(System of inequality word problem.)

Frankie is saving his money to buy the new Nintendo Switch. The switch is on sale for $300. He already has $215 saved up and his mother tells him she will pay him $7 for each extra chore he completes around the house. What is the minimum number of chores he must complete to have enough money for the Switch?

A. 12 chores
B. 14 chores
C. 13 chores
D. 11 chores

Answer:

Step-by-step explanation:

2x + 3y = 2

x = 2 - 3y /2

x + y = 0

substitute the value of x

[tex]\frac{2 \\- 3y}{2}[/tex] + y = 0

2 - 3y + 2y = 0

2 = y

again,substitute the value of y

x = 2 - 3y / 2

=2 - 3*2 / 2

=2 - 6 / 2

=-2

Answer:

x = 2, y = -2

Step-by-step explanation:

This is an alternate way. You can also solve simultaneous equations using matrices. First, rewrite the simultaneous equations in matrix form.

[tex]\displaystyle \large{\left[\begin{array}{ccc}2&3\\1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}2\\0\end{array}\right]}[/tex]

Let:

[tex]\displaystyle \large{A= \left[\begin{array}{ccc}2&3\\1&1\end{array}\right]}\\\displaystyle \large{X = \left[\begin{array}{ccc}x\\y\end{array}\right]}\\\displaystyle \large{B =\left[\begin{array}{ccc}2\\0\end{array}\right]}[/tex]

So now we have [tex]\displaystyle \large{AX = B}[/tex] and we have to solve for X which:

[tex]\displaystyle \large{A^{-1}AX = A^{-1}B}\\\displaystyle \large{X = A^{-1} B}[/tex]

Where:

[tex]\displaystyle \large{A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]}[/tex]

**ad-bc is determinant of 2*2 matrices and shortened as det(var) or |var|**

Therefore, from A:

Find detA:

[tex]\displaystyle \large{\det A = |A| = ad-bc = 2(1)-3(1) = 2-3 = -1}[/tex]

Therefore, detA = -1. Hence:

[tex]\displaystyle \large{A^{-1}=-1\left[\begin{array}{ccc}1&-3\\-1&2\end{array}\right]}[/tex]

And [tex]\displaystyle \large{X = A^{-1}B}[/tex]:

[tex]\displaystyle \large{X = -1\left[\begin{array}{ccc}1&-3\\-1&2\end{array}\right] \left[\begin{array}{ccc}2\\0\end{array}\right] }[/tex]

Evaluate the matrices:

[tex]\displaystyle \large{X = -1\left[\begin{array}{ccc}1 \cdot 2-3 \cdot 0\\-1 \cdot 2+2\cdot 0\end{array}\right] }\\\displaystyle \large{X = -1\left[\begin{array}{ccc}2-0\\-2+0\end{array}\right] }\\\displaystyle \large{X = -1\left[\begin{array}{ccc}2\\-2\end{array}\right] }\\\displaystyle \large{X = \left[\begin{array}{ccc}-2\\2\end{array}\right] }\\\displaystyle \large{\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-2\\2\end{array}\right] }[/tex]

Therefore, x = -2 and y = 2.

Answer:

63.7°

Step-by-step explanation:

supplementary_interier angle 180_116.3=63.7

Answer:

(B) 10

Step-by-step explanation:

x = 15

y = 3

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

9(5) - x / y =

The value of the given expression [tex]\dfrac{9(5)-x}{y}[/tex] is 10 when x = 15 and y = 3. So, the correct answer is (b) 10.

An expression is a combination of numbers, variables, mathematical operations, and many more.

To obtain the value of the given expression, the values of x and y will be inserted in the expression and the concepts of PEMDAS will be used.

Let's assume that the given expression is as follows:

[tex]z = \dfrac{9(5)-x}{y}[/tex]

Substitute x = 15 and y = 3 in the given expression:

[tex]z = \dfrac{9(5)-x}{y}\\z = \dfrac{9(5)-15}{3}\\z = \dfrac{45-15}{3}\\z = \dfrac{30}{3}\\z = 10[/tex]

Therefore, option (d) is correct, i.e., for x = 15 and y = 3, the value of the given expression is 10.

