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3 years ago

Lengths of Rectangles

Mathematics

1 answer:

Furkat [3]3 years ago

6 0

Answer:

AB = 5

BC = 12

AC = 13

Step-by-step explanation:

A rectangle is a quadrilateral and therefore, opposite sides are parallel and congruent to each other. Thus:

AB = CD = 12

AB = 12

BC = AD = 5

BC = 5

AC is a diagonal of the rectangle, use Pythagorean theorem to find it's length as follows:

AC² = AD² + CD²

Plug in the values

AC² = 5² + 12²

AC² = 169

AC = √169

AC = 13

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a group of students went hiking in wildlife sanctuary. during the hike a total of 180 ticks and mosquitoes were slapped. if thes

SVEN [57.7K]

Answer:

m = 100, t = 80

Step-by-step explanation:

m + t = 180

6m + 8t = 1240

3 0

2 years ago

If f(x) = x2 - 2x and g(x) = 6x + 4 for which value of x does (t +g)(x)=0

Vinil7 [7]

Answer:

-2

Assumption:

Find the value of x such that $(f+g)(x)=0$ .

Step-by-step explanation:

$(f+g)(x)=0$

$f(x)+g(x)=0$

$(x^2-2x)+(6x+4)=0$

Combine like terms:

$x^2+4x+4=0$

This is not too bad too factor on the left hand side since 2(2)=4 and 2+2=4.

$(x+2)(x+2)=0$

$(x+2)^2=0$

So we need to solve:

$x+2=0$

Subtract 2 on both sides:

$x=-2$

Let's check:

$(f+g)(-2)$

$f(-2)+g(-2)$

$((-2)^2-2(-2))+(6(-2)+4)$

$(4+4)+(-12+4)$

$(8)+(-8)$

$0$

0 was the desired output of $(f+g)(x)$ .

7 0

3 years ago

Use the quadratic formula to solve the equation. 5x2-3x + 1 = 0 X=

mr_godi [17]

Answer:

x= 11/3

Step-by-step explanation:

8 0

2 years ago

Please help me 33/2 + 3y/5 = 7y/10 + 15

8090 [49]

We are given with an equation in variable y and we need to solve for y . So , now let's start !!!

We are given with ;

${:\implies \quad \sf \dfrac{33}{2}+\dfrac{3y}{5}=\dfrac{7y}{10}+15}$

Take LCM on both sides :

${:\implies \quad \sf \dfrac{165+6y}{10}=\dfrac{7y+150}{10}}$

Multiplying both sides by 10 ;

${:\implies \quad \sf \cancel{10}\times \dfrac{165+6y}{\cancel{10}}=\cancel{10}\times \dfrac{7y+150}{\cancel{10}}}$

${:\implies \quad \sf 165+6y=7y+150}$

Can be further written as ;

${:\implies \quad \sf 7y+150=165+6y}$

Transposing 6y to LHS and 150 to RHS

${:\implies \quad \sf 7y-6y=165-150}$

${:\implies \quad \bf \therefore \quad \underline{\underline{y=15}}}$

8 0

2 years ago

My product is 30. The differencd of the two factors is 1. The zum of the two factors is 11. What numbers am i

timurjin [86]

A * b = 30
a - b = 1
a + b = 11

take ur last 2 equations, and add them
a - b = 1
a + b = 11
--------------add
2a = 12
a = 12/2
a = 6

now its just a matter of subbing
a + b = 11
6 + b = 11
b = 11 - 6
b = 5

so a = 6 and b = 5...whose product is 30, whose difference is 1, and whose sum is 11.

5 0

2 years ago