Whats the square root of 49

The value of the square root of negative 49 will be ± 7i.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ √(-49)

We know that √-1 = i, then we have

⇒ √(-1 x 49)

⇒ ± 7i

The value of the expression √(-49) will be ± 7i.

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Final answer:

The square root of negative 49 simplifies to 7i, where i is the imaginary unit.

Explanation:

The simplify question involves finding the square root of negative 49, which is a mathematical operation dealing with complex numbers. To simplify the square root of a negative number, we use the imaginary unit i, where i is defined as the square root of negative one. Therefore, to simplify √-49, we break it down into the product of √-1 and √49. Since √-1 equals i, and √49 equals 7, the simplification results in 7i.

Answer:

Step-by-step explanation:

Let, it will take x years to be of same height for these trees.

We know that 1 ft = 12 inches.

8 ft = [tex]12\times8 = 96 inch[/tex]. 2 ft = 24 inch.

After x years, the height of type A will be (96 + 6x) inch and the height of type B will be (24 + 15x) inch.

We need find the value of x, for which 96 + 6x = 24 + 15x or, 9x = 72 or, x = 8.

Answer:

B. 13.1

Step-by-step explanation:

To find the range of a set of data, first, order the numbers from least to greatest:

2.8, 4.3, 7.9, 9.6, 10.3, 11.5, 12.8, 12.9, 13.6, 15.3, 15.9

Next, find the least and greatest number:

2.8, 4.3, 7.9, 9.6, 10.3, 11.5, 12.8, 12.9, 13.6, 15.3, 15.9

Subtract the least number from the greatest number:

15.9 - 2.8 = 13.1

B. 13.1 is your answer.

~

Answer:

Eric earned last month US$ 9,786.25

Step-by-step explanation:

Commission of Eric on each house sold = 5% = 0.05

House 1 $55,000

55,000 * 0.05 = $ 2,750

House 2 $105,525

105,525 * 0.05 =  $ 5,276.25

House 3 $35,200

35,200 * 0.05 = $ 1,760

Eric earned last month =  $ 2,750 +  $ 5,276.25 + $ 1,760

Eric earned last month US$ 9,786.25

Answer:

Step-by-step explanation:

What's the question?

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]x+2y > 4[/tex]

Isolate the variable y

subtract x both sides

[tex]2y > -x+4[/tex]

Divide by 2 both sides

[tex]y > -\frac{1}{2}x+2[/tex]

The solution of the inequality is the shaded area above the dashed line

[tex]y=-\frac{1}{2}x+2[/tex]

The slope of the dashed line is negative

The y-intercept of the dashed line is (0,2)

The x-intercept of the dashed line is (4,0)

therefore

The graph in the attached figure

Answer: RS = 3[tex]\sqrt{10}[/tex]

Step-by-step explanation:

To calculate the length RS , all we need do is to find the distance between R and S. The formula for finding the distance between two points is given as :

D = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

[tex]x_{1}[/tex] = 3

[tex]x_{2}[/tex] = -3

[tex]y_{1}[/tex] = 2

[tex]y_{2}[/tex] = -1

Substituting the values we have :

RS = [tex]\sqrt{(-3-3)^{2}+(-1-2)^{2}}[/tex]

RS = [tex]\sqrt{9^{2}+3^{2} }[/tex]

RS = [tex]\sqrt{81+9}[/tex]

RS = [tex]\sqrt{90}[/tex]

this can also be written as

RS = [tex]\sqrt{9}[/tex] X

RS = 3[tex]\sqrt{10}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

B: 3.844x10^5

E: 3.844x10^6

Step-by-step explanation:

Fred and Wilma's home increases in value by 4% every 3 years. Using the compound interest formula, it's calculated that after approximately 6 full periods in 20 years, the value of the home is approximately $189,740.10.

Fred and Wilma's home value increases by 4% every 3 years. To calculate the value of the home after 20 years, we need to first determine how many 3-year periods fit into 20 years, which is approximately 6.67 periods. However, since the home value increases only at the end of each 3 year period, we only consider the full periods, making it 6. We use the formula for compound interest: A = P(1 + r/n)^(nt), where:

Substituting the values into the formula, we get: A = $150,000 (1 + 0.04/1)^(1*6). After performing the calculations, the future value of the home after 20 years approximately equates to $189,740.10.

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Final answer:

The probability of rolling factors of 3 on two six-sided dice is 13 out of 36 possible outcomes, which simplifies to approximately 0.361 or 36.1%.

