All categories

3 years ago

Using (x + a) (x + b) = x² + (a + b) x + ab, evaluate 75 x 77

Mathematics

1 answer:

Gre4nikov [31]3 years ago

4 0

(x + a) (x + b) = x² + (a + b) x + ab

75 * 77=

=(70+5)(70+7)

=70²+(5+7)*70+5*7

=4900+12*70+35

=4900+840+35

=5775

You might be interested in

1. You are standing on top of a ridge using a clinometer trying to figure out how far your dog has wandered off in

olga_2 [115]

Given:

It is given that the ridge is 360 inches tall.

Assumptions:

Assume you are 170.1 cm tall which equals 67 inches tall, the height from your eye to the floor is $360+67 = 427$ inches.

The distance from your eye level to the bottom of the ridge is 427 inches.

Assume the angle A is 60°.

To find the distance from you to your dog.

Solution:

A right-angled triangle can be formed where the angle is 60°, the distance between you and the dog is the hypotenuse of the triangle and your height from the floor is the adjacent side of the triangle.

Assume the hypotenuse of the triangle measures x inches.

To determine the length of the hypotenuse, we determine the cos of the angle.

$cos \theta = \frac{adjacent side}{hypotenuse} .$

$cos A = \frac{427}{x} , x = \frac{427}{cos60} , cos60=0.5.$

$x=\frac{427}{0.5} = 854.$

So if the ridge is 360 inches tall and you are 67 inches tall and the angle A is 60°, the distance between your dog and you is 854 inches.

3 0

3 years ago

9mph in still water it takes 5hrs longer to travel 74 miles upstream than downstream find the rate of current and round to neare

prohojiy [21]

Answer:

The rate of current is 2.5 mph.

Step-by-step explanation:

The speed in the water when current is absent is 9 mph.

If the speed of the current is v mph then the upstream speed is (9 - v) mph and the downstream speed is (9 + v) mph.

Now, it takes 5 hours longer to travel 74 miles upstream than down stream, then we can write the equation as

$\frac{74}{9 - v} - \frac{74}{9 + v} = 5$

⇒ $\frac{2v}{81 - v^{2} } = \frac{5}{74}$

⇒ 148v = 405 - 5v²

⇒ 5v² + 148v - 405 = 0

Applying Sridhar Acharya's formula we can write

$v = \frac{-148 + \sqrt{148^{2} - 4(5)(-405) } }{2(5)}$ (Neglecting the negative root)

⇒ $v = \frac{- 148 + 173.2166}{10} = 2.5$ mph (Rounded to the nearest 10th) (Answer)

7 0

4 years ago

Name the vertex of <4

Licemer1 [7]

Hey there!

The vertex of any angle refers to the place where the angles forms (the middle most point in an angle). In <4, U is the vertex of the angle.

Hope it helps ya!

8 0

3 years ago

Evaluate f(x) = 8 + 2x for f(-6)

shusha [124]

Answer:

f(-6)= -4

Step-by-step explanation:

f(x)=8+2x for f(-6)

-----

x= -6

substitute: 8+2(-6)

simplify using PEMDAS: 8+ (-12)

simplify using PEMDAS: -4

7 0

3 years ago

Read 2 more answers

Angel has xx dimes and yy nickels. He has at most 13 coins worth no less than $0.95 combined. Solve this system of inequalities

ivanzaharov [21]

Answer:

a possible solution is (10,1)

Step-by-step explanation:

Here, we want to solve the given inequality and determine one possible solution

From the question, we have it that;

x + y ≤ 13

Mathematically, we have it that 1 dime is worth $0.1

A nickel is worth $0.05

0.1x + 0.05y ≥ 0.95

please check the attachment for the graph of both equations

The point of intersection represents the solution.

we have a point here as (10,1)

8 0

3 years ago