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Firlakuza [10]
3 years ago
15

What is the distance between the points (4,5) and (10,13) on a coordinate plane?

Mathematics
1 answer:
Readme [11.4K]3 years ago
7 0
The distacne between the points (x1,y1) and (x2,y2) is
D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
so the distance between (4,5) and (10,13) is
well, first
x1=4
y1=5
x2=10
y2=13
so

D=\sqrt{(10-4)^2+(13-5)^2}
D=\sqrt{(6)^2+(8)^2}
D=\sqrt{36+64}
D=√100
D=10
the distance is 10 units
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Danika signs up to work for 3 1/2 hours at the science fair. If each work shift is 3/4 hour, how many shifts will Danika work?
forsale [732]

namely, how many times does 3/4 go into 3½?  Let's firstly convert the mixed fraction to improper fraction.

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5 0
3 years ago
Read 2 more answers
5u^2 + 6 = -13u please help
Komok [63]

Answer:

u = -2, -3/5

General Formulas and Concepts:

<u>Algebra I</u>

  • Standard Form: ax² + bx + c = 0
  • Factoring
  • Finding roots

Step-by-step explanation:

<u>Step 1: Define equation</u>

5u² + 6 = -13u

<u>Step 2: Solve for </u><em><u>u</u></em>

  1. Rewrite:                    5u² + 13u + 6 = 0
  2. Factor:                      (u + 2)(5u + 3) = 0
  3. Find roots:                u = -2, -3/5
5 0
3 years ago
A rectangle has perimeter 28cm. Its area is 42sq.cm. Determine the dimensions of the rectangle. Include a diagram in your soluti
yawa3891 [41]

The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

Perimeter=28cm

Area= 42 cm²

If the perimeter is the sum of all sides of the rectangle, you have:

Perimeter= 2b+2h=28

If the area of the rectangle is 42cm², you have:

Area=bh=42 cm²

You can write a system of linear equations.

2b+2h=28 (1)

bh=42 (2)

From equation 2, you have  b=\frac{42}{h}. Then, you can replace it in equation 1.

2*\frac{42}{h}+2h=28 \\ \\ 84+2h^2=28h\\ \\ 2h^2-28h+84=0 \; dividing\; by\; 2\\ \\ h^2-14h+42=0

Now, you should solve the quadratic equation.

h_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:42}}{2\cdot \:1}

h_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{7}}{2\cdot \:1}

h_1=\frac{-\left(-14\right)+2\sqrt{7}}{2\cdot \:1}=7+\sqrt{7}=9.65 cm

h_2=\frac{-\left(-14\right)-2\sqrt{7}}{2\cdot \:1}=7-\sqrt{7}=4.35cm

If h1=9.65 cm, then b_1=\frac{42}{9.65} =4.35 cm, and if  h2=4.35 cm, then b_1=\frac{42}{4.35} =9.65 cm.

Read more about the quadratic function here:

brainly.com/question/1497716

#SPJ1

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2 years ago
two classmates have decided to read all the volumes in a popular series of books. Katie has already read 4 volumes and will cont
scoray [572]
To solve this we can make it into an equation, which looks like this

y = 2x (for Rebecca)
y = x + 10 (for Alice)

The we subtract one equation from the other to solve

0 = x - 10
10 = x
x = 10

Now we replace x in whichever equation and we get 20

So, each girl will read 20 books for them to be at the same book.

Hope this helps, remember that Jesus loves you
5 0
3 years ago
Macy is painting a design that contains two repeating patterns. One pattern repeats every 8 inches. The other repeats every 12 i
spayn [35]

Answer:

8-inch pattern is fully printed 28 times.

12-inch pattern is fully printed 19 times.

Patterns start at the same place 9 times

Step-by-step explanation:

1. 19 feet is 228 inches.

2. 8-inch pattern is fully printed 28 times.

3. 12-inch pattern is fully printed 19 times.

4. 8-inch patterns starts at`0,8,16,24,32,40,48...

5. 12-inch pattern starts at 0,12,24,48...

6. As you see they start at the same place after 24 inches.

7. 228/24=9.5, => They start at the same place 9 times.

3 0
4 years ago
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