The main goal of a personal budget is to

have income equal expenses

have expenses be greater than income

have income be greater than expenses

create personal savings

Looks like the system is

x + 4y - z = -14

5x + 6y + 3z = 4

-2x + 7y + 2z = -17

or in matrix form,

[tex]\mathbf{Ax} = \mathbf b \iff \begin{bmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -14 \\ 4 \\ -17 \end{bmatrix}[/tex]

Cramer's rule says that

[tex]x_i = \dfrac{\det \mathbf A_i}{\det \mathbf A}[/tex]

where [tex]x_i[/tex] is the solution for i-th variable, and [tex]\mathbf A_i[/tex] is a modified version of [tex]\mathbf A[/tex] with its i-th column replaced by [tex]\mathbf b[/tex].

We have 4 determinants to compute. I'll show the work for det(A) using a cofactor expansion along the first row.

[tex]\det \mathbf A = \begin{vmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{vmatrix}[/tex]

[tex]\det \mathbf A = \begin{vmatrix} 6 & 3 \\ 7 & 2 \end{vmatrix} - 4 \begin{vmatrix} 5 & 3 \\ -2 & 2 \end{vmatrix} - \begin{vmatrix} 5 & 6 \\ -2 & 7 \end{vmatrix}[/tex]

[tex]\det \mathbf A = ((6\times2)-(3\times7)) - 4((5\times2)-(3\times(-2)) - ((5\times7)-(6\times(-2)))[/tex]

[tex]\det\mathbf A = 12 - 21 - 40 - 24 - 35 - 12 = -120[/tex]

The modified matrices and their determinants are

[tex]\mathbf A_1 = \begin{bmatrix} -14 & 4 & -1 \\ 4 & 6 & 3 \\ -17 & 7 & 2\end{bmatrix} \implies \det\mathbf A_1 = -240[/tex]

[tex]\mathbf A_2 = \begin{bmatrix} 1 & -14 & -1 \\ 5 & 4 & 3 \\ -2 & -17 & 2 \end{bmatrix} \implies \det\mathbf A_2 = 360[/tex]

[tex]\mathbf A_3 = \begin{bmatrix} 1 & 4 & -14 \\ 5 & 6 & 4 \\ -2 & 7 & -17 \end{bmatrix} \implies \det\mathbf A_3 = -480[/tex]

Then by Cramer's rule, the solution to the system is

[tex]x = \dfrac{-240}{-120} \implies \boxed{x = 2}[/tex]

[tex]y = \dfrac{360}{-120} \implies \boxed{y = -3}[/tex]

[tex]z = \dfrac{-480}{-120} \implies \boxed{z = 4}[/tex]

Answer:

in photo attached.

Step-by-step explanation:

The volume of a cone with radius of 4x and a height of 21xy² is 352 x³y²

Using the formula:

V=πr²h/3

Where r= radius = 4x

h= height = 21xy∧2

Substitute the values into the equation

V = 22/7 × 4x × 4x × (21 × x × y × y) ÷ 3

V = 22/7 × 16x² × 7xy²

V= 22 × 16x² × xy²

Multiply all through

Volume, V = 352 x³y²

Therefore, the volume of the cone is 352 x³y²

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Answer:

option c I think as the correct answer.

Step-by-step explanation:

hope this helps you.

Answer:

They are both right-angled triangles.

Step-by-step explanation:

The break-even sales price per umbrella if sun cover manufactures the units is $120.99.

This can be done by using the formula:

Break even units = Total fixed cost / (Price - Variable cost)

8573 = 675921/(Price - 42.15)

8573(P - 42.15) = 675921

8573P - 361351.95 = 675921

8573P = 675921 + 361351.95

8573P = 1037273.4

P = 1037273.4/8574

P = $120.99

Therefore, the price is $120.99.

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Answer:

[tex]4\sqrt[3]{307}[/tex] o 26.98398684 en forma decimal

Step-by-step explanation:

Answer:

125.6 in²

Step-by-step explanation:

Area shaded :

Answer:

A

Step-by-step explanation:

height (y-axis) = constant × width (x-axis)

let's look at the point coordinates.

remember, an ordered pair of point coordinates consists of an x value and an associated (typically calculated by a function) y value.

we see that all y values are half of the x values (3 and 1.5, 2 and 1, 7 and 3.5, 8 and 4).

so, the constant in our equation is responsible for returning half of the x value back as the y value.

what constant factor turns a number in half ?

x × c = x/2

c = 1/2

and so, A is the right answer.

This exercise is about creating two-dimensional shapes. The resulting shape is a quadrilateral - Square. See the attached for the lines drawn.

What was noticed about the two lines drawn?

When two lines intersect with one another such that they create a right angle, perpendicularity has occurred and both lines are said to be perpendicular to one another.

Hence:

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Hey there!

