Shawna was going to sell all of her stamp
collection to buy a video game. After selling half of them she changed her mind. She then bought five more. How many did she start with if she now has 30?

Answer:

The correct options for the possible lengths of the third side are;

13 inches

28 inches

Step-by-step explanation:

The given lengths of two sides of the triangle are;

The length of one side of the triangle = 1 foot = 12 inches

The length of the other side of the triangle = 20 inches

The question can be solved by the triangle inequality theorem as follows;

A + B > C

B + C > A

A + C > B

Let the given sides be A = 12 inches and B = 20 inches

We have;

12 + 20 = 32 > C

Therefore, by the triangle inequality theorem, the third side, 'C', is less than 32 inches

Similarly, when C = 6 inches, we have;

A + C = 12 + 6 = 18 < B = 20

Therefore, the third side cannot be 6 inches

when C = 13 inches, we have;

A + C = 12 + 13 = 25 > B = 20

Therefore, the third side can be 13 inches

when C = 28 inches, we have;

A + C = 12 + 28 = 30 > B = 20

Therefore, the third side can be 28 inches

Based on the triangle inequality theorem, the possible lengths of the third side of the triangle are: 13 inches and 28 inches.

The Triangle Inequality Theorem

The triangle inequality theorem states that, sum of the length of any two sides of a given triangle = length of the third side.

Given the measures,

The possible third side must make the three set of numbers conform to the triangle inequality theorem.

Thus, for 13 inches, we have:

13 + 12 > 20; 12 + 20 > 13; 20 + 13 > 12

Also, for 28 inches, we have:

28 + 12 > 20; 12 + 20 > 28; 20 + 28 > 12

Therefore, based on the triangle inequality theorem, the possible lengths of the third side of the triangle are: 13 inches and 28 inches.

Learn more about triangle inequality theorem on:

https://brainly.com/question/26037134

Answer:

-88

Step-by-step explanation:

If a=2, we can say that -[tex]a^{2}[/tex] would be -4.

Secondly, if a=2 and b=-6 we can assume that 4ab would become -48.

Finally, if b=-6 we can say that -[tex]b^{2}[/tex] would become -36.

Adding all of those up gives you -88, your answer.

9514 1404 393

Answer:

  $1571

Step-by-step explanation:

If we assume that y is profit in dollars, the maximum value of y is revealed by a graph to be ...

  ymax = $1571

The maximum profit the company can make is $1571 at a selling price of $45 each.

_____

The function can be written in vertex form as ...

  y = -(x^2 -90x) -454

  y = -(x^2 -90x +45^2) -454 +45^2

  y = -(x -45)^2 +1571

Because the leading coefficient is negative, we know this vertex represents a maximum. (x, y) = (45, 1571) at the vertex. Maximum profit is $1571.

Answer:

positive + positive is negative

negative+ positive = negative ii think

Step-by-step explanation:

Answer: 8x = 72

Step-by-step explanation:

and in case you need to go any further at any point, x = 9

Answer:

B

Step-by-step explanation:

Distributive property: a*(b + c)= (a*b) + (a*c)

[tex]\frac{3}{4}*(\frac{1}{2}+\frac{-2}{5})=\frac{3}{4}*\frac{1}{2}+\frac{3}{4}*\frac{-2}{5}\\\\=\frac{3}{8}+\frac{-6}{20}\\\\=\frac{3*5}{8*5}+\frac{-6*2}{20*2}\\\\=\frac{15}{20}+\frac{-12}{40}\\\\=\frac{15-12}{40}\\\\=\frac{3}{40}[/tex]

Answer:

el precio de la biciclete entre 3 es lo que van a pagar cada quien.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Add the equations together and solve for x.

[tex](2x + y )+ (3x - y) = 11 + 4[/tex]

[tex]5x=15[/tex]

[tex]x=3[/tex]

Use equation [tex]2x+y=11[/tex]  to solve for y.

[tex]2(3) +y=11[/tex]

[tex]6+y=11[/tex]

[tex]y=11-6[/tex]

[tex]y=5[/tex]

Answer:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825  

Step-by-step explanation:

Answer: 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

Step-by-step explanation:

Answer:

let

a=9cm

b=8cm

c=10cm

Step-by-step explanation:

now

s=(a+b+c)/2=(9+8+10)/2=13.5

area of traingle=√(s(s-a)(s-b)(s-c))=√(13.5(13.5-9)(13.5-8)(13.5-10))=34.197cm²

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Simplifying

(3x + -2)(4x + -1) = 0

Reorder the terms:

(-2 + 3x)(4x + -1) = 0

Reorder the terms:

(-2 + 3x)(-1 + 4x) = 0

Multiply (-2 + 3x) * (-1 + 4x)

(-2(-1 + 4x) + 3x * (-1 + 4x)) = 0

((-1 * -2 + 4x * -2) + 3x * (-1 + 4x)) = 0

((2 + -8x) + 3x * (-1 + 4x)) = 0

(2 + -8x + (-1 * 3x + 4x * 3x)) = 0

(2 + -8x + (-3x + 12x2)) = 0

Combine like terms: -8x + -3x = -11x

(2 + -11x + 12x2) = 0

Solving

2 + -11x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(1 + -4x)(2 + -3x) = 0

Subproblem 1

Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying

1 + -4x = 0

Solving

1 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -4x = 0 + -1

-4x = 0 + -1

Combine like terms: 0 + -1 = -1

-4x = -1

Divide each side by '-4'.

x = 0.25

Simplifying

x = 0.25

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying

2 + -3x = 0

Solving

2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.