Learn more about Expressions here:

https://brainly.com/question/34132400

#SPJ3

Answer:

44.58

Step-by-step explanation:

[tex]v=\frac{4}{3}\pi r^{3}\\ given r= 2.2\\\pi =3.14\\hence:v=\frac{4}{3} (3.14)(2.2)^3=44.58[/tex]

Answer:

Step-by-step explanation:

first of all you need to do is make a lemonade stand and make the lemonade taiste good then you can sell it for 15 dollars which is a good price to get you started with your life

Answer:

1. (4,5)  2. D  3. J  4.D  5. 64.8 oz

Step-by-step explanation:

math

Answer:

Angles in a triangle adds to 180

Step-by-step explanation:

Hope this helps!

Answer:

17

Step-by-step explanation:

Seeing that traingle ABC is = to triangle DEF.

It means that the angles are equal too.

So you would equate them to each other.

Hence 5X+2=87

5X=87-2

5X=85 (divide by 5)

X=17

Hope that helps :)

Answer: 25.5 feet

Step-by-step explanation:

if each hat requires 30 inches of material, then 3 hats will require 3(30) = 90 inches.

if each scarf requires 2 yds of material, then 3 scarfs will need 3(2) = 6 yds.

The question wants us to give our answer in feet, so we will be converting:

Using 12in = 1ft:

90 in = 90/12 feet = 7.5 feet

Using 1 yd = 3 ft:

6 yds = 6(3) = 18 feet.

Now that the units are the same, we can add them up to get our answer:

7.5 + 18 = 25.5 feet

So Terry will need 25.5 feet of material to make 3 sets of hat and scarves.

Answer:

Mari watch died of eating Boba drinks

Answer:

3.

Step-by-step explanation:

Since angle DBC and DBA are supplementary (they add up to a straight angle-180 degrees) we can subtract 121 from 180 and find out the answer of  angle DBA.

Answer:

3.............

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

Answer:

40 minutes later

Step-by-step explanation:

6:15 + 40 minutes = 6:55

Answer:

The number of students that prefer to do homework from the group of all students

Step-by-step explanation:

The question says that the ratio between the student who prefer doing homework before school and the students who prefer doing homework after school is 7:15.

That means 7 students prefer doing homework before school and 15 students prefer doing after school.

In this scenario, the total number of students is 7 + 15 i.e. 22

So the percentage 7/22 is the number of students that prefer to do homework before school from the group of all students

Answer:

600,000

Step-by-step explanation:

Your answer would be 600,000 because in the hundred thousands place there is a 6.

And that 6 in the hundred thousands place is asking the ten thousands place for help also the digit in the ten thousands place is a 1.

So if you know the rule the 6 can't round up because the 1 is below 4./the rule is 4 and below keep it low 5 or more give it one more.

Ok so the 1 is below 4 and can't bring 6 up so 6 has to stay in it's lane at 600,000

Hope this helps have a great afternoon:)

Answer:

Its 600000

Step-by-step explanation:

Hundred thousand refers to 6 numbers so we look at the number after 6 and its less than 5 so we round it back to 0

Answer:

4x+13

Step-by-step explanation:

Answer:

7x+15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distance = d

d² = [1 - (-3)]² + [y - (-6)]²

5² = 16 + (y + 6)²

25 = 16 + (y + 6)²

(y + 6)² = 25 - 16 = 9

y + 6 = ±3

y = -6 ±3

so

y = -3 or -9

The answer is 40cm in cube 3

Considerando la definición de número complejo, su opuesto, conjugado y afijo, siendo z= -2-2i, se obtiene:

Los números complejos son combinaciones de números reales y números imaginarios. Su representación más común es la suma de una parte real y una parte imaginaria. Al mismo tiempo, la parte imaginaria se divide entre la parte imaginaria y la unidad imaginaria.

Esto es: z= a +bi

donde:

Dado un número complejo z = a+bi, se llama opuesto de z al número -z = -a-bi.

Esto es, el opuesto de un número complejo se calcula cambiando el signo de la parte real y de la parte imaginaria.

Dado un número complejo z = a+bi, se llama conjugado de z al número z = a-bi.

Esto es, el conjugado de un número complejo se obtiene al cambiar el signo de la parte imaginaria.

