Expressed as the product of prime factors,
198 = 2 x 32 x 11 and 90 = 2 x 32 x 5.
Use these results to find
(a) the smallest integer, k, such that 198k is a perfect
square,

Answer:

[tex]1.\ 8n+4\\\\2.\ 5x+13\\\\3.\ x+3\\\\4.\ x-6\\\\5.\ 4x+1[/tex]

Step-by-step explanation:

1.

[tex]Sum=2n+6+6n-2\\\\Sum=2n+6n+6-2\ \ \ \ \ \ \ \ (using\ commutative\ property\ of\ addition\ a+b=b+a)\\\\Sum=8n+4[/tex]

2.

[tex]Sum=3x+9+2x+4\\\\Sum=3x+2x+9+4\ \ \ \ \ \ \ \ (using\ commutative\ property\ of\ addition\ a+b=b+a)\\\\Sum=5x+13[/tex]

3.

[tex]Difference=(3x+5)-(2x+2)\\\\Difference=3x+5-2x-2\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=3x-2x+5-2\ \ \ [commutative\ property]\\\\Difference=x+3[/tex]

4.

[tex]Difference=(4x+3)-(3x+9)\\\\Difference=4x+3-3x-9\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=4x-3x+3-9\ \ \ [commutative\ property]\\\\Difference=x-6[/tex]

5.

[tex]Difference=(6x+2)-(2x+1)\\\\Difference=6x+2-2x-1\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=6x-2x+2-1\ \ \ [commutative\ property]\\\\Difference=4x+1[/tex]

Answer:

B) Unlikely

Step-by-step explanation:

Your chance drawing a quarter is a low 20%

Answer:

B:Unlikely

Step-by-step explanation:

Because you have 7 dimes and 5 nickels so those ones would be more likely to be picked than the quarter but it is still possible.

Answer:

[tex]4x+3[/tex]

Step-by-step explanation:

Let

x ----> the cost of a pretzel

we  know that

The phrase" $3 more than four times the cost of a pretzel" is equal to multiply the cost of a pretzel x by 4 and adds the number 3

so

The algebraic expression is

[tex]4x+3[/tex]

Answer:

4p + $3

Step-by-step explanation:

more than= + (plus sign)

four times the cost of a pretzel= 4p

Remember 4 times cost of pretzel

times= multiplication sign

p=cost of pretzel

So: 4p + $3

P = perimeter

L = length

W = width

Formula for the perimeter of a rectangle = L + L + W + W  or  P = 2L + 2W

You know:

P = 110ft

L = W + 5  [length is 5ft greater than the width]

So plug this into the formula:

P = 2L + 2W             Substitute/plug in (W + 5) for L

110 = 2(W + 5) + 2W           Distribute/multiply 2 into (W + 5)

110 = (2)W + (2)5 + 2W

110 = 2W + 10 + 2W       Combine like terms (2W + 2W)

110 = 4W + 10       Subtract 10 on both sides

110 - 10 = 4W + 10 - 10

100 = 4W     Divide 4 on both sides to get "W" by itself

[tex]\frac{100}{4}=\frac{4W}{4}[/tex]

25 = W        Now that you know the width, plug it into the equation for length

L = W + 5       Plug in 25 for W

L = 25 + 5

L = 30

L = 30 ft

W = 25 ft

PROOF

P = 2L + 2W

110 = 2(30) + 2(25)

110 = 60 + 50

110 = 110

Answer:

The two numbers are 21 and 9

Step-by-step explanation

(15+6) minus (15-6) gives a difference of 12

21- 9 = 12

Final answer:

The algebraic expression for half the quantity of X plus Y is (1/2) × (X + Y) or (X + Y) / 2.

Explanation:

To write an algebraic expression for half the quantity of X plus Y, you start by adding X and Y together. This can be represented as (X + Y). To find half of this quantity, you multiply the sum by 1/2 or divide by 2. Therefore, the algebraic expression that represents half the quantity of X plus Y is (1/2) × (X + Y) or (X + Y) / 2.

Answer:

Step-by-step explanation: Area =length × width

7050m^2 = X× 75m

7050 =75X

Divide both sides by 75

7050÷75 =75÷75

74m= X

Answer:

52lbs

Step-by-step explanation:

To find out how much weight the black bear lost during hibernation, subtract the weight after hibernation from the weight before hibernation: 265 - 260 = 5 pounds.