2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0

0 + -3x = 0 + -2

-3x = 0 + -2

Combine like terms: 0 + -2 = -2

-3x = -2

Divide each side by '-3'.

x = 0.6666666667

Simplifying

x = 0.6666666667

Solution

x = {0.25, 0.6666666667}

2.) 5x^2-3x=2

We move all terms to the left:

5x^2-3x-(2)=0

a = 5; b = -3; c = -2;

Δ = b2-4ac

Δ = -32-4·5·(-2)

Δ = 49

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

x1=−b−Δ√2ax2=−b+Δ√2a

Δ−−√=49−−√=7

x1=−b−Δ√2a=−(−3)−72∗5=−410=−2/5

x2=−b+Δ√2a=−(−3)+72∗5=1010=1

Answer:

81

Step-by-step explanation:

A composite number has factor more than just one and itself.

Factors of 81=

1, 3, 9, 27, 81

Answer:

Graph below

Step-by-step explanation:

Graph of the Quadratic Function

We are given the function:

[tex]y=f(x)=-x^2+8x-15[/tex]

Select 5 values of x={2,3,4,5,6}

And calculate the corresponding values of y:

[tex]f(2)=-2^2+8*2-15=-4+16-15=-3[/tex]

[tex]f(3)=-3^2+8*3-15=-9+24-15=0[/tex]

[tex]f(4)=-4^2+8*4-15=-16+32-15=1[/tex]

[tex]f(5)=-5^2+8*5-15=-25+40-15=0[/tex]

[tex]f(6)=-6^2+8*6-15=-36+48-15=-3[/tex]

We have obtained the points

(2,-3) (3,0) (4,1) (5,0) (6,-3)

Now we plot them in the graph below.

It can be noted three remarkable points:

The roots of the equation

[tex]-x^2+8x-15=0[/tex]

Are x=3 and x=5.

Answer:

Angle FEG

Step-by-step explanation:

Answer:

layla is savege score in mobile legends and diego's score in ml is 20

Answer:

7/10 70%

Step-by-step explanation:

based on the coin flips, 7 out of 10 of the results have at least 2 female puppies. I hope this is correct :)

Answer: A

Step-by-step explanation: took the quiz and got it right

Answer:

Softballs = (48/b)

Step-by-step explanation:

Given that,

Total number of softballs = 48

She wants to divide them evenly among b softball bags.

We need to find an expression that represents how many softballs she should put into each bag.

As it is dividing among b softball, it means we divide 48 and b. So,

[tex]s=\dfrac{48}{b}[/tex]

Hence, the required expression is (48/b).

Answer: 14

Step-by-step explanation:

Answer:

A. No

Step-by-step explanation:

We know that the sum of the angles of a triangle is always equal to 180°. The sum of the angles of a triangle is not equal to 180° in this equation. Hence, we cannot form a triangle.

Answer:

30 feet

Step-by-step explanation:

3x8=24 ft

3/4x*8= 6 ft

Answer:

b and c

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

This is a right triangle because it has the small square in the corner.

And when you have a right triangle the angle with the square in it is ALWAYS going to be 90 degrees.

It gave you one of the angle measurements which is 61.

90+61=151

And When you add all the angle measurements of a triangle it will ALWAYS be a total of 180 no matter what kind of triangle it is.

To find "x" you subtract the sum of the two angles you you know from 180.

180-151=29

Answer:

i dont know for sure but I think it would be 0.07

Answer:

35.36

Step-by-step explanation:

For Class A

Class A has 11 pupils

The mean score for Class A is 32.

The total score of the students =

Mean score × Number of pupils

= 32 × 11

= 352

For Class B

Class B has 14 pupils. The mean score for class B is 38.

The total score of the students =

Mean score × Number of pupils

= 38 × 14

= 532

Total number of pupils for both classes = (11 + 14)pupils

= 25 pupils

Total score for both class = 532 + 352

= 884

The mean score(rounded to 2DP) in the maths test across both classes is calculated as:

Total score of both classes÷ Total number of pupils

884 ÷ 25

35.36

Answer:

cosC = 30/50

Step-by-step explanation:

Before you find cosC, you should know that:

tangent = opposite side/adjacent side

sine = opposite side/hypotenuse

cosine = adjacent side/hypotenuse

You should also know that trigonometric ratios work for only right triangles.

If cosine = adjacent side/hypotenuse, then:

cosC = 30/50

cosC = 0.6

If rounding to the nearest four decimals, it should be 0.6000.