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Wittaler [7]
3 years ago
6

The ratio of girls to boys in a student basketball league is 5:6. Juan says that there must be exactly 11 students in the league

. Is Juan's statement correct? Explain your answer.
Mathematics
1 answer:
Nikitich [7]3 years ago
4 0

Answer:

She is correct.

Step-by-step explanation:

5:6 means that you add 5 + 6 = 11 which means that the answer is 11.

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y = 2x squared + 5x -3 can be written in the form y= 2( x+a) squared + b . Find the value of a and the value of b.
Elan Coil [88]

General vertex form:

y = m(x − a)² + b  \: with  \: vertex \:  at \:  (a, b)

Given :

y = 2x² + 5x  - 3

Extract "spread factor" m

y = 2( x² +  \frac{5}{2} x) - 3

Complete the square

y = 2(x²  +  \frac{5}{2}x + ( \frac{5}{4})²) - 3

- 2( \frac{5}{4})²

Write as a squared binomial and simplify the constant

y = 2(x +  \frac{5}{4})² - 6 \frac{1}{8}

Re-write to match signs of standard general form:

y = 2(x - ( -  \frac{5}{4}))² \:  + ( - 6 \frac{1}{8})

3 0
2 years ago
Which triangle congruence postulates can be used to prove that Triangle ABD is congruent to Triangle CDB in Rectangle ABCD?
kramer

Answer:

SSS, SAS, ASA, AAS, HL

Step-by-step explanation:

1. SSS (side side side) says if 3 sides of one triangle are congruent to 3 sides of another triangle, then the 2 triangles are congruent.

2. SAS (side angle side) says if 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent.

3. ASA (angle side angle) says if 2 angles and the included side of a triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent.

4. AAS (angle angle side) says if 2 angles and the none included side of one triangle are congruent to the corresponding parts of another triangle, then the 2 triangles are congruent.

5 HL (hypotenuse leg) says if 2 right triangles that have a congruent hypotenuse and a corresponding congruent leg, then the 2 triangles are congruent.

Because it is a rectangle, the sides are equal, and they share the same hypotenuse.

4 0
2 years ago
Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of bottles
kirza4 [7]

Answer:

The equation for this should be 1.49x + 1.25y = 100

Barbara needed to find the total of iced teas AND the total of water bottles that sells.

Step-by-step explanation:

7 0
3 years ago
Peter has built a gazebo, whose shape is a regular heptagon, with a side length of $1$ unit. He has also built a pathway around
Sholpan [36]

Answer:

Area of pathway = 10.375 unit²

Step-by-step explanation:

Given - Peter has built a gazebo, whose shape is a regular heptagon, with

             a side length of 1 unit. He has also built a pathway around the

             gazebo, of constant width 1 unit, as shown below.

To find -  Find the area of the pathway.

Proof -

Central angle = \frac{360}{7} = 51.43°

Now,

Central angle / 2 = \frac{360}{14} = 25.71°

And

height = \frac{1}{2}.\frac{1}{tan25.41} = 1.038

Now,

Inner area of gazebo = 7·\frac{1}{2}·1·(1.038) = 3.634 unit²

Outer area of gazebo = (\frac{2.038}{1.038})²·(3.364) = 14.009 unit²

∴ we get

Area of pathway = Outer area - Inner area

                            = 14.009 - 3.634

                            = 10.375 unit²

⇒Area of pathway = 10.375 unit²

5 0
3 years ago
Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled for the flowers to last
igor_vitrenko [27]
For the problem, we are asked t o calculate the volume of the cylindrical vase and it will represent the amount of water that Mary should pour. For a cylinder, the volume is calculated as follows:

V = πr²l
V = π(3)²(8)
<span>V = 226.19 in³ water needed</span>
5 0
3 years ago
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