Triangle Theorem ( sss, sas, asa )

Answer:

2 and 3.

Step-by-step explanation:

Four to the second power is 16.

Four to the third power is 64.

30 lies between 16 and 64, thus the exponent must lie between 2 and 3.

The solution to the equation \(4^x = 30\) must lie between 2 and 3

The given exponential equation is:

\(4^x = 30\)

To find the value of x, find the natural logarithm of both sides of the equation

\(ln 4^x =ln30\\\\xln4 = ln30\\\\1.39x = 3.4\\\\\)

Divide both sides by 1.39

\(\frac{1.39x}{1.39} = \frac{3.4}{1.39} \\\\x = 2.45\)

Since 2.45 falls between 2 and 3, we can conclude that the solution to the equation must lie between 2 and 3

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The volume of the different shapes have been calculated in the space below

Volume of rectangular prism = lwh

where we define the variables as :

l = length

w = width

h = height

then when we multiply, we will have

= 4 x 10 x 6

= 240

Volume of triangular pyramid = 1 / 3 b x h

where b = base

h = height

1 / 3 x 1.5 x 2

= 1

Volume of rectangular pyramid = lwh / 3

= 7.5 x 4.5 x 5 / 3

= 56.25

= 1/2 x b x h x l

= 1/2 x 3 x 8.5 x 7

= 89.25

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Answer:

it would be 6:10

Step-by-step explanation:

\(6:57-0:47 = 6:10\)

Answer:

Step-by-step explanation:

Answer:

37 x 4 = 148

148 cards

Step-by-step explanation:

Would really appreciate it if you could give me brainliest. Have a good day! :)

Answer:

37×4 = 148

Step-by-step explanation:

so your answer is 148

9514 1404 393

Answer:

  47 -6√10

Step-by-step explanation:

As you know, the area of a square is the square of the side length. It can be helpful here to make use of the form for the square of a binomial.

  (a -b)² = a² - 2ab + b²

  (√2 -3√5)² = (√2)² - 2(√2)(3√5) + (3√5)²

  = 2 - 6√10 + 3²(5)

  = 47 -6√10

__

Check

  √2-3√5 ≈ -5.29399 . . . . . . . . note that a negative value for side length makes no sense, so this isn't about geometry, it's about binomials and radicals

  (√2-3√5)² ≈ 28.02633

  47 -6√10 ≈ 28.02633

There are no dimensions that minimize the cost of the box while maintaining a volume of 20.

To find the dimensions that minimize cost, we need to consider the relationship between the volume of the box and the cost of the materials used.

Let's start by determining the dimensions of the box. We know that the box has a volume of 20. Since the box is constructed out of two different types of metal, we can divide the box into two parts: the top and bottom, which are both squares, and the sides.

Let's assume the length of each side of the top and bottom squares is x. Therefore, the area of each square is x * x = x^2.

The height of the box can be represented by h.

Since the box has a volume of 20, we can set up an equation:
x^2 * h = 20

Now, let's determine the cost of the materials used.

The metal for the top and bottom squares costs 1/ft^2, so the cost for each square is x^2 * (1/ft^2) = x^2/ft^2.
The metal for the sides costs 2/ft^2, so the cost for the sides is 4 * (x * h) * (2/ft^2) = 8xh/ft^2.
The total cost of the materials is the sum of the cost for the top and bottom squares and the cost for the sides:
Cost = (x^2/ft^2) + (8xh/ft^2)

To minimize the cost, we can differentiate the cost function with respect to x and h, and then set the derivatives equal to zero:
dCost/dx = 2x/ft^2 + 8h/ft^2 = 0  (equation 1)
dCost/dh = 8x/ft^2 = 0  (equation 2)

From equation 2, we can see that x = 0 is not a valid solution since it represents a box with zero dimensions. Therefore, x ≠ 0.

From equation 1, we can solve for h:
2x/ft^2 + 8h/ft^2 = 0
8h/ft^2 = -2x/ft^2
h = -2x/8

Since h represents the height of the box, it cannot be negative. Therefore, h ≠ -2x/8.
To find the valid values of x and h, we can substitute the value of h into the equation for the volume:
x^2 * (-2x/8) = 20

Simplifying this equation gives:
-2x^3/8 = 20
-2x^3 = 160
x^3 = -80

Since we're looking for dimensions, x cannot be negative. Therefore, there are no valid values of x and h that satisfy the equation for the volume.

In conclusion, there are no dimensions that minimize the cost of the box while maintaining a volume of 20.

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Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

Equation: \( 4x\degree + 2x\degree = 180°\)

Answer:

120°, 60°

Step-by-step explanation:

Since, sum of any two Supplementary angles is always 180°.