[tex] \displaystyle{\orange{\boxed{\bold{\green{d = -5}}}}}[/tex]

[tex] \\ [/tex]

[tex] \displaystyle{ \frac{4}{5}d + 3 = -2 - \frac{1}{5}d} \\ [/tex]

[tex] \hookrightarrow [/tex] Subtract 3 from both sides :

[tex] \\ \displaystyle{ \frac{4}{5}d + 3 \bold{ \red{ - 3} }} = \displaystyle{ - 2 - \frac{1}{5}d \bold{ \red{ - 3}} } \\ \\ \implies \displaystyle{\frac{4}{5}d = - \frac{1}{5}d - 5 } \: \: \: \: [/tex]

[tex] \\ \hookrightarrow [/tex] Add [tex] \frac{1}{5}d [/tex] to both sides :

[tex]\\ \displaystyle{\frac{4}{5}d \: \bold{ \blue{ + \frac{1}{5}d }} = \displaystyle{ - \frac{1}{5}d - 5 \: \bold{ \blue{ + \ \frac{1}{5}d }}}} \\ \\ \implies \displaystyle{\frac{5}{5}d = - 5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \displaystyle{\green{ \boxed{ \orange{{d = - 5}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Therefore, our answer is d = -5

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add [tex]\bf{\frac{1}{5}d }[/tex] on both sides.

[tex]\boldsymbol{\dfrac{4}{5}d+3+\dfrac{1}{5}d=-2 }[/tex]

combine [tex]\bf{\frac{4}{5}d }[/tex] and [tex]\bf{\frac{1}{5}d }[/tex] to get d.

[tex]\boldsymbol{d+3=-2}[/tex]

Subtract 3 from both sides.

[tex]\boldsymbol{d=-2-3}[/tex]

Subtract 3 from −2 to get −5.

[tex]\boxed{\boldsymbol{d=-5}} \ \ \to \ \ \bf{Answer}[/tex]

Let d=-5.

[tex]\sf{\dfrac{4}{5}\times-5+3=-2-\dfrac{1}{5}\times-5 }[/tex]

[tex]\rm{Apply \ this \ rule:\dfrac{a}{b}\times c=\dfrac{ac}{b} }[/tex]

[tex]\sf{\dfrac{4\times-5}{5}+3=-2-\dfrac{1}{5}\times-5 \ \ \to \ \ Multiply \ 4 \ by \ -5 }[/tex]

[tex]\sf{\dfrac{-20}{5}+3=-2-\dfrac{1}{5}\times-5 }[/tex]

[tex]\rm{Move \ the \ negative \ symbol \ to \ the \ left. }[/tex]

[tex]\sf{-\dfrac{20}{5}+3=-2-\dfrac{1}{5}\times-5 \ \ \to \ \ Simplify \ \frac{20}{5} \ to \ 4. }[/tex]

[tex]\sf{-4+3=-2- \dfrac{1}{5}\times-1 }[/tex]

[tex]\rm{Move \ the \ negative \ symbol \ to \ the \ left.}[/tex]

[tex]\sf{-4+3=-2-(-1) \ \ \to \ \ Simplify \ -4+3 \ to \ -1. }[/tex]

[tex]\sf{-1=-2-(-1) \ \ \to \ \ \to \ \ Remove \ parentheses. }[/tex]

[tex]\sf{-1=-2+1 \ \ \to \ \ Simplify \ -2+1 \ to \ -1.}[/tex]

[tex]\sf{-1=-1 \ \to \ Equality \ is \ met.}[/tex]

Checked ✅

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

The ratio between the perimeter of the largest and smallest pentagon is 2.

We know that the pentagons are similar, meaning that the dimensions of one of the pentagons is k times the dimensions of the other.

Because of this, the ratio between the areas is k squared. And because the perimeter depends linearly on the dimensions, the ratio between the perimeters will be equal to k.

So we need to find k, we will have:

[tex]\frac{144 in^2}{36 in^2} = k^2 = 4\\\\k = \sqrt{4} = 2[/tex]

Then we conclude that the ratio between the perimeters is k  =2.

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[tex]~~~~~~k = \dfrac{3n+2}{n+1}\\\\\implies k(n+1) = 3n+2\\\\\implies kn+k=3n+2\\\\\implies kn -3n= 2-k\\\\\implies n(k-3) = 2-k\\\\\implies n = \dfrac{2-k}{k-3}\\\\\implies n = -\dfrac{k-2}{k-3}~~~~~~~~;[k\neq 3][/tex]

Answer:

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.

[tex] \: first the formula of quadratic equation \: = - b ≠ \: \sqrt{ \frac{ \: {b }^{2} - 4ac}{ \: 2a} } [/tex]

let's begin to solve this equation,,,

[tex]ax² + bx + c = 0 \\

ax² + bx + c =0 \\ {x}^{2} + \frac{b}{a} \: + \frac{ {b}^{2} }{2a} = \frac{b2}{a} - \frac{c}{a}

\\ x + \frac{ {b}^{2} }{2a} = - \frac{ {b}^{2} }{2a} - \frac{c}{a} [/tex]

an equation having the maximum power of the variable equal to is called the quadratic equation the general form of quadratic equation is ax² + bx +c =0 where a,b,c are real numbers a ≠0 x is variable •

a quadratic equation can be solved by two method by factorization and by formula

by factorization a quadratic equation can be solved by factorization only when the product AC can be divided into two such part that it had the sum of the difference of the two part is equal to b

[tex]by the formula of quadratic equation can be solved by \ - } [/tex]

[tex]x = \frac{ - b \sqrt{ {b}^{2} - 4ac } }{2a } \\ root \: of \: equation \: {ax}^{2} + bx + c = 0 \\ - b - \sqrt{ \frac{ {b}^{2} - 4ac}{2a} } [/tex]

Answer:

3/7

Step-by-step explanation:

Probability=Number of possible items÷Number of total items.