Explanation:

Calculating the Probability of Rolling Factors of 3

To find the probability of rolling factors of 3 when tossing two dice, we must consider the combinations that result in multiplying to three or being a multiple of three. Each die has six faces, so there are a total of 6 x 6 = 36 possible outcomes when rolling two dice. The factors of 3 are 1 and 3. So we have to count the outcomes where at least one of the dice shows a 3 or both dice show 1, which are the relevant factors of 3. If we roll a 3 on one die, the other die can show any number from 1 to 6, giving us 6 outcomes. If we roll a 3 on the other die, we again have 6 different outcomes. However, this would double-count the scenario where both dice show 3, so we must subtract this outcome once.

Therefore, the number of favorable outcomes is (6 + 6 - 1 = 11). The probability can be computed as the number of favorable outcomes divided by the total number of possible outcomes, giving us a probability of 11/36.

If we want the probability of getting one 1 and one 3 in two tosses, we must add to this the probability of tossing a 3 first and a 1 second. The event of rolling a 1 and then a 3, or 3 and then a 1, each has a probability of 1/36. As there are two ways this can happen (1 then 3, or 3 then 1), the probability for this event is 1/36 + 1/36 = 2/36 or 1/18, which must be added to our initial 11/36.

Hence, the final probability of rolling factors of 3 on two dice is (11/36) + (1/18) = (11/36) + (2/36) = 13/36.

Final answer:

The total length of a race course would be the perimeter if it's a closed loop. Without specific details of the race course, the exact measurement cannot be provided, but several examples hint at how the length can be determined if more information is available.

Explanation:

The student's question pertains to the total length of a race course. To ascertain the total length, one would typically consider the perimeter of the race track if the course returns to the start line or the straight distance from start to finish if not returning. This question does not provide specific details about the dimensions or shape of the race course, which are necessary to give an exact measurement. However, if we refer to the provided information, option (a) says that the perimeter is the distance, and the shortest distance between the start and finish line is the magnitude of displacement. This suggests that the total length could be measured by the perimeter if it's a closed loop.

Some examples include a marathon which has a set length of 42.188 km, or a soccer field where the perimeter would be the sum of all sides, assuming the field was used for a running event. For an actual racecourse, you would need to know the specific dimensions or shape to calculate the total length.

Answer:

[tex]10\frac{1}{2}\ \frac{acres}{hour}[/tex]

Step-by-step explanation:

The correct question is:

Darcy harvests 8 3/4 ​ acres of corn every 5/6​  of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour?

we know that

To find out the corn rate harvested per hour or the unit rate, divide the number of acres of corn harvested by the total time it takes

so

[tex]8\frac{3}{4} :\frac{5}{6}[/tex]

Convert mixed number to an improper fraction

[tex]8\frac{3}{4}=8+\frac{3}{4}=\frac{8*4+3}{4}=\frac{35}{4}[/tex]

substitute

[tex]\frac{35}{4} :\frac{5}{6}=\frac{210}{20}=\frac{21}{2}\ \frac{acres}{hour}[/tex]

Convert to mixed number

[tex]\frac{21}{2}\ \frac{acres}{hour}=\frac{20}{2}+\frac{1}{2}=10\frac{1}{2}\ \frac{acres}{hour}[/tex]

Answer:

[tex]10\frac{1}{2}[/tex] or [tex]\frac{21}{2}[/tex]

Answer:

[tex]k=-5[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]6x^{2} +7x+k=0[/tex] 

so

[tex]a=6\\b=7\\c=k[/tex]

substitute in the formula

[tex]x=\frac{-7\pm\sqrt{7^{2}-4(6)(k)}} {2(6)}\\\\x=\frac{-7\pm\sqrt{49-24k}} {12}[/tex]

so

[tex]x_1=\frac{-7+\sqrt{49-24k}} {12}\\\\x_2=\frac{-7-\sqrt{49-24k}} {12}[/tex]

Remember that

[tex]2x_1+3x_2=-4[/tex]

substitute

[tex]2(\frac{-7+\sqrt{49-24k}} {12})+3(\frac{-7-\sqrt{49-24k}} {12})=-4\\\\(\frac{-14+2\sqrt{49-24k}} {12})+(\frac{-21-3\sqrt{49-24k}} {12})=-4[/tex]

Multiply by 12 both sides

[tex](-14+2\sqrt{49-24k})+(-21-3\sqrt{49-24k})=-48\\\\-35-\sqrt{49-24k}=-48\\\\\sqrt{49-24k}=48-35\\\\\sqrt{49-24k}=13[/tex]

squared both sides

[tex]49-24k=169\\24k=49-169\\24k=-120\\k=-5[/tex]

therefore

The equation is

[tex]6x^{2} +7x-5=0[/tex]

The roots are

[tex]x=\frac{-7\pm\sqrt{49-24(-5)}} {12}\\\\x=\frac{-7\pm\sqrt{169}} {12}\\\\x=\frac{-7\pm13} {12}\\\\x_1=\frac{-7+13} {12}=\frac{1} {2}\\\\x_2=\frac{-7-13} {12}=-\frac{5} {3}[/tex]