\( \therefore 4x\degree + 2x\degree = 180°\\

\therefore 6x\degree = 180°\\

\therefore 6x = 180\\\\

\therefore x = \frac{180}{6}\\\\

\therefore x = 30\\

\implies \\

4x° = (4\times 30)° = 120°\\

\&\\

2x° = (2\times 30)° = 60°\\

\)

A regular polygon with angles that all measure 162 degrees has 20 sides.

Let's first consider a formula to find the measure of an interior angle of a regular polygon. We can use the formula:

Interior angle = (n-2) x 180 / n,

where n is the number of sides of the polygon.

If all angles of the polygon measure 162 degrees, then we can set up an equation:

(n-2) x 180 / n = 162

Multiplying both sides by n, we get:

(n-2) x 180 = 162n

Expanding the left side, we get:

180n - 360 = 162n

Subtracting 162n from both sides, we get:

18n - 360 = 0

Adding 360 to both sides, we get:

18n = 360

Dividing both sides by 18, we get:

n = 20

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Answer:

I believe it is 17.50$

Step-by-step explanation:

Because 0.75 x 10 = 7.5 + 10 = 17.50$

\(xy=(a+2)(a-2)=a^2-2a+2a-4=a^2-4\)

The irrational numbers between 1 and √2 are 1.247......, 1.367.... and  1.1509....

From the question, we have the following parameters that can be used in our computation:

1 and square root 2

Rewrite as

1 and √2

When evaluated, we have

1 and 1.41421356.....

The irrational numbers between the numbers are numbers that cannot be expressed as fractions

Some of these numbers are

1.247......

1.367....

1.1509....

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The value of c₂ = 1. Substituting the values of c₁ and c₂ back into the general solution, we get y(t) = 2cos(3t) + sin(3t).The correct solution is y(t) = 2cos(3t) + sin(3t), and it satisfies the initial conditions y(0) = 2 and y'(0) = 3.

The given differential equation is y" + 9y = 0. The characteristic equation is r² + 9 = 0 and it gives us the roots r = ±3i.

We know that the general solution to this differential equation is y(t) = c₁cos(3t) + c₂sin(3t). Given y = sin(3t)2cos(3t), we can write this as y = 1/2sin(6t).

Now we can compare the coefficients of y(t) and y'(t) with the coefficients of the given initial values: y(0) = 2 and y'(0) = 3. y(0) = 2 => c₁ = 2/cos(0) = 2 y'(0) = 3 => -3c₁sin(0) + 3c₂cos(0) = 3 => 3c₂ = 3

Therefore, c₂ = 1. Substituting the values of c₁ and c₂ back into the general solution, we get y(t) = 2cos(3t) + sin(3t). Hence, y = sin(3t)2cos(3t) is not a solution to the given initial value problem.

The correct solution is y(t) = 2cos(3t) + sin(3t), and it satisfies the initial conditions y(0) = 2 and y'(0) = 3.

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Answer:

As 1000g=1 kg ⟹1g=

1000

1

​

 kg.

26 kg 50 g.

=26 kg+50 g

=26 kg+50(

1000

1

​

)kg.

=26+0.05 kg.

=26.05 kg.

Answer: 26kg, 0.045kg

Step-by-step explanation:

The measure of one of the congruent base angles is 65°.

It's important to note that any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. A triangle has three sides, three angles and the sum of the angles equal 180°.

It should be noted that a triangle has 3 side, 3 angles and a sum of 180°.

In this situation, DEF is an isosceles triangle. If m∠D = (3x + 5)° , m∠E = (4x − 15)° and m∠F = (2x + 10)°.

The value will be illustrated thus:

3x + 5 + 4x - 15 + 2x + 10 = 180

Collect the like terms

9x = 180 - 5 + 15 - 10

9x = 180

x = 180 / 9

x = 20

The measure of one of the congruent base angles will be:

= 4x - 15

= 4(20) - 15

= 65°

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Answer:

Step-by-step explanation:

B

The second option shows a pair of triangles which are congruent by the SSS congruence theorem.

The SSS (Side - Side - Side) congruence theorem states that if two triangles have three sides that are congruent to each other, then the two triangles are congruent by the SSS theorem.

The congruent sides for the second option are given as follows:

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Answer:

Step-by-step explanation:

3(23-2b) + 3b = 48

1. Use the distributive property and distribute the 3 before the parenthesis

             3(23-2b)   (make sure you read the (-) as part of the 2b so it's -2b

              69 - 6b

2. 69 - 6b +3b = 48   (combine like terms...the bs: -6b + 3b)

    69 -3b=48

3. 69 - 3b = 48         (subtract 69 from both sides)

   -69           -69

4. -3b = -21      (divide both sides by negative three...we want the b to be +

   /-3    /-3

Answer: b = 7

So, C is your answer

Answer:                69 cm

To find the perimeter of the triangle, add together the length of all sides.

