Task 2
Carla has $30 in her piggy bank. Starting this week, Carla decided to save $1.50 per week and her sister
Darla decided to save $3.00 per week.
a) Write an equation to model each of the situations.
b) Will Darla and Carla have the same amount saved at any time? Explain.
c) Graph the equations from Part a to verify your answer from Part b

Step-by-step explanation:

Bro who give 5 point for this type of questions. This question deserve 50 points.

A 5th point that would maintain the function is (11, 31)

Given the following pairs of coordinates

Four of the points are given as (1,3) (2,5), (6, 13), (9,27)

Using the coordinates  (1,3) (2,5), to determine the slope

[tex]Slope=\frac{5-3}{2-1} = \frac{13-5}{6-2}=2\\[/tex]

Let the required coordinate be (x, y) to have:
[tex]2 = \frac{y - 27}{x - 9} \\[/tex]

Since the x coordinate of (9, 27) is greater than 8, hence the best x-coordinate will be 11. Substitute to get the y-coordinate

[tex]2 = \frac{y - 27}{11- 9}\\2(2) = y - 27 \\4 = y - 27\\y=27 + 4\\y=31[/tex]

Hence a 5th point that would maintain the function is (11, 31)

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Answer:

The length of the field = 24.5 yards

The width of the field = 12 yards.

Step-by-step explanation:

If "w" is the width, then the length is 49 - 2w.

The area of the rectangle field = length × width

= w(49 - 2w)

Area =

This a quadratic equation, the vertex of x coordinate is w

w =

Here a = -2 and b = 49

w = .

So width of the field is 12.25 yards.

The length of the filed = 49 - 2(12.25) = 24.5

Area = 12.25 × 24.5 = 300.125 square yards.

The field has an area of 294.

Therefore, the length must be 24.5 yards and width must be 12 yards.

24.5 × 12 =294 square yards.

Therefore, the length of the field = 24.5 yards

the width of the field = 12 yards.

Answer:

let

custard pie be x

Step-by-step explanation:

1/7 x = 185

x=185× 7

x=1395

1/8 of x= 1395/8

1/8 of x=174.3

1/4 of x = 1395/4

=348.75

1/6 of x =1395/6

=232.5

Answer:

exact: 1.5
rounded: 2

Step-by-step explanation:

Using division 18/12 we get 1.5 but you cant have half a person so we need a whole number which is 1

The rate at which customers were entering the store is approximately 2 (exact 2/3) customers per minute.

Here, we have to find the rate at which customers were entering the store in customers per minute, we need to divide the total number of customers by the total time in minutes.

Given:

Total customers = 12

Total time = 18 minutes

Rate = Total customers / Total time

Rate = 12 / 18

Rate = 2/3

so, we get,

exact: 1.5

rounded: 2

So, the rate at which customers were entering the store is approximately 2 customers per minute.

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#SPJ3

Answer:

131

Step-by-step explanation:

When we attempt to find the square root of 5607, we get a remainder of 131. (5607=74^2 + 131) That means 5607-131 is a perfect square. (Which is 5476=74^2)    

Consider the given quadratic equation that we have :

[tex]{:\implies \quad \sf -5x^{2}+5=-2x}[/tex]

Multiplying both sides by -1 will yield ;

[tex]{:\implies \quad \sf 5x^{2}-5=2x}[/tex]

Write the above quadratic equation in the form of standard quadratic equation ax² + bx + c = 0 ,

[tex]{:\implies \quad \sf 5x^{2}-2x-5=0}[/tex]

Now , comparing this with the standard form of quadratic equation we will get a = 5 , b = -2 , c = -5 . So now , Discriminant (D) = (-2)² - 4 × 5 × -5 = 4 + 100 = 104

Now , by the quadratic formula ;

[tex]{:\implies \quad \sf x=\dfrac{-(-2)\pm \sqrt{104}}{2\times 5}}[/tex]

[tex]{:\implies \quad \sf x=\dfrac{2\pm 2\sqrt{26}}{2\times 5}}[/tex]

[tex]{:\implies \quad \sf x=\dfrac{\cancel{2}(1\pm \sqrt{26})}{\cancel{2}\times 5}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{x=\dfrac{1\pm \sqrt{26}}{5}}}}[/tex]

For any quadratic equation of the form ax² + bx + c , the Discriminant (D) is given by D = b² - 4ac , and the root [tex]\bf x[/tex] of the quadratic equation is given by the quadratic formula as

Answer:

That its a problem there u go

Step-by-step explanation:

Answer:

Line D

Step-by-step explanation:

Two points that passes through line D :  (0,-2) & ( -4 , 0)

[tex]Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\dfrac{0-[-2]}{-4-0}\\\\\\=\dfrac{0+2}{-4}\\\\\\=\dfrac{2}{-4}\\\\\\=\dfrac{-1}{2}[/tex]

Answer:

  (b)  y -5 = 3/4(x -6)

Step-by-step explanation:

The point-slope form of the equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Your graph has two points marked: (-2, -1) and (6, 5). Even if you don't know the slope, these tell you the form of the equation will be ...

  y +1 = m(x +2) . . . . no match

  y -5 = m(x -6) . . . . matches choice B

__

If you like, you can figure out the slope to be ...

  m = (y2 -y1)/(x2 -x1)

  m = (5 -(-1))/(6 -(-2)) = 6/8 = 3/4

All the answer choices agree that this is the slope of the line.