To find out how much weight the black bear lost during hibernation, we can use the information that black bears lose 1/5 of their body weight during hibernation. We know that the black bear weighed 265 pounds before hibernation and weighs 260 pounds after hibernation. To calculate the weight loss, we subtract the weight after hibernation from the weight before hibernation: 265 - 260 = 5 pounds. Therefore, the black bear lost 5 pounds while hibernating.

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In the image, the length of the segment will be 120 units.

Step-by-step explanation:

Whatever may be transformation, either rotation, reflection or translation, the length the line segment will not change.

Here one segment with 120 units and other segment with 240 units is rotated 90 degrees about the origin and then it is translated 50 units up, we will get the image of the segment with the same size.

In the image, the length of the segment will be 120 units.

Yo sup??

P(A)=0.5

P(C|A)=0.4

Therefore

P(A and C)=0.5*0.4

=0.2

Hope this helps.

The required probability is P(A and C) is 0.2 which is represented in the tree diagram.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The given tree diagram represents an experiment consisting of two trials.

The tree diagram represents an experiment consisting of two trials. In this case, the probability of event A and event C occurring is represented by the intersection of branches A and C in the tree diagram.

This probability can be calculated by multiplying the probability of each individual event together.

As per the given question, we have

P(A) = 0.5

P(C|A) = 0.4

So, P(A and C) = 0.5 × 0.4 = 0.2

Thus, the required probability is P(A and C) is 0.2

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Answer:

|z| = |a + ib| = [tex]\sqrt{a^{2} + b^{2}}[/tex].

Step-by-step explanation:

By the definition of complex numbers the modulus of any complex number z = x + iy is given by |z| = |x + iy| = [tex]\sqrt{x^{2} + y^{2}}[/tex].

Say for example, z = 3 + 4i is a complex number then

|z| = |3 - 4i| = [tex]\sqrt{3^{2} + 4^{2}} = 5[/tex]

In a complex plane modulus of a complex number z = x + iy means the distance of the point (x, iy) from the origin. (Answer)

Answer:

(t - 4)(t + 2) = 0  

Step-by-step explanation:

The general formula for a quadratic expression is

y = ax² + bx + c

Your expression is

y = t² - 2t - 8 = 0

By comparison, we see that

a = 1; b = -2; c = -8

1. Find two numbers that multiply to give ac and add to give b.

In this case, find two numbers that multiply to give -8 and add to give -2.

It helps to list the factors of  -8.

They are ±1, ±2, ±4, and ±8

After a little trial and error, you should find the numbers -4 and +2.

-4 × 2 = -8, and -4 + 2 = -2)

2. Rewrite the middle term with those numbers

t² -4t + 2t - 8 = 0

3. Factor the first and last pairs of terms separately

t(t - 4) +2(t - 4) = 0

4. Separate the common factor

The common factor is t - 4.

(t - 4)(t + 2) = 0

19 small mowers and 11 large mowers are sold

Solution:

Let "a" be the number of small mowers sold

Let "b" be the number of large mowers sold

Cost of each small mower = $ 249.99

Cost of each large mower = $ 329.99

30 total mowers were sold

Therefore,

a + b = 30

a = 30 - b ------------- eqn 1

The total sales for a given year was $8379.70

Thus we frame a equation as:

number of small mowers sold x Cost of each small mower + number of large mowers sold x Cost of each large mower = 8379.70

[tex]a \times 249.99 + b \times 329.99 = 8379.70[/tex]

249.99a + 329.99b = 8379.70 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

249.99(30 - b) + 329.99b = 8379.70

7499.7 - 249.99b + 329.99b = 8379.70

80b = 8379.70 - 7499.7

80b = 880

Divide both sides by 80

b = 11

Substitute b = 11 in eqn 1

a = 30 - 11

a = 19

Thus 19 small mowers and 11 large mowers are sold

Answer:

x=4

Step-by-step explanation:

3(9-8x-4x)+8(3x+4)=11

Subtract  4 x  from  − 8 x

3 ( 9 − 12 x ) + 8 ( 3 x + 4 ) = 11

Distribute

27 − 36 x + 24 x + 32 = 11

Simplify

− 12 x + 59 = 11

Subtract 59 to both sides

− 12 x = − 48

Divide by -12

x=4

Answer:

Step-by-step explanation:

The wavelength of an electromagnetic wave with a frequency of 135,000 Hz is approximately 2,222 meters. This can be calculated using the equation λ = c / f, with c being the speed of light and f the frequency of the wave.

