All categories

3 years ago

Find two consecutive positive integers such that the square of the first decreased by 17 equals 4 times the second.

Mathematics

1 answer:

Zina [86]3 years ago

3 0

Answer:

The two consecutive positive integers are 7 and 8

Step-by-step explanation:

Let

x ----> the first positive integer

x+1 ----> the second consecutive positive integer

we know that

$x^{2} -17=4(x+1)$

Solve for x

$x^{2} -17=4x+4\\ \\x^{2}-4x-21=0$

Solve the quadratic equation by graphing

The solution is x=7

see the attached figure

Find the value of x+1

x+1=7+1=8

therefore

The two consecutive positive integers are 7 and 8

You might be interested in

What's an equation that the passes through (-6,4) and is parallel to y=1/2x+8

deff fn [24]

By definition, if two lines share the same gradient, they are said to be parallel. So, we know for this equation, it must have a gradient of 1/2.

Now, since the point (-6, 4) passes through the line, we know it must satisfy the equation. Since we have a gradient/slope and a point, we can use the point-gradient form:

$y - y_1 = \frac{1}{2}(x - x_1)$ , where $(x_1, y_1)$ represents the points being passed through.

$y - 4 = \frac{1}{2}(x + 6)$
$2y - 8 = x + 6$
$2y = x + 14$
$y = \frac{1}{2}x + 7$

3 0

3 years ago

What are the solutions of the equation (x−13)2=400?

Slav-nsk [51]

Answer:

Step-by-step explanation:

$(x-13)^2=400\\\\ (x-13)^2=(\pm20)^2\\\\x-13=20\quad\vee\quad x-13=-20\\\\x=33\qquad\vee\qquad x=-7$

7 0

3 years ago

A table is on sale for 65% off. the sale price is $154 . what is the regular price?

Yuliya22 [10]

The original price is $254.10 or 254 rounded. 154 times .65 is 100.1. Add 100.1 to the sale price which is 154 and you'll get the original, 254.
Hope this helps :)

7 0

3 years ago

Of sugar in the syrup made of 10 kg of water and 4 kg of sugar?

snow_lady [41]

Answer:

The answer to your question is 60%, I will say health wise that sugar is not good for you.

Step-by-step explanation:

8 0

3 years ago

John is traveling at 48 miles per hour and his distance can be written as d = 48t.

MakcuM [25]

240 miles
d=48(5) which equals 240

3 0

2 years ago