Find the slope of the line if it exists.

Step-by-step explanation:

there is no real number solution for the square root of a negative number.

a sqare root multiplied by itself had to deliver exactly the number inside the square root.

so for sqrt(-49), what can be the answer ?

which number multiplied by itself gives -49 ?

it any negative number at that.

because

a × a = a²

and

-a × -a = a² but definitely not -a².

we get a negative number only, when we multiply a positive number with a negative number or vice versa.

the only solution is complex or imaginary (based on the imaginary number i):

i² = -1

i = sqrt(-1)

so, sqrt(-49) = sqrt(49 × -1) = 7×sqrt(-1) = 7i

but again, no real solution.

Tanisha takes 5/6 hours longer to mow all the lawns last week than this week.

Here, we are given that Tanisha mowed 5 lawns last week in 7/ 12 hours each.

Thus, the total time taken by her to mow 5 lawns = 5(7/12)

= 35/ 12 hours

Now, this week she mows the five lawns in 5/12 hours each

Thus, the total time taken by her = 5(5/12)

= 25/12 hours

Therefore, the difference between the time taken by her last week and this week will be-

35/ 12 - 25/ 12

= (35 - 25)/ 12

= 10/ 12

= 5/6

Thus, Tanisha takes 5/6 hours longer to mow all the lawns last week than this week.

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Answer: 58 degrees

Step-by-step explanation:

a+b=90  ==> angles a and b are on a right angle which measures 90 degrees.

32+b=90

b=58 degrees

This relationship is not true.

[tex]1 + \sec^2(x) = 1 + (1 - \tan^2(x)) = 2 - \tan^2(x)[/tex]

and

[tex]\cot^2(x) = \dfrac1{\tan^2(x)}[/tex]

Rewrite the equation in terms of only tangent.

[tex]2 - \tan^2(x) = \dfrac1{\tan^2(x)} \iff \tan^4(x) - 2\tan^2(x) + 1 = 0[/tex]

Factorize the left side.

[tex]\left(\tan^2(x) - 1\right)^2 = 0[/tex]

Solve for [tex]\tan(x)[/tex].

[tex]\tan^2(x) - 1 = 0[/tex]

[tex]\tan^2(x) = 1[/tex]

[tex]\tan(x) = \pm 1[/tex]

[tex]x = \pm\tan^{-1}(1) + n\pi = \pm\dfrac\pi4 + n\pi[/tex]

where [tex]n[/tex] is an integer. That is, the equation only holds for certain values of [tex]x[/tex], as opposed to all [tex]x[/tex], so it's not an identity.

Answer:

Yes

Step-by-step explanation:

It is a function look at the numbers

The percent will be less than 30% after the year 2017

Let 'p' be the percent of 12th graders in a certain state who have ever used cigarettes for each of the years 2000 through 2014.

Let 't' be the number of years after 2000.

We have to find when the percent is less than 30%.

The function modelling the percent and the number of years through 2000 and 2014 is p= -1.773t+60.442

So first we need to find the number of years corresponding to 30%.

Substitute p = 30 in the above linear equation.

i.e., 30 = -1.773t+60.442

-1.773t = 30 - 60.442 = -30.442

Therefore, t = 30.442/1.773 = 17.17 ≈ 17 years

Since t denotes the number of years after 2000, when t = 17, the year is 2000+17 = 2017

So the percent will be less than 30% after the year 2017

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Answer:

Neck

Step-by-step explanation:

Which one is closest to your head?

T-T

Answer:

Exact Distance = [tex]\boldsymbol{\sqrt{73}}[/tex] units

Approximate Distance = 8.544 units

====================================================

Explanation:

I'll relabel the points as A and B, and I'll be using the distance formula.

[tex]A = (x_1,y_1) = (-2,4) \text{ and } B = (x_2, y_2) = (6,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-6)^2 + (4-1)^2}\\\\d = \sqrt{(-8)^2 + (3)^2}\\\\d = \sqrt{64 + 9}\\\\d = \sqrt{73}\\\\d \approx 8.544\\\\[/tex]

The exact distance is [tex]\sqrt{73}[/tex] units.

The approximate distance is roughly 8.544 units.

Round the approximate value however your teacher instructs.

I will need $1,61,884.2 to pay off the mortgage.

This problem is related to simple interest and we have to calculate the amount after 10 years which is payable in the form of mortgage.

The monthly mortgage payment is $1,345.

Rate of interest is 3.6% per annum.

Time is given to be 10 years.

Simple interest for 10 years = 1345×3.6×10/100

                                            = $ 484.2

So, the total money required to clear the mortgage

= $(1345×12×10) + $ 484.2

= $161400 + $484.2

= $ 1,61,884.2

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The amount paid for the refrigerator is $740.25.

From the information, the sale price of a new refrigerator is $705 and sales tax is figured at 0.05 times the price.