The wavelength of an electromagnetic wave can be calculated from the frequency when we understand their relationship through the wave's speed. In the case of an electromagnetic wave, this speed is the speed of light (denoted by c), which is approximately 3.00 x 108 m/s. This relationship is expressed by the equation c = fλ, where f is the frequency and λ is the wavelength.

To calculate the wavelength (λ) from the frequency (f), we rearrange the equation to λ = c / f. Substituting 3.00 x 108 m/s for c and 135,000 Hz for f, gives λ = 3.00 x 108 m/s / 135,000 Hz. After performing the calculation, we find the wavelength to be approximately 2,222 meters.

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The wavelength of an electromagnetic wave with a frequency of 135,000 Hz is approximately 2,222 meters, based on the relationship provided by the equation c = fλ.

The wavelength of an electromagnetic wave is directly related to its frequency by the equation c = fλ, where 'c' is the speed of light in vacuum, 'f' is the frequency and 'λ' is the wavelength. In this equation, the speed of light 'c' is typically 3.00 × 108 m/s. Therefore, if we want to figure out the wavelength of an electromagnetic wave with a frequency of 135,000 Hz, we can rearrange the equation to solve for the wavelength: λ = c/f. Substituting the given values, we have λ = (3.00 × 108 m/s)/(135,000 s-1), which simplifies to λ = 2,222 m.

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Answer:

2/3x = 10.....multiply both sides by 3/2 giving u :

x = 10 * 3/2  

x = 30/2 which equals 15

Step-by-step explanation:

So your answer is 3/2 or 32

Answer: 10ft

Step-by-step explanation:

Using the Pythagorean theorem (a² + b² = c²) you would end up with an equation like this: 36 + 64 = 100. You would then square root 100 and the answer would be 10 ft

Answer:

x=4

Step-by-step explanation:

The given equation, the value of x is :

Solving the equation

        [tex]3/4(x+8)=9\\0.75(x+8)=9\\0.75x+6.00=9\\0.75x=3\\x=3/0.75\\x=4[/tex]

The value of x is 4 .

Answer:

[tex]\frac{23}{32}\ hours[/tex]

Step-by-step explanation:

step 1

Find out the number of hours worked by April on her math project

Multiply 1 1/8 by 5 3/4

so

[tex]1\frac{1}{8} (5\frac{3}{4})[/tex]

Convert mixed number to an improper fraction

[tex]1\frac{1}{8}=1+\frac{1}{8}=\frac{1*8+1}{8}=\frac{9}{8}[/tex]

[tex]5\frac{3}{4}=5+\frac{3}{4}=\frac{5*4+3}{4}=\frac{23}{4}[/tex]

substitute

[tex]\frac{9}{8} (\frac{23}{4})=\frac{207}{32}\ hours[/tex]

Convert to mixed number

[tex]\frac{207}{32}=\frac{192}{32} +\frac{15}{32} =6\frac{15}{32}\ hours[/tex]

step 2

How many more hours did April work?

Subtract the hours worked by Carl from the hours worked by April

[tex]\frac{207}{32}-\frac{23}{4}=\frac{207-8*23}{32}=\frac{23}{32}\ h[/tex]

The solution to the system of equations is x = -2 and y = 4

How to solve the equation

To solve this system of equations using Cramer's rule, we need to first express the equations in standard form: Ax + By = C

According to the problem, we have the equations

4x + 3y - 4 = 0

6x = 8 - 5y.

This is the same as

4x + 3y = 4

6x + 5y = 8

The determinants required for Cramer's rule:

Coefficient matrix (D)

[tex]\[D = \begin{vmatrix} 4 & 3 \\ 6 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 6) = 20 - 18 = 2\][/tex]

For Dₓ

[tex]\[D_x = \begin{vmatrix} 4 & 3 \\ 8 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 8) = 20 - 24 = -4\][/tex]

For D y

[tex]\[D_y = \begin{vmatrix} 4 & 4 \\ 6 & 8 \end{vmatrix} = (4 \times 8) - (4 \times 6) = 32 - 24 = 8\][/tex]

Using Cramer's rule:

[tex]\[x = \frac{D_x}{D} = \frac{-4}{2} = -2\][/tex]

[tex]\[y = \frac{D_y}{D} = \frac{8}{2} = 4\][/tex]

complete question

Solve the following simultaneous equations using Cramer's rule.

4x + 3y - 4 = 0

6x = 8 - 5y

Answer:

The number 1.256 is  A)rational number.

Step-by-step explanation:

                     [tex]\frac{1256}{1000} =1.256[/tex]

The number 1.256... is a rational number because it can be expressed as a ratio of two integers. It is not an integer, whole number, or irrational number.

