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Equation for charges of first plan

C₁ = 24.t

Equation for charges of second plan

C₂ = 9t + 2995

If we talk for _199.7__ minutes the two plans will cost the same.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

First plan charges rate of 24 cents per minute

C₁ = 24.t

C₁ is the charge of first plan

t is the number of minutes

Second plan charges $29.95 plus 9 cents per minute.

C₂ = 9t + $29.95

1 dollar = 100 cents

C₂ = 9t + 2995

Where C₂ is the charge of first plan

t is the number of minutes.

Let after x minutes the cost of both plans will be same

C₁ = C₂

24x = 9x + 2995

24x - 9x = 2995

15x = 2995

x = 2995/15

x = 199.667 ≈ 199.7 minutes

Hence, C₁ = 24.t and C₂ = 9t + 2995 are the equations for the charges of first plan and second plan respectively.

After talking 199.7 minutes the cost of two plans will be same.

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Answer:

the vertex of the parabola is at the point; (5, -1)

which agrees with answer "B" in the list of options

Step-by-step explanation:

Notice that this is the equation of a parabola with branches that open horizontally (not vertically), since the variable the goes squared is the y-variable instead of "x".

By analyzing it we can then write it by isolating the term in "x" on one side of the equation, and use at the same time the fact that it is being written in "vertex" form:

\(-8\,(x-5)=(y+1)^2\\(x-5)=-\frac{1}{8} (y+1)^2\)

Therefore, the "y-value" of the vertex must be that which renders zero in the expression squared, that is y = -1. On the other hand, the x-value of the vertex is that which renders zero for the variable "x":  x=5.

Then, the vertex of the parabola is at the point; (5, -1)

Answer:

6n+2

Step-by-step explanation:

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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Answer:

Circumference=18.84 m

Area = 28.26 \(m^{2}\)

Step-by-step explanation:

Circumference = 2πr

                         = 2 x 3.14 x 3 (radius = 6/2 = 3)

                         = 18.84 m

Area = π\(r^{2}\)

        = 3.14 x \(3^{2}\)

        = 28.26 \(m^{2}\)

Answer:

Circumference=18.84 m

Area = 28.26

Step-by-step explanation:

The statement(B)The slope of the hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI is true .

The slope of  a line passing through two points A(x₁,y₁) and B(x₂,y₂) is calculated using the formula

slope = (y₂-y₁)/(x₂-x₁)

In  the question ,

given that ΔDEF and ΔGHI are similar ,

and hypotnuse of ΔDEF is DF and hypotnuse of ΔGHI is GI ,

we can see that the coordinates of D = (-9,6) , F = (-6,4) and

coordinates of G = (-3,2) and I = (6,-4)

Using slope formula for line DF

we get ,

slope = (4-6)/(-6 - (-9))

= -2/(-6+9)

= -2/3        ...(i)

Using slope formula for line GI

we get ,

slope = (-4-2)/(6 - (-3))

= -6/(6+3)

= -6/9

In simpler form

= -2/3         ...(ii)

From equation (i) and equation (ii) , we can see that slope of hypotnuse of both the triangles are equal .

Therefore , only statement(B)The slope of the hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI ,  is true .

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Answer:

1) Linear pair postulate

2) Definition of supplementary angles

Step-by-step explanation:

The required blank space will be filled by a linear pair postulate and definition of supplementary angles.

GIven that,
Proof of measures of angles is given to fill the blank statement.

The angle can be defined as the one line inclined over another line.

Here,
After the step
∠ABD and ∠DBC both are supplymentary angles implies,
linear pair postulate [blank 1]
And,
ABD + ∠DBC = 180
by definition of supplementary angles, the sum is 180. [blank 2]

Thus, the required blank space will be filled by a linear pair postulate and definition of supplementary angles.

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Answer:

2

Step-by-step explanation:

Answer:

9p-25

Step-by-step explanation:

always do parentheses first

-5(-10p + 8p -5)-p

multiply negative with negative gives positive

-5(-2p-5)-p

variable always has a 1 in front

10p-1p-25

9p-25

Answer:

Step-by-step explanation:

Answer 1

Answer 2

Area = 1/2 * 6 * 11

\(x^3=216\\x=\sqrt[3]{216}=6\)

This is a simple example. You (should) know that \(6^3=216\).

But you can solve it like this:

\(\begin{array}{r|l}216&2\\108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}\)

Therefore

\(\sqrt[3]{216}=\sqrt[3]{2^3\cdot3^3}=\sqrt[3]{2^3}\cdot\sqrt[3]{3^3}=2\cdot3=6\)

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the value of x in the equation \(\pmb{x^3=216}\).

\(\triangle~\fbox{\bf{KEY:}}\)

Is x by itself? No, it's cubed, or multiplied times itself three times.

So we need to use the opposite operation.

The opposite of cubing is taking the cube root, so we take the cube root of both sides:

\(\star~\large\pmb{\sqrt[3]{x^3}=\sqrt[3]{216}}\)

On the left, the cube root sign and the cube cancel, because they're opposite, and we're left with x.

On the right, we take the cube root of 216, which gives us:

\(\star~\large\pmb{x=6}\)

Hope it helps you out! :D

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Answer:

5-4=12x+x

1=13x

1/13=×