Question 12
7 pt
Marcus bought school supplies for $42.00, not including tax. If the tax rate was 8.5%,
what was the total cost of the school supplies, including tax?

Answer:

2 is the correct answer

Answer:

The answer is below

Step-by-step explanation:

Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.

The distance between two points on the coordinate plane is given as:

[tex]Distance=\sqrt{(x_2-x_1}^2+(y_2-y_1)^2 \\\\Therefore\ in\ triangle\ PQR:\\\\|QR|=\sqrt{(-2-(-2))^2+(4-0)^2}=4\\\\|PQ|=\sqrt{(-2-4)^2+(0-4)^2}=\sqrt{52}=2\sqrt{13} \\\\|PR|=\sqrt{(-2-4)^2+(4-4)^2}=6[/tex]

In triangle STU:

[tex]|ST|=\sqrt{(-1-2)^2+(-2-(-4))^2}=\sqrt{13}\\\\|SU|=\sqrt{(-1-2)^2+(-4-(-4))^2} =3\\\\|TU|=\sqrt{(-1-(-1))^2+(-4-(-2))^2}=2[/tex]

|QR| / |TU| = 4/2 = 2

|PR| / |SU| = 6/3 = 2

|PQ| / |ST| = 2√13 / √13 = 2

Hence:

|QR| / |TU| = |PR| / |SU| = |PQ| / |ST|

Therefore, △PQR and △STU are similar triangles since the ratio of their sides are in the same proportion.

Similar triangles may or may not be congruent

Triangles PQR and STU are similar by SSS theorem.

The vertices of triangle PQR are given as:

[tex]P= (4, 4)[/tex]

[tex]Q= (-2, 0)[/tex]

[tex]R = (-2, 4)[/tex]

The vertices of triangle STU are given as:

[tex]S = (2, -4)[/tex]

[tex]T = (-1, -2)[/tex]

[tex]U =(-1, -4)[/tex]

Start by calculating the side lengths of the two triangles, using the following distance formula

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

For triangle PQR, we have:

[tex]PQ = \sqrt{(4 --2)^2 + (4 -0)^2} = \sqrt{52}[/tex]

[tex]PR = \sqrt{(4 --2)^2 + (4 -4)^2} = 6[/tex]

[tex]QR = \sqrt{(-2 --2)^2 + (0 -4)^2} = 4[/tex]

For triangle STU, we have:

[tex]ST= \sqrt{(2 --1)^2 + (-4 --2)^2} = \sqrt{13}[/tex]

[tex]SU= \sqrt{(2 --1)^2 + (-4 --4)^2} = 3[/tex]

[tex]TU= \sqrt{(-1 --1)^2 + (-2 --4)^2} = 2[/tex]

Check if the side lengths of both triangles are similar, by dividing corresponding sides

[tex]k = \frac{PQ}{ST} = \frac{\sqrt{52}}{\sqrt{13}} = 2[/tex]

[tex]k = \frac{PR}{SU} = \frac{6}{3} = 2[/tex]

[tex]k = \frac{QR}{TU} = \frac{4}{2} = 2[/tex]

Because the scale factors of the side lengths are the same, then both triangles are similar by SSS theorem.

Read more about similar triangles at:

https://brainly.com/question/8691470

Answer:

Rs. 3923.08

Step-by-step explanation:

First principal invested = Rs. 10000

Interest rate = 5%

The interest is compounded yearly.

Time = 1 year

1 year compound interest is equal to simple interest.

Formula for simple interest:

[tex]SI = \dfrac{PRT}{100}[/tex]

Interest on first sum = [tex]\frac{10000\times 5\times 1}{100} = Rs\ 500[/tex]

Another sum is on fixed deposit 8% compounded half yearly.

Let the sum = Rs [tex]x[/tex]

Formula for compound interest is given as:

[tex]CI = P(1+\frac{R}{100})^T - P[/tex]

It is compounded half - yearly, therefore T = 2

[tex]CI = x (1+\frac{8}{100})^2 - x\\\Rightarrow CI = x(1.08)^2-x = 0.1664x[/tex]

As per question statement:

[tex]0.1664x - 500 = 152.80\\\Rightarrow x = \dfrac{652.80}{0.1664} = Rs\ 3823.08[/tex]

9514 1404 393

Answer:

  25

Step-by-step explanation:

As always, you identify the possible relationships between the given values. Make use of those to find the unknown. Then use that value as required to answer the question(s) posed.

The triangle is isosceles, so AB = AC.

  AB = AC

  4x +1 = 2x +23

  2x = 22 . . . . . . . . . subtract (2x+1)

  x = 11

With this value of x, we can find BC.

  BC = 3x -8

  BC = 3×11 -8

  BC = 25 . . . . units

Answer:

379.94

Step-by-step explanation:

area of a circle is, pi times radius powered by 2, with this in mind-

r= 11, pi=3.14

3.14(11)^2

3.14(121)

=379.94

Answer:

2y + 4z = x

Step-by-step explanation:

Given

[tex]x = -4[/tex]

[tex]y = -8[/tex]

[tex]z = 3[/tex]

Required

Write an equation that which is true for the above parameters

This question will be answered using trial by error method and the solution is not limited to one equation.

One equation that matches the values above is:.

[tex]2y + 4z = x[/tex]

To check:

Substitute the values of x, y and z in the above equation.

