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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.

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