A square has side lengths that measure units 2√5 units

Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

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The centre coordinates would be the opposite value of what is in the brackets

For example, the x value in the brackets is -3, the centre coordinate x value would be positive 3

The same would apply to the y value

The radius would be the square root of 36

Thus, your answer would be option A

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Answer:

t=13.28382 ≈ 13.3 years

It takes 13.3 years to amount $15700 from the principal $6500.

Given that, a person invests 6500 dollars in a bank. the bank pays 6.75% interest compounded semi-annually.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = A = P(1+r/n)^nt

Now, 15700 =6500(1+6.75/2×100)^2t

⇒ 15700/6500=(1+6.75/200)^2t

⇒ 15700/6500=1.03375^2t

⇒ 2.415=1.03375^2t

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form:

t=ln(2.415)/2ln(1.03375)

Decimal Form:

t=13.28141707

≈ 13.3 years

Therefore, it takes 13.3 years to amount $15700 from the principal $6500.

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Answer:

D

Step-by-step explanation:

We know that the value of x is 120, so we can substitute it into the equation they gave you.

T(x) = 0.06x + 4.5

T(x) = 0.06(120) + 4.5

Now just solve.

0.06 × 120 = 7.2

7.2 + 4.5 = 11.7

So the tax on the room is $11.70

The system of equations as an augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

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

x                  = 100

   -5m  - 7c  = 350

   -5m  - 9c  = 200

The above means that the variables in the system of equations are

x, m and c

So, we have the following representation

x    m     c        

1    0      0        100

0   -5    -7        350

0   -5    -9        200

When represented as an augmented matrix, we have

\(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

Hence, the augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

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Triangle PQR is isosceles. It's a unique side-angle-side triangle (both PQ and QR are congruent), so the other two angles in it are congruent and have the same measure. The interior angles of any triangle sum to 180° in measure, so

64° + m∠QPR + m∠PRQ = 180°

2 m∠QPR = 116°

m∠QPR = 58°

Angles PRQ and TRS form a vertical pair, so they are also congruent and m∠TRS = 58°.

This in turn means triangle RST is isosceles (again due to the side-angle-side postulate) so that angles RST and RTS have the same measure. Then

58° + m∠RST + m∠RTS = 180°

2 m∠RST = 122°

m∠RST = 61°

making the answer B.

The value of x is 50 and FTD = 130°

Both of the angles in the diagram must have the same measure because are vertical, then:

3x - 20 = 2x + 30

3x - 2x = 30 + 20

x = 50

That is the value of x.

And we can see that FTD = 2x + 30 = 2*50  + 30 = 130

That is the measure.

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The statement about probability that is correct would be that the probability of landing on yellow is less than the probability of landing on blue. That is option B.

Probability is defined as the total number of possible outcome of an event.

The repeated colour which are numbered from 1 to 8 are as follows:

Therefore, the probability of landing on yellow is less than the probability of landing on blue because 1/4 is less than 3/8.

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Answer: B: The probability of landing on yellow is less than the probability of landing on blue.

Step-by-step explanation:

Answer: 10,000

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

x3+x-5

3*4=12

12+4-5

16-5=11

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Step-by-step explanation:

given,

length = 4x²

breadth/width = y²

we know,

perimeter = 2l + 2b

so,

2(4x²) + 2(y²)

→ 8x² + 2y²

option A is correct

hope this answer helps you dear...take care and may u have a great day ahead!

Cumulative costs of the investments of a mutual fund you currently hold are the amount invested. Net Investment is one investment action's net amount of inflow.

Solution:

The formula for calculating the simple interest:  

\(\to \text{Simple interest} = principal \times rate \times time\)

Total amount = 10000

Let :

From both investments total earned interest  = $620

\(\to \bold{PP \ investment \ return + TT \ investment\ return = 620}\)

\(\to (r \times 10\% \times 1) + (10000 - r \times 5\% \times 1) = 620\\\\\to (r \times \frac{10}{100} \times 1) + (10000 - r \times \frac{5}{100} \times 1) = 620\\\\\to (r \times 0.10 \times 1) + (10000 - r \times 0.05 \times 1) = 620\\\\\to 0.1r + 500 - 0.05r = 620\\\\\to 0.05r = 620 - 500\\\\\to 0.05r = 120\\\\\to r =\frac{ 120}{0.05}\\\\\to r = 2400\)

Therefore,

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Answer:

0.003, 0.08, 0.3, 0.83

Answer:

26244π in³

Step-by-step explanation:

Applying,

Voluem of a sphere

V = 4/3(πr³).......... Equation 1

Where r = radius of the sphere, π = pie

From the diagram,

Given: r = 54/2  = 27 in

Substitute these value in equation 1

V = 4/3(27³)(π)

V = 26244π in³

Hence the volume of the figure expressed in terms of π is 26244π in³

Answer:

3.2mm

Step-by-step explanation:

Answer:

3.2mm

Step-by-step explanation:

Answer:

eyeyywhwywhwhehehhehehehehhehe the answer is a

22°

Step-by-step explanation:

15 - -7

Two -'s = +

15 + 7 = 22

Answer:

$1797.12

Step-by-step explanation:

For starters

Dorothy earns $28.08 per hour on normal hours

Dorothy would be earning $56.16 per hour on overtime hours, since it's double the rate of normal hours.