The line is rising up to the left and it starts at -2,-2

If you were to continue the line to cross the y a is it would cross at (0,-3)

Find the slope

Slope = (-2 - -1) / (—2 - -4) = -1/2

It would be y= -1/2x-3 when x<-2

Answer:

*100% CORRECT ANSWERS (SEE ATTACHMENTS)

Answer:

E

Step-by-step explanation:

7+8+4=19

4/6 + 3/6 + 1/6 = 1 2/6

19 + 1 1/3

20 1/3

Answer:

more than 16 squares

Answer:

product

Step-by-step explanation:

Answer:

The Correct Answer is product of powers

Step-by-step explanation:

Answer:

(y + 2)(y + 3)

Step-by-step explanation:

Answer:12.57

Step-by-step explanation:

To find the area of a circle with the radius, square the radius, or multiply it by itself. Then, multiply the squared radius by pi, or 3.14, to get the area. To find the area with the diameter, simply divide the diameter by 2, plug it into the radius formula, and solve as before.

The area of the button is approximately 12.56 square centimeters.

To find the area of a circle, we use the formula A = πr², where A is the area and r is the radius. In this case, the diameter of the button is 4 centimeters, so the radius is half of the diameter, which is 2 centimeters. Plugging this value into the formula, we get A = π(2 cm)². To calculate the area, we need to use an approximation of π, which is 3.14. Therefore, the area of the button is approximately 12.56 square centimeters.

Answer:

-95/36

Step-by-step explanation: I think that's right.

Answer:24 red roses

Step-by-step explanation:

You would multiply 12 by two

Answer:

8 red roses

Step-by-step explanation:

If you multiply 2 and 3 by 4 you will get 12 white roses and 8 red ones.

Answer:$198

Step-by-step explanation:

.10 x 220= 22

220-22= 198

To find the sale price of the suit, calculate 10% of the original price, which is $22. Subtract this amount from the original price to get the sale price of $198.

To figure out the sale price of the suit, we need to begin by determining the amount of the discount. Because the discount is 10%, we will calculate 10% of $220. The way to calculate this is by multiplying 220 by 0.10 (which is the decimal equivalent of 10%). This comes out to $22. Next, we subtract this discount from the original price of the suit. So, $220 - $22 equals $198. The sale price is therefore $198.

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Volume is length x width x height.

A cube has the same length, width and height.

The volume of the cube is 2 x 2 x 2 = 8cm

Answer: 8 cm

Happy to help!

Answer: the answer is 8

Step-by-step explanation: The answer is 8 because the equation LxHxW and since It is a cube it is 2x2x2

Answer:

Step-by-step explanation:

Sin x = opp/hyp

Sin x = 4/7

Sin x = 0.5714

X =sin-¹(0.5714)

X = 34.8

X = 35°

The required measure of angle x in the triangle is 35°.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

From triangle,

Sin x = perpendicular/hypotenuse

Sin x = 4/7

Sin x = 0.57

X =sin⁻¹(0.57)

X = 34.9
x = 35°

Thus, the required measure of angle x in the triangle is 35°.

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The claims "marking up the wholesale price by 33% for retail" and "having a 25% profit margin" are not equivalent. While both involve pricing strategies, a 33% markup results in a profit margin of approximately 24.81%, demonstrating that markup and profit margin describe different aspects of pricing.

The question asks if the claims "We mark up the wholesale price by 33% to come up with the retail price" and "The store has a 25% profit margin" are equivalent, in conflict, or not comparable. To examine this, we need to understand the definition of markup and profit margin. Markup refers to the percentage increase over the cost price to arrive at the selling price, while profit margin is the percentage of revenue that remains as profit after covering all costs.

Considering a hypothetical item with a wholesale price of $100:

Therefore, these two claims are not equivalent. A 33% markup on the wholesale price results in a profit margin of approximately 24.81%, not 25%. This slight difference indicates that while related, markup and profit margin describe different aspects of pricing strategy. They are not direct conversions of one another but are interrelated in determining the final retail price and the resulting profit from sales.

Answer:

slope = - 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, 7) and (x₂, y₂ ) = (0, 3) ← 2 ordered pairs from the table

m = [tex]\frac{3-7}{0+4}[/tex] = [tex]\frac{-4}{4}[/tex] = - 1

Hey!

~Set up the equation: -5(x-1)=40

~ Divide 5 on both sides: 40/-5

~ Simplify: x-1=-8

~ We want to get x by itself, so subtract +1 to both sides.

~ Simplify: x = -7

~ Therefore, x = -7.

Answer:

x = - 7

Step-by-step explanation:

-5(x - 1) = 40

-5x + 5 = 40

- 5x = 40 - 5

- 5x = 35  | x(-)

5x = - 35

x = - 35 : 5

x = - 7