A right triangle has three sides and we know that:

When we know two sides in a right triangle, we can find the third side using the Pythagorean theorem:

a² + b² = c²

The variables 'a' and 'b' represent the base and height. The variable 'c' represents the hypotenuse, the longest side.

Since we know the base and height, substitute them into the formula and solve for the hypotenuse.

a² + b² = c²                Start with the Pythagorean theorem.

24² + 16² = c²            Substitute the base and height.

576 + 16² = c²            Solve 24².

576 + 256 = c²          Solve 16².

832 = c²                     Add.

Now, let's start to isolate 'c', which means making it alone on one side of the equal sign.

√832 = √c²               Square root both sides.

√832 = c                   Square root is the opposite of ², so it cancels out.

c ≈ 28.8...                  Keep the variable on the left side.

The question says to find the approximate perimeter, so let's round 28.8 to the nearest whole number.

The hypotenuse, 'c', is about 29 cm.

Now, we know the three sides:

Add together all three sides.

Perimeter = base + height + hypotenuse

Perimeter = 24 cm + 16 cm + 29 cm

Perimeter = 69 cm

∴ The perimeter of the right triangle is approximately 69 cm.

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The probability of selecting both defective gadgets out of 100 gadgets is 1/110, which is calculated using the basic concepts of probability theory.

What is a random experiment?

An experiment that is repeated several times and produces more than one possible outcome is called as the random experiment. It contains a well-defined set of values which constitutes a sample space. Eg: Rolling a die, tossing a coin etc.

Calculation of the probability of selecting both gadgets as defective

The total amount of gadgets = 100

Number of defective gadgets = 10

The probability of selecting a defective gadget is 10 / 100 or 1 / 10

Now, the total number of gadgets and defective gadgets are decreased by 1

So, the probability of selecting another gadget as defective is 9 / 99 or 1 / 11

P(E) = P(when two selected gadgets are defective) = 1 / 10 x 1 / 11

P(E) = 1 / 110

Hence, the probability of selecting both defective gadgets is 1/110.

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Answer: The expected number of digits that need to be scanned to identify one defective bowling ball is 1/p, and the expected number of digits that need to be scanned to identify three defective bowling balls is the sum of three such expected values, or 3/p.

Step-by-step explanation:

To use a table of random digits to simulate how long it would take to identify three defective bowling balls, we can follow these steps:

1. Define a defective bowling ball as one that is damaged or does not meet the required standards.

2. Assign a unique identification number to each bowling ball in the lot, and assume that there are N total bowling balls in the lot.

3. Create a table of random digits that includes the digits 0 through 9, with each digit appearing with equal probability and independently of the other digits.

4. Scan the table of random digits, starting at any position, and record the first identification number of a defective bowling ball encountered. If no defective bowling ball is encountered, record "none".

5. Continue scanning the table of random digits, starting from the position immediately after the first defective bowling ball, until a second defective bowling ball is identified.

Record the identification number of the second defective bowling ball, or "none" if no such ball is encountered.

6. Repeat step 5 to identify the third defective bowling ball.

7. Record the total number of digits scanned in steps 4-6, and repeat the process multiple times to obtain a distribution of the number of digits scanned to identify three defective bowling balls.

Note that the probability of encountering a defective bowling ball on any given digit depends on the proportion of defective bowling balls in the lot.

If p is the proportion of defective bowling balls in the lot, then the probability of encountering a defective bowling ball on any given digit is p.

Thus, the expected number of digits that need to be scanned to identify one defective bowling ball is 1/p, and the expected number of digits that need to be scanned to identify three defective bowling balls is the sum of three such expected values, or 3/p.

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Answer:1.5 x 2=3 teaspoons vanilla

Step-by-step explanation: simply double the 1.5 teaspoons which is 3 teaspoons of vanilla

An expression is a collection of variables and constants that are bound by some mathematical operation the value for w for the given expression w -5.36=10+w/6 is 18.432.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given expression,

w - 5.36 = 10 + w/6

Subtract w/6 both sides,

w - w/6 - 5.36 = 10 + w/6 - w/6

5w/6 = 10 + 5.36

w = 18.432

Hence "The value for w for the given expression w -5.36=10+w/6 is 18.432".

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Answer:  (a-b+c)²-(b-c+a)²​

=((a-b+c)) - ((b-c+a)) ((a-b+c)) - ((b-c+a))

= (a-b+c-b+c-a) ( a-b+c+b-c+a)

= (-2b + 2c ) (2a)

= (2( -2b/2+2c/2)) (2a)

=(2(-b+c)) (2a)

=2(-b+c) (2a)

Answer;

T=100+40c

Step-by-step explanation:

T is the total cost so everything has to add up to that. 100 is a flat cost, plus 40 dollars a month for however long you stay with that program.