In a week,

Dorothy works 40 hours of normal time

Dorothy works 12 hours of overtime.

In a week, Dorothy would earn 40 * $28.08 of normal time pay

In a week, Dorothy would earn 12 * $56.16 of overtime pay. Calculating and summing this up, we have

40 * 28.08 = $1123.2

56.16 * 12 = $673.92

$1123.2 + $673.92 = $1797.12

Therefore, we say that Dorothy Katz earns a total of $1797.12 at the end of every week.

The correct answer is A) 3 feet.

A 15-foot statue casts the shadow of 20 food, then a 4-foot-long shadow will be cast by a 3-foot-tall person.

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

From the data in the question,

15-foot statue = 20-foot shadow

x-foot man's height = 4-foot long shadow

20x = 60

x = 60/20

x = 3 foot.

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Answer:

\(\dfrac{11^{-4}}{11^8}=\dfrac{1}{11^{12}}\)

Step-by-step explanation:

Apply exponent rule:   \(a^{-b}=\dfrac{1}{a^b}\)

\(11^{-4}=\dfrac{1}{11^4}\)

\(\implies \dfrac{11^{-4}}{11^8}=\dfrac{1}{11^8 \cdot 11^4}\)

Apply exponent rule:  \(a^b \cdot a^c=a^{b+c}\)

\(\implies \dfrac{1}{11^8 \cdot 11^4}=\dfrac{1}{11^{(8+4)}}\)

\(\implies \dfrac{1}{11^{(8+4)}}= \dfrac{1}{11^{12}}\)

The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

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complete question;

Find the values of x and y. Find value of x.

Answer:

Step-by-step explanation:

Find the attachment in the diagram. According to the diagram, the sum of angle on the straight line AOB is 180°. Also the < AOD is equal to <COB (oppositely directed angle)

From the diagram;

m∠COE+m∠EOF+m∠FOB = <COB

Given

m<AOD = 152

m∠COE = 3x

m∠EOF = x

m∠FOB = x+ 12

Since < AOD  = < COB, the expression above becomes;

m∠COE+m∠EOF+m∠FOB = m<AOD

Next is to substitute the given parameters into the formula above to get x;

3x+x+x+12 = 152

5x+12 = 152

subtract 12 from both sides of the equation

5x+12-12 = 152-12

5x = 140

divide both sides by 5;

5x/5 = 140/5

x = 28°

Hence the measure of angle x is 28°

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

The inequality that represents the age of the group, "x", is: \(17 < x \leq 54\)

Step-by-step explanation:

To express this problem in an inequality we will attribute the age of the members on the group with the variable "x". There are two available information about "x", the first states that every member of the group is older than 17 years, therefore we can create a inequality based on that:

\(x > 17\)

While the second data from the problem states that none of than is older than 54 years old, this implies that they can be at most that old, therefore the inequality that represents this is:

\(x\leq 54\)

In order for both to be valid at the same time x must be greater than 17 and less or equal to 54, therefore we finally have:

\(17 < x \leq 54\)

The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2

To solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:

8x²(x² - 4) = 0

Now we can use the difference of squares identity to factor the quadratic expression:

8x²(x + 2)(x - 2) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.

Therefore, we can set each factor equal to zero and solve for x:

8x² = 0 or x + 2 = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = -2 or x = 2

So the solution set for the equation is {0, -2, 2}.

To check the solution, we can substitute each value into the original equation and verify that it equals zero.

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Answer:

-18x+8

Step-by-step explanation:

First you have to distribute the -2 to the 3x and the -5 in the parenthesis giving you -6x+10-12x-2.

Next you combine like terms which gives you -18x+8

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

Answer:

\((f\cdot g)(x) = 2x^3 + 5x^2-x-6\)

Step-by-step explanation:

We are given the two functions:

\(f(x)=2x^2+x-3\text{ and } g(x)=x+2\)

And we want to find:

\((f \cdot g)(x)\)

Recall that this is equivalent to:

\(=f(x)\cdot g(x)\)

Substitute. Hence:

\((f\cdot g)(x)= (2x^2+x-3)(x+2)\)

Expand if desired:

\(\displaystyle = x(2x^2+x-3)+2(2x^2+x-3) \\ \\ = (2x^3+x^2-3x)+(4x^2+2x-6) \\ \\\ = 2x^3 + 5x^2-x-6\)

Answer:

2x^3+5x^2-x-6

Step-by-step explanation:

f(x) = 2x^2 + x − 3 and g(x) = x + 2.

(f • g)(x) = (2x^2 + x − 3 ) * (x + 2)

Distribute

           =  (2x^2 + x − 3 )*x + (2x^2 + x − 3 )*2

            = 2x^3 +x^2 -3x + 4x^2 +2x -6

Combine like terms

            =2x^3+5x^2-x-6