Los números complejos se representan mediante vectores. Al extremo del vector se le llama afijo del complejo. Esto es, el afijo del número complejo z=a +bi es (a,b)

Considerando las correspondientes definiciones:

Aprende más sobre números complejos:

https://brainly.com/question/5564133

Answer:

4

Step-by-step explanation:

[tex] ln(x) = ln(16) + ln(4) [/tex]

Use the Produxt Rule

[tex] ln(a) + ln(b) = ln(a + b) [/tex]

Remeber that Ln is a log function with base e,

so know we have

[tex]3 ln(x) = ln(64) [/tex]

[tex] ln(a) = ln(b) [/tex]

Only if a=b So we have

x^3=64

x=4

[tex]x = 64[/tex]

Step-by-step explanation:

See the picture for steps

Answer:

Step-by-step explanation:

There will be a +1 becuase the lines y intercept is +1.

We can then take two points on the line and then find the slope through them.

(0,1) and (4,2). 4-0 and 2-1.

4 and 1. The slope is 1/4.

y = mx + b

y = 1/4x + 1

Answer:

[tex]\huge\boxed{\sf 58\ m\²}[/tex]

Step-by-step explanation:

The figure is made up of two rectangles.

Area of the larger rectangle:

Length = 5 m

Width = 10 m

= Length × Width

= 5 × 10

= 50 m²

Area of smaller rectangle:

Length = 4 m

Width = 2 m

= Length × Width

= 4 × 2

= 8 m²

Area of the figure:

= Area of larger rectangle + Area of smaller rectangle

= 50 + 8

= 58 m²

[tex]\rule[225]{225}{2}[/tex]

Answer: 592330

Step-by-step explanation:

Answer:

BFG

Step-by-step explanation:

The segment BF is the diagonal of the top face of the cube (GBCF)

Therefore, it is the hypotenuse of ΔBFG and ΔBFC

See attached diagram for visual of the cube.

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

[tex]u\cdot v=\langle4,-7\rangle\cdot\langle-6,9\rangle=(4*-6)+(-7*9)=-24-63=-87[/tex], so A is correct. Remember to multiply the horizontal components with each other and then add that to the product of the vertical components to get the dot product.

Problem 2

Two vectors are orthogonal if their dot product is 0, which also means that they must be perpendicular to each other, so we can check this:

[tex]u\cdot v=(6*-24)+(-9*36)=-144-324=-468[/tex]

Since the dot product of the two vectors is 0, they aren't orthogonal. Therefore, they are parallel since [tex]v=4u[/tex], making A the best choice.

Problem 3

Recall that the angle between two vectors is [tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})[/tex] where [tex]u\cdot v[/tex] is the dot product of vectors [tex]u[/tex] and [tex]v[/tex] while [tex]||u||[/tex] and [tex]||v||[/tex] are the magnitudes of vectors [tex]u[/tex] and [tex]v[/tex] respectively. If we let [tex]F_1=u[/tex] and [tex]F_2=v[/tex], we can then continue on:

[tex]u\cdot v=(190*128)+(160*-121)=24320+(-19360)=4960[/tex]

[tex]||u||=\sqrt{190^2+160^2}=\sqrt{61700}=10\sqrt{617}[/tex]

[tex]||v||=\sqrt{128^2+(-121)^2}=\sqrt{31025}=5\sqrt{1241}[/tex]

[tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})\\\\\theta=cos^{-1}(\frac{4960}{10\sqrt{617}*5\sqrt{1241}})\\\\\theta\approx83.49^\circ\approx83^\circ[/tex]

Therefore, B is the correct answer

Problem 4

We observe that [tex]u=\langle-8,-9\rangle[/tex] and [tex]v=\langle3,7\rangle[/tex], so [tex]-3(u\cdot v)=-3[(-8*3)+(-9*7)]=-3[-24+(-63)]=-3(-87)=261[/tex]. This means that B is the correct answer.

Problem 5

Recall that the projection of a vector [tex]u[/tex] onto [tex]v[/tex] is [tex]proj_vu=(\frac{u\cdot v}{||v||^2})v[/tex], thus:

[tex]proj_vu=(\frac{u\cdot v}{||v||^2})v\\\\proj_vu=(\frac{(-10*4)+(-3*8)}{\sqrt{4^2+8^2}^2})\langle4,8\rangle\\\\proj_vu=(\frac{-40+(-24)}{\sqrt{80}^2})\langle4,8\rangle\\\\proj_vu=(\frac{-64}{80})\langle4,8\rangle\\\\proj_vu=(-\frac{4}{5})\langle4,8\rangle\\\\proj_vu=\langle-\frac{16}{5},-\frac{32}{5}\rangle[/tex]

Therefore, D is the correct answer