-12 + 18. = 70<br><br> complete the square

Vlad1618 [11]

110% of 90 is:
90*1.10 = 99

5 0

2 years ago

Tim and Cynthia leave Cynthia's house at the same time. Tim drives north and Cynthia drives west. Tim's average speed is 10 mph

RSB [31]

Answer:

54.2 mph

Step-by-step explanation:

Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...

70² = c² +(c -10)²

4900 = 2c² -20c +100 . . . . eliminate parentheses

c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form

(c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form

c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical

c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution

Cynthia's average speed was 54.2 miles per hour.

6 0

2 years ago

Help me please asap I need to know fully how to solve this problem

vivado [14]

Consider the absolute value, because we only worry about the quadrant later.

$\text{Consider: } sin(A) = |-\frac{\sqrt{3}}{4}|$
$sin(A) = \frac{\sqrt{3}}{4}$

Thus, we know that the hypotenuse has a length of 4 units, and the side opposite the angle, A is √3, because this is the nature of the sine function in relation to its triangular component.

The missing side can be found using Pythagoras' Theorem:
4² - (√3)² = x²
16 - 3 = x²
13 = x²
x = √13

$\therefore tan(A) = \pm \sqrt{\frac{3}{13}}$

Since angle A is in the third quadrant, the tangent function will produce a positive angle.

$tan(A) = \sqrt{\frac{3}{13}}$
$\text{Rationalise the denominator: } \frac{\sqrt{3}}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$

$tan(A) = \frac{\sqrt{39}}{13}$

7 0

3 years ago

Translate this sentence into an equation.

ElenaW [278]

Answer:

The product of Victor's age and 7 is 84 in equation form is 7v=84

Step-by-step explanation:

Let v be the Victor's age.

We are supposed to Translate this sentence into an equation

The product of Victor's age and 7 is 84

Victor's age = v

Product of victor's age and 7 = $7 \times v$

We are given that their product is 84

So, $7 \times v =84$

Hence The product of Victor's age and 7 is 84 in equation form is 7v=84

7 0

2 years ago

Please answer ASAP. A baseball is hit upward from a platform that is m high at an initial speed of 29m/s. The approximate height

kotegsom [21]

Answer:

a) about 0.7 seconds to 5.1 seconds.

b) Listed below.

Step-by-step explanation:

h - 1 = -5x^2 + 29x

h = -5x^2 + 29x + 1

a) We will find the amount of time it takes to get to 18 meters.

18 = -5x^2 + 29x + 1

-5x^2 + 29x + 1 = 18

-5x^2 + 29x - 17 = 0

We will then use the quadratic formula to find the answer.

[please ignore the A-hat; that is a bug]

$\frac{-29±\sqrt{29^2 - 4 * -5 * -17} }{2 * -5}$

= $\frac{-29±\sqrt{841 - 340} }{-10}$

= $\frac{-29±\sqrt{501} }{-10}$

= $\frac{-29 ± 22.38302929}{-10}$

= $\frac{-6.616970714}{-10}$ and $\frac{-51.38302929}{-10}$

= 0.6616970714 and 5.138302929

So, the time period for which the baseball is higher than 18 metres ranges from about 0.7 seconds to 5.1 seconds.

b) Restrictions on the domain and range of the function are that the domain and range can never be negative, since time cannot be negative, and height cannot be negative. The height cannot exceed the vertex of the parabola, since that is the highest the ball will ever go. It cannot exceed that height since gravity will cause the ball to fall down.

Hope this helps!

5 0

3 years ago

-12 + 18. = 70 complete the square