The price of the refrigerator will be:

= $705 + (0.05 × $705)

= $705 + $35.25

= $740.25

Therefore, the amount paid for the refrigerator is $740.25

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Answer:

u = 7 OR u = 13

Step-by-step explanation:

Using the zero property of multiplication, you know you have to make either u-7 or u-13 equal to zero. You get the two solutions from these two cases, where you make either of the equations equal to 0:

u - 7 = 0

Add 7 to both sides

u = 7

u - 13 = 0

Add 13 to both sides

u = 13

FINAL ANSWER: u = 7 OR u = 13

The answer is 18 months as per the asked question and visible graph

Step-by-step explanation:

Find $900 and follow the horizontal line until it touches the red tilted line

As soon as it touches the red line, go down vertically and find where the line leads you and voila, it leads you to 18 months!

Answer:

The value of x = 2/5

Step-by-step explanation:

=>(5x - 2)²

=> (5x)² + 2² - 2(5x)(2)

=> 25x² -20x +4

=> 25x² -10x -10x +4

=> (5x-2) (5x-2)

=> x = 2/5 or 2/5

The simplified form of the following expression is 51.3.

Given,

11(9²-5²)/(2²+8)

= 11(81-25)/(4+8)

= 11(56)/(12)

= 51.3

Expressions are simplified when they are rewritten in a concise manner and without any similar phrases. When simplifying an expression, we combine all similar terms and, if necessary, solve all of the supplied brackets, leaving just the, unlike words that cannot be further reduced.

Combining like terms together and leaving unlike terms alone is the fundamental principle for simplifying phrases. The following is a list of some of the guidelines for simplifying expressions:

Add the coefficients of two or more similar terms together, then include the common variable in the equation.

In the phrase a (b + c) = ab + ac, open the brackets using the distributive property.

Change the sign of all the phrases placed inside that bracket if there is a negative sign right outside the parenthesis to make things simpler.

Simply remove the bracket and put the words as they are, keeping the terms' original signs if there is a "plus" or other positive sign outside of it.

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The expression of [tex] \mathbf{sec( \theta)}[/tex] in terms of [tex]tan( \theta)[/tex] in Quadrant IV is presented as follows;

[tex] sec( \theta) = \sqrt{{tan( \theta)}^{2} + 1} [/tex]

The given trigonometric functions are;

[tex]sec( \theta)[/tex]

[tex]tan( \theta)[/tex]

[tex] {sec( \theta)}^{2} = {tan( \theta)}^{2} + 1[/tex]

In Quadrant IV, the tangent of an angle is -ve, while the secant is +ve

However, the square of -ve is positive;

Therefore;

[tex] \left({tan( \theta)}^{2} + 1 \right) \: is \: positive[/tex]

Which gives;

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Answer:

  30 mL/h

Step-by-step explanation:

You want the rate 336 ml in 11.2 h as a rate in simplest form.

The rate can be expressed in simplest form in a number of ways. We usually want rates involving time to be expressed with time units in the denominator:

  (336 mL) / (11.2 h) = 30 mL/h

__

Additional comment

Medicine is often prescribed on a "per day" basis. In 24 hours, this rate would be ...

  (30 mL/h)×(24 h/day) = 720 mL/day

The machine setup to dispense this medicine might use time units of minutes:

  (30 mL/h) / (60 min/h) = (1/2) mL/min

The speed of Makayla and Nathan are 12 mph and 20 mph respectively.

Let the speed of Makayla is 'x' mph.

and the speed of Nathan is 'y' mph.

The total distance travelled by both is 129 miles.

The time taken by each is 6 hours, same for both.

Speed  = distance / time

Distance =  speed × time

Makayla's covered distance = xt

Nathan's covered distance = yt

Total distance = xt + yt

xt + yt = 192

As, Nathan travels 8 mph faster than makayla.

The,

y = x + 8, t = 6 hours substitute;

xt + (x+ 8)t = 192

2x + 8 = 192/6

On simplification;

x = 12 mph (Makayla's speed)

Y = x + 8

y = 12 + 8

y = 20 mph (Nathan's speed)

Therefore, the speed of Makayla and Nathan are x = 12 mph and y = 20 mph respective;y.

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Answer: Your computer will be worth $1,171.12

Step-by-step explanation:

[tex]a_n = 1500(0.94)^4\\a_n=\boxed{1171.12}[/tex]

Answer:

2 is the y-int.

Step-by-step explanation:

Becuase the line runs through the y-axis at 2.

1. The temperature change on each day is as follows:

2. The temperature change on Day 1 was 32.31°C.

3. The temperature changed the most on Day 2.

A temperature change is a process whereby the degree of hotness or coldness varies from one time to another.

In this instance, the temperature changes can be computed by subtracting the temperature at Sunrise from the temperature at Sunset in degrees Centigrade or degrees Fahrenheit, as the case may be.

Daily Temperatures

                   Temperature at    Temperature at   Temperature

                       Sunrise (°C)           Sunset (°C)          Change

Day 1                - 13.94                    18.37                   32.31°C

Day 2                 - 9.12                   28.17                   37.29°C

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A basketball court has symmetry; one half of the court is a mirror image of the other. The entire basketball court ( is 94 feet by 50 feet. On each half-court, painted lines show the free throw lane and circle, as well as the three-point arc, whose distance from the basket varies based on the level of hoops being played.