The vertical distance from the ground to your eye is 10.9 feet and the height of the tree is 20.5 feet.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse² = Adjacent² + Opposite²

From the diagram, let d represent the horizontal distance, hence:

d² = 9.2² + 4.8²

d = 10.9 feet

Let h represent the height of the tree, hence:

h / 10.9 = 10.9 / 5.8

h = 20.5 feet

The vertical distance from the ground to your eye is 10.9 feet and the height of the tree is 20.5 feet.

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Answer:

The answer to this is option C: $12,794.36

Step-by-step explanation:

I just completed the test and this was the corrected answer.

The total cost of an item bought at a negotiated price of $14,380 is $12495.36.

Item bought at a negotiated price of $14,380, a $2,700 trade-in allowance,

A sales tax of 7.2 percent, and a $79  registration fee.

Let us find the cost of the item after 7.2% of sales tax.

A cost is an expenditure required to produce or sell a product or get an asset ready for normal use.

The cost of an item after 7.2% of sales tax will be equal to 15640 plus 7.2% of 15640.

The cost of items after sales tax

[tex]=14,380+(\frac{7.2}{100}\times 14,380)[/tex]

[tex]=14,380+(0.072 \times 14,380)[/tex]

[tex]=15415.36[/tex]

Therefore the cost of an item after 7.2% of sales tax will be 15415.36

Now let us add the registration fee to the cost of the item.

The cost after registration fees is to the cost of items

=15415.36+79

=15495.36

Now let us subtract $2700 trade allowance to find the total cost of the item.

=15495.36- 2700

=12795.36

Therefore the total cost is $12495.36.

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Answer:

63.7°

Step-by-step explanation:

supplementary_interier angle 180_116.3=63.7

Step-by-step explanation:

there is an official formula for this. this can be truly found very easily on the internet ...

the formula for the sum of all angles in a regular polygon with n sides or vertices is

(n-2)×180

so, since an octagon has 8 sides and vertices, this gives us

(8-2)×180 = 6 × 180 = 1080°

that's it ...

Answer:

(8-2)×180 = 6 × 180 = 1080°

Step-by-step explanation:

hope this help

Answer:

1920

Step-by-step explanation:

64 x 5/6

Multpying each side by the LCM which is 6

u will get (64 x 6) x 5

384 x5

1920

Answer:

D : -14

Step-by-step explanation:

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

7(-2) = x

-14 = x

x = -14

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

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:

I am not sure but the answer may be 36 w

Answer:

A.1600

Step-by-step explanation:

I hope its help keep safe

Answer:

40 minutes later

Step-by-step explanation:

6:15 + 40 minutes = 6:55

Answer:

The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years

[tex]\fbox{Answer ~}[/tex]

Here ,

[tex]\bold\purple{3x + 12 + 7 = - 5x - 5} \\\\\bold{3x + 19 = - 5x - 5}[/tex]

gather and solve the like terms together ,

[tex]\bold{3x + 5x = - 5 - 19} \\\\ \bold{8x = - 24} \\\\\bold{ x = \cancel{ \frac{ - 24}{8} }} \\ \\\bold\red{ x = - 3}[/tex]

hope helpful~

Answer:

Step-by-step explanation:

f(x) = 2x - 5

When x = -2,

     f(-2) = 2*(-2) - 5 = - 4-5 =  (-9)

When x = 0,

f(0) = 2*0 - 5 = -5

When x = 5,

   f(5) = 2*5 - 5 = 10 - 5 = 5

x          -2           0             5

y          -9           -5            5

For the triangle, the following statements are correct: The third angle measures 50° and all sides have different lengths.

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angled triangle.

Let x represent the third angle. The other angles measures of 100° and 30°. Hence:

x + 100 + 30 = 180° (sum of angles in a triangle)

x = 50°

Since the angles are different, hence all the sides have different lengths.

The third angle measures 50° and all sides have different lengths.

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!Answer:

Mrs. Thomas put 1/4 icing on the remaining cupcakes

Step-by-step explanation

Step-by-step explanation:

[tex]2 ln(3) = ln(x - 4) [/tex]

For logarithms, this is a property

[tex] ln(x {}^{n} ) = n ln(x) [/tex]

So we have

[tex] ln( {3}^{2} ) = ln(x - 4) [/tex]

[tex] ln(9) = ln(x - 4) [/tex]

If

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

a=b

So

[tex]9 = x - 4[/tex]

[tex]13 = x[/tex]

The length of the missing side of the triangle is 129.96

Right angle triangle are triangle that has one of its sides as 90 degrees. The sides can be found using Pythagoras theorem. Therefore,

c² = a² + b²

where

c = hypotenuse

a and b are the other legs.

Therefore,

19² - 15.2² = a²

a = 361 - 231.04

a = 129.96

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Answer:

[tex]\frac{20r^5}{c}[/tex]

Step-by-step explanation:

[tex]4c^{4}[/tex]·[tex]5c^{-5} r^{5}[/tex]

=[tex]4c^{4}[/tex]·[tex]\frac{5 r^{5}}{c^{5} }[/tex]

=[tex]\frac{20c^{4}r^{5} }{c^5}[/tex]

=[tex]\frac{c^4}{c^4} \frac{20r^5}{c}[/tex]

=[tex]\frac{20r^5}{c}[/tex] or =[tex]20c^{-1}r^5[/tex]