[tex]2y + 4z = x[/tex]

[tex]2 * -8 + 4 * 3 = -4[/tex]

[tex]-16 + 12 = -4[/tex]

[tex]-4 = -4[/tex]

Hence,

Because both sides of the equation are one and the same (-4), [tex]2y + 4z = x[/tex] is true for the above values of x, y and z.

Answer:

Divide the percentage by 100 to get a decimal number. Use that number as the numerator (top) of a fraction. Put a 1 in the denominator (bottom) of the fraction. Convert the decimal to a whole number: Count how many places are to the right of the decimal.

Answer:

[tex]20[/tex]

Step-by-step explanation:

Let [tex]x[/tex] = games played in total

From the fact that [tex]15\%[/tex] of the games the team played is equivalent to [tex]3[/tex] games, we can write:

[tex]15\%x = 3[/tex]

[tex]x=3\div 15\%[/tex]

[tex]=20[/tex]

∴ Lola's hockey team played a total of 20 games.

Hope this helps :)

Answer:

(a) The zeroes of f(x) are rational numbers

(b) The smallest integer value of a is 3

Step-by-step explanation:

In the quadratic function f(x) = ax² + bx + c, we can know the number and the types of its roots using the discriminant  Δ, where Δ = b² - 4ac

Note: In the first case if Δ is a perfect square number then the zeroes are rational, if not then the zeroes are irrational

(a)

∵ The equation function is f(x) = ax² + 11x + 12

∵ a = 2

∴ a = 2, b = 11 and c = 12

→ Substitute them in the rule of Δ

∵ Δ = (11)² - 4(2)(12) = 121 - 96

∴ Δ = 25

∵ Δ > 0

∴ f(x) has two different real zeroes

∵ 25 is a perfect square number

→ That means the zeroes of the function are rational numbers

∴ The zeroes of f(x) are rational numbers

(b)

∵ f(x) ha imaginary zeroes

→ By using the third rule above

∴ Δ < 0

∵ a = a, b = 11 and c = 12

→ Substitute them in the rule of Δ

∴ (11)² - 4(a)(12) < 0

∴ 121 - 48a < 0

→ Add 48a to both sides

∵ 121 - 48a + 48a < 0 + 48a

∴ 121 < 48a

→ Divide both sides by 48

∴ 2.52083 < a

∴ a > 2.52083

∵ The smallest integer greater than 2.52083 is 3

∴ The smallest integer value of a is 3

Answer:

463mi

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Speed = 25miles per hour

Step-by-step explanation:

Represent the time with x and the distance with y

So, from the attachment; we have the following details:

[tex](x_1,y_1) = (0.5,12.5)[/tex]

[tex](x_2,y_2) = (1,25)[/tex]

[tex](x_3,y_3) = (1.5,37.5)[/tex]

Required

Determine the constant speed

Because the train travelled at a constant speed, the speed can be calculated using:

[tex]Speed = \frac{y_3}{x_3}=\frac{y_2}{x_2}=\frac{y_1}{x_1}[/tex]

[tex]Speed = \frac{12.5}{0.5}=\frac{25}{1}=\frac{37.5}{1.5}[/tex]

[tex]Speed = 25=25=25[/tex]

Notice that the result of each division is the same.

Hence, the constant speed is:

Speed = 25miles per hour

Answer:

9

Step-by-step explanation:

18/2=9

Answer:

1 1/2 quarts per hour

Step-by-step explanation:

To do this you would divide 3/4 by 1/2 to do divide you flip 1/2 to 2/1 then multiply.

3/4*2/1=6/4 which is also equal to 1.5 quarts of paint per hour.

Answer:

54 ounces

Step-by-step explanation:

A box of granola weighs 24 ounces and a box of bran flacks weighs 6/8 as much as the ronal

The number of ounces of the bran flakes = 6/8 of the box of the granola

= 6/8 × 24 ounces

= 18 ounces

A box of Corn Pops weighs 1 1/8 as much as the granola

Hence, the number of ounces of the box of corn pops =

1 1/8 of the granola box

= 9/8 × 24 ounces

= 27 ounces

The least number of ounces found in either box or ronal bran flakes or Corn Pops is calculated as:

We solve using LCM Method

Multiples of 18:

18, 36, 54, 72, 90

Multiples of 27:

27, 54, 81, 108

Therefore,

LCM(18, 27) = 54

The least number of ounces found in either box or ronal bran flakes or Corn Pops is 54 ounces

Answer:

The second one .......

Amino acids

Step-by-step explanation:

In a DNA molecule Your going to find what's called, Nucleotides, Nucleotides contain phosphate group, a sugar group, and a nitrogen base.

Answer:

-9 feet per second

Step-by-step explanation:

Answer:

can you state what point I is?

Answer:

X=13

Step-by-step explanation:

Answer:

The answer is 30 V=whl=3·2·5=30

Step-by-step explanation:

Answer:

$5.25

Step-by-step explanation:

23.75-2.75= is the price of four cheeseburgers, which is 21. 21/4 is the price of one. So its 5.25

Answer:

i hope this helps you

7.4+(-2)

28-2

26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

Plug 4 in for y and -2 in for z giving you: 7(4)+(-2). 7*4=28 giving you 28+(-2). the portion +(-2) is the same as -2. This gives you 28-2 which is 26.

Answer:

The answer is A

Step-by-step explanation:

There are opposite angles

Answer:

No because if you set them equivelent to each other you get 12=0

Step-by-step explanation:

1/4(12x + 24) - 9x = -6(x + 1)

3x + 6 - 9x = -6x - 6

-6x + 6 = -6x - 6

12 = 0x

I hope this helps