The number 1.256 repeated is a rational number because it can be expressed as the ratio of two integers, which fits the definition of a rational number as ratios of integers such as 2/1, 3/4, and so on.

Even though the decimal representation may appear to continue forever, if the pattern of digits repeats indefinitely, it is still rational.

This number is not an integer, whole number, or irrational number, so it does not belong to those sets. An integer is a whole number without any fractional or decimal part, positive or negative, including zero.

Therefore, the correct option that defines the sets to which the number 1.256... belongs is Option A: Rational number.

It costs $ 30240 to stain floor of the entire room

Solution:

Given that,

Sgt. Merritt has bought a house now that his tour of duty is up

He wants to stain the wood floors of the living room, which measure 18 x 14

Therefore,

length = 18 yards

Width = 14 yards

[tex]Area = length \times width\\\\Area = 18 \times 14\\\\Area = 252[/tex]

Thus area of wood floors is 252 square yards

The stain costs $120 per square yard

[tex]Cost = 252 \times 120\\\\Cost = 30240[/tex]

Thus it costs $ 30240 to stain floor of the entire room

To stain Sgt. Merritt's living room floors, which measure 18x14 feet, first calculate the area in square feet, convert to square yards, and then multiply by the cost per square yard. The total cost will be $3,360.

To determine the cost to stain the wood floors in the living room, first we need to calculate the total area in square yards since the stain is sold by square yard. The room measures 18 feet by 14 feet.

Step 1: Calculate Square Footage

Multiply the length and width in feet to get the square footage:

18 feet × 14 feet = 252 square feet

Step 2: Convert Square Feet to Square Yards

There are 9 square feet in 1 square yard. Therefore, we divide the total square footage by 9 to convert to square yards:

252 square feet / 9 square feet per square yard = 28 square yards

Step 3: Calculate the Cost

The cost to stain one square yard is $120. So, we multiply the total square yards by $120 to get the total cost:

28 square yards × $120 per square yard = $3,360

Therefore, the cost to stain the entire living room floor will be $3,360.

Answer:

The correct answer is B

Step-by-step explanation:

If we plug in x=10 to the equation, we get y=47

Since y is positive, A is not an counterexample

Since y is a function of x, C is not an counterexample

Since the graph of y is a parabola, D is not an counterexample

Hope this helped and mark as brainliest!

The  algebraic expression can be used to find the nth term of the sequence  is:

[tex]a_n = 5+3n[/tex]

Where, [tex]n\geq 1[/tex] and n is a positive whole number

Solution:

Given sequence is:

8, 11, 14, 17, 20, 23

Let us find the common difference between terms

11 - 8 = 3

14 - 11 = 3

17 - 14 = 3

20 - 17 = 3

23 - 20 = 3

Thus the common difference between successive term and previous term is constant

Thus this is a arithmetic sequence

The formula for nth term term of arithmetic sequence is given as:

[tex]a_n = a_1+(n-1)d[/tex]

Where,

[tex]a_n[/tex] is the nth term of sequence

[tex]a_1[/tex] is the first term of sequence

d is the common difference between terms

Here in this sequence, 8, 11, 14, 17, 20, 23

[tex]a_1 = 8\\\\d = 3[/tex]

Therefore,

[tex]a_n = 8+(n-1)3\\\\a_n = 8+3n -3\\\\a_n = 5+3n[/tex]

Where, [tex]n\geq 1[/tex] and n is a positive whole number

Thus algebraic expression can be used to find the nth term of the sequence is found

Step-by-step explanation:

Given,

y = [tex]x^2[/tex] - 10x + 25

To find, the total number of solutions = ?

∴ y = [tex]x^2[/tex] - 10x + 25

⇒ y = [tex]x^2[/tex] - 2(x)(5) + [tex]5^2[/tex]

⇒ y = [tex](x-5)^{2}[/tex]

There are infinite solution of y.

Thus, there are infinite solution of y.

x = 0,1

y = 0,-5

hope this helped  ___~ ~___

                                      0

\

Answer:

3.48

Step-by-step explanation:

12%=0.12

0.12*29=3.48

Answer:

20+9

Step-by-step explanation:

Answer: 20x+9 (I THINK that’s the answer but I’m not completely sure so...)

Step-by-step explanation: (12x-15) + (8x+24)

12x+8x= 20x

-15+24 (or 24-15)= 9

20x+9

Answer:

100%

Step-by-step explanation:

You cant get a number on a 6 sided die higher than 7.