We will make the possible item 3 because we are looking for the probability whether a boy will be picked.

The number of total items will therefore be: the number of boys + the number of girls; that will be 3+4 =7.

So the probability of picking a boy will be 3/7

THANK YOU.

Answer:

How tall are you

ez clappp

Answer:

they are 10km 32 degrees far from each other

Step-by-step explanation:

scott - 100km - 30 degrees

spork - 110km - 62 degrees

how far = difference between them

as spork's distance and degrees are greater than scott we substract Scott's from spork's

110 - 100 = 10 km

62 - 30 = 32 degrees

they are 10km 32 degrees far from each other

Answer:

A) 24 cm²

Step-by-step explanation:

Area of a triangle formula:

A = 0.5bh

Given:

b = 6

h = 8

Work:

A = 0.5bh

A = 0.5(6)(8)

A = 3(8)

A = 24

[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]

Right answer is option A

24 cm²

Step-by-step explanation:

The area of triangle

a = 6 cm, b = 8 cm, c = 10 cm

He know

[tex] \mathfrak {Area \: of \: triangle = \frac{1}{2} \times base \times height}[/tex]

Here (a) acts like base

while (b) acts like height

Now substituting the values

[tex] \sf \longmapsto Area = \frac{1}{2} \times a \times b \\ \\ \\ \sf \longmapsto Area = \frac{1}{2} \times 6 \times 8 \\ \\ \\ \sf \longmapsto Area = 3 \times 8 \\ \\ \\ \sf \purple{\boxed {\longmapsto Area = 24 \: {cm}^{2} }}[/tex]

The score(s) that will be obtained respectively in an independent-measures design and repeated-measures design are; 1 and 2

There are different ways to carry out an experiment in mathematics. This is because there are various means of research and also ways to interpret the results.

Now, when comparing two treatment conditions, an independent-measures design would always obtain 1 score for each subject. However, when a repeated-measures design is carried out on the same sample, it will obtain 2 scores.

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The system of equations have one solution

The equations are given as:

2x + 2y = 5

3x + 3y = 7

The above equations are distinct linear equations.

This means that they would have one point of intersection, if plotted on a graph

Hence, the system of equations have one solution

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Answer:

3  7/50

Step-by-step explanation:

so you need them to become common denominators

a common multiple they both have would be is 77

6/7 becomes 66/77 and 3/11 becomes 21/77

now we divide

keep the 66/77 as is and flip 21/77 (keep, change, flip)

so now our equation looks like this: 66/77 x 77/21

and your answer is 3.14

but as a fraction it is 157/50 and to simplified it would be 3 7/50 (mixed fraction)

Answer:

I'm not 100% sure about this question but the formula to get that is

(x-1) x 2 =y

Answer:

-4.67

Step-by-step explanation:

first find f^-1(x)

let f(x)=y

y=3x+2

3x=y-2

x=y-2/3

Therefore f^-1(x)=x-2/3

Now f^-1(-12)=-12-2/3

=-14/3

=-4.67

Answer:

simple interest

Step-by-step explanation:

SI = principal x rate x time

The probability that the student selected at random is a freshman is; 29%

From the given table;

Total number of male students = 4 + 6 + 2 + 2 = 14

Number of freshmen students = 4 students

Thus;

Probability that the student selected at random is a freshman is;

P(Freshman | Male) = 4/14 * 100% = 28.57% ≈ 29%

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Answer:

-3y+8z

Step-by-step explanation:

2x-2y+5z-2x-y+3z

you don't need to change their signs just place them accordingly

2x-2x-2y-y+5z+3z

-3y+8z

[tex]~~~~~~~\log_{10} N = 3.8609\\\\\\\implies N = 10^{3.8609} ~~~~~~~~~;[\log_b c =d \implies b^d = c]\\\\\\\implies N \approx 7259[/tex]

The distance of the robot from the charging base is gotten as; 62 cm

From the image attached showing the movement of Kapil's robot, we can use cosine rule to find the value of h which is the distance of the robot from the charging base.

The distance of the robot from the charging base is gotten by;

h = x² + b² - 2xb cos 60

h = 50² + 70² - 2*50*70 * 0.5

h = 62 cm

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Answer:

$17.60

Step-by-step explanation:

20% of $22 is $4.4 - Subtract $4.40 from $22 to calculate the discounted price: $17.60

Hope this helped! :)

Answer:

uh I'm not so sure but

Step-by-step explanation:

it might be 1664