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GalinKa [24]
3 years ago
13

The sides of a triangle have lengths 2x + 2, 4x, and 5x + 1. The longest side of the triangle has a length of 5x + 1. For what v

alues of x is the triangle obtuse?
Mathematics
1 answer:
Savatey [412]3 years ago
4 0

Answer:

Step-by-step explanation:

(5x+1)²>(2x+2)²+(4x)²

25x²+10x+1>4x²+8x+4+16x²

5x²+2x-3>0

5x²+5x-3x-3>0

5x(x+1)-3(x+1)>0

(x+1)(5x-3)>0

x+1=0,gives x=-1

5x-3=0,gives x=3/5

x >0(because 4x should be >0)

side is always positive.

so x>3/5

again 5x+1<2x+2+4x

5x-6x<2-1

-x<1

x>-1

x=all real values >3/5

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Hellen has 10 sweets,shelly has 30 sweets.Faith has 4 fewer sweets than the average number of sweets that hellen,shelly and fait
allsm [11]

Answer:

The sum of all the sweets is 54 sweets

Step-by-step explanation:

Here, we want to calculate the number of sweets the three have altogether.

Let the number of sweet Faith has be x

Mathematically;

Faith has 4 sweets fewer than the average number of sweets

The average is the sum of all the sweets divided by 3

The average will be (10 + 30 + x)/3

Thus;

(10 + 30 + x)/3 - 4 = x

(40 + x)/3 = x + 4

40 + x = 3(x + 4)

40 + x = 3x + 12

40-12 = 3x -x

28 = 2x

x = 28/2

x = 14 sweets

So the sum of all the sweets would be 10 + 30 + 14 = 54 sweets

7 0
3 years ago
Which expression is a difference of cubes?
Tanzania [10]

Answer:

Option 4 is correct.

Step-by-step explanation:

Given the following options

we have to choose the difference of cubes.

Option 1:

9w^{33}-y^{12}

9(w^{11})^{3}-(y^4)^3

which is not the difference of cubes

Option 2:

18p^{15}-q^{21}

18(p^5)^3-(q^7)^3

which is not the difference of cubes

Option 3:

36a^{22}-b^{16}

(6a^{11})^2-(b^8)^2

which is the difference of square

Option 4:

64c^{15}-a^{27}

(4c^5)^3-(a^9)^3

which is the difference of cubes.

8 0
3 years ago
Stacey filled her 1/2 cup of measuring cup seven times to have enough flour for a cake recipe how much flour does the cake recip
Reptile [31]
The answer would be 3 1/2 cups
7 0
3 years ago
How to differenciate natural,whole,integers,rational,irrational numbers and real numbers sets from -12 to 49 and draw numbers li
slavikrds [6]

Answer:

Step-by-step explanation:

Natural Numbers :

These are numbers used for counting, they are the numbers on a number line. From -12 to 49, the natural numbers are 1, 2, 3, ..., 49.

Whole Numbers:

These are numbers that can be written without havin to write in fractions. They are 0, 1, 2, ..., 49.

Rational Numbers:

These are numbers that can be expressed as fractions.

Irrational numbers :

These are numbers that cannot be expressed as fractions.

Real Numbers:

These are numbers that can be used to measure quantities, they include negative, positive numbers and zero. From -12 to 49, all the numbers are real.

Prime Numbers:

These are numbers that are divisible only by one and themselves.

From 7 to 49, the numbers divisible by 7 are 7, 14, 21, 28, 35, 42, and 49.

Only 7 is prime.

3 0
3 years ago
What is the product?
Kipish [7]
The denominator of the second fraction can be factored as (a-2)(2a-7), then it becomes doable. You cancel the (2a-7) factors, and are left with:

\frac{3a^2}{a(a-2)} \implies \frac{3a}{a-2}

Do note that you have erased the fact that a≠0 and a≠7/2, so you should always mention that.


7 0
3 years ago
Read 2 more answers
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