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The perimeter of a triangle with two equal sides is 50 cm. If its base were lengthened by 3 cm and each leg were shortened by 4

Nataly [62]

Answer:

Base of the original triangle is 12 cm.

Step-by-step explanation:

Let base of triangle be x

two equal legs of triangles by y

therefore perimeter of triangle

x+y+y = 50 or x+2y =50

according to the question

if base is x+3 and leg is y-4

then both are equal

that is x+3 = y-4

y-x = 7 or y =x+7

x+2y =50

x+2(x+7) = 50

x+2x +14 =50

3x +14 =50

3x = 50 -14

3x = 36

x = 12

therefore base of the original triangle is 12 cm

6 0

3 years ago

(d) Jim walks three miles in 45 minutes. How long does it take for him to walk 5 miles?

kramer

Answer:

5 miles = 75 minutes

Step-by-step explanation:

We know that:

3 miles = 45 minutes

Solution:

3 miles = 45 minutes
=> 1 mile = 45/3 minutes
=> 5 miles = 45/3 x 5
=> 5 miles = 15 x 5
=> 5 miles = 75 minutes

Hence, it takes 75 minutes for Jim to walk 5 miles.

6 0

2 years ago

Four times the cube of a number is less than the difference between forty and the number. Select the inequality that represents

tigry1 [53]

Answer:

$4x^3 < 40 - x$

Explanation:

let the number be x, now we are given that four times the cube of a number which means four multiplied by the cube of number

i.e 4 multiplied by $x^3$ is less than the difference of 40 and the number x i.e 40 - x

x is for sure less than 40 as $x^3$ is less than the difference between 40 and x so if we write x - 40 then we will obtain negative value which will be greater than $x^3$ .

So, the inequality obtained can be written as $4x^3 < 40 - x$

6 0

3 years ago

Read 2 more answers

Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

Answer: The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

$L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.$

Then, the series will be convergent if L < 1 and divergent if L > 1.

For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

7 0

4 years ago

Read 2 more answers

I will give brainliest!!!!!

STALIN [3.7K]

Answer:

44 because it goes into both of the numbers twice without going over

Step-by-step explanation:

Hope this helps and i am 100% sure it is correct if you are having doubts. Brainliest please

3 0

3 years ago