The borders of the court have their own commonsense names:

Along the length of the court, the borders are the sidelines.

Along the ends, the borders are the endlines, or baselines.

Separating both halves of the court is a midcourt line.

In the very center of the midcourt line is the center circle (12 feet in diameter), where the center toss takes place to begin the game.

The free throw lane is the hub of the action in each half-court. This rectangle is 12 feet wide — 16 feet at the men's pro level. Its length, as measured from the basket to the free throw line, is 15 feet at all levels. An offensive player may not stand inside the lane for more than three seconds unless he or one of his teammates is shooting the ball. After a shot is taken, the count starts over again. A defensive player may remain inside the lane for as long as he desires.

A player fouled by another player sometimes receives free throws, also known as foul shots. She takes these shots (they aren't really "throws") from the free throw line at the end of the lane — 15 feet from the basket. The shots are "free" because a defender does not guard the shooter .The remaining players line up alongside the free throw lane (or behind the shooter) and cannot interfere with the shot. They line up in order, on either side of the lane, of defense-offense-defense-offense. (Up to four players may stand on one side of the lane.) If a player opts not to take a spot (say, for example, the second defensive spot), then a player from the opposing team is permitted to step into that spot. The fans behind the basket usually scream, jump up and down, and wave their hands to try to distract an opposing team's shooter during free throws.

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The value of the expression is  -311/35

The expression is given as

negative 2 and 3 over 5 minus 6 and 2 over 7.

Rewrite properly as

- 2 3/5  - 6 2/7

Express as improper fraction

-13/5 - 44/7

Take the LCM

(-13 * 7 - 44 * 5)/35

Evaluate

-311/35

Hence, the value of the expression is  -311/35

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The coordinates of L are: (8,-4)

Here, triangle is rotated 270° counterclockwise. So the rule that we have to apply here is

(x, y) → (y, -x)

Based on the rule given in step 1, we have to find the vertices of the rotated figure.

(x, y) → (y, -x)

L(4,8) → L'(8.-4)

M(4,3) → M'(3,-4)

N(8,8) → N'(8,-8)

Vertices of the rotated figure are:

L'(8.-4)  M'(3,-4)  N'(8,-8)

Hence we get the desired result.

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The logical function that represents the amount of workout Laura does in each week along with her simultaneous increase in workout can be given by Arithmetic Progression.

It is represented as An = A + (n-1)d. Here, A represents the first term, or the amount of workout done in first week, d represents common difference or the difference in workout done in next week to its previous week, n represents the number of terms or the number of weeks for which data is to be calculated and An represents the workout done in nth week.

Arithmetic progression refers to the sequence of numbers such that each succeeding number increases with respect to previous number by fixed/ constant value. Thus, there exists constant amount of difference between each consecutive pair of number.

Since, Laura's workout pattern varies such that the amount of workout she does in one week increases by same amount in next week, so we get an arithmetic progression of her workout pattern.

Hence, her workout pattern can be traced as A, A+d, A+2d, A+3A, ..., An.

Thus, An = A + [(n-1)*d]

A3 = A +[(3-1)*d] = A + [2d] = 20 ...(1)

A9 = A +[(9-1)*d] = A + [8d] = 50 ...(2)

A11 = A +[(11-1)*d] = A + [10d] = 60 ...(3)

Solving equation (1) and (2), we get d = 5 and A = 10.

Thus, we conclude by saying that the function of her exercise routine is given by arithmetic progression and the amount of workout that she increases each week is given by 'd' that is 5 minutes.

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The upper class limits are- 29, 39, 49, 59, 69, 79, 89

The lower class limits are- 20, 30, 40, 50, 60, 70, 80

The class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5

The class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5

And the number of individuals included in the summary is 84.

Here, we are given the following dataset-

Age (yr) when          Frequency

award was won

20-29                       27

30-39                       32

40-49                       15

50-59                       3

60-69                       5

70-79                        1

80-89                       1

Upper class limit is the largest data value that can go in a class.

Thus, the upper class limits are- 29, 39, 49, 59, 69, 79, 89

Lower class limit is the smallest data value that can go in a class.

Thus, the lower class limits are- 20, 30, 40, 50, 60, 70, 80

The class midpoint is the average of the upper and lower limits of a class. Class midpoint = (upper limit + lower limit)/ 2

Thus, the class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5

Class boundary is the midpoint of the upper class limit of a class and the lower class limit of the previous class.

Thus, the  class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5

Frequency gives us the number of individuals/ objects belonging to a particular class.

Thus, the number of individuals included in the summary = 27 + 32 + 15 + 3 + 5 + 1 + 1 = 84

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The domain is:

D: {-4, 5, 6, 8}

The range is:

R: {-4, 3, 5}

And yes, the relation is a function.

For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).

Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}

The domain is the set of the first values of each pair, so we have:

D: {-4, 5, 6, 8}

The range is the set of the second values of each pair:

R: {-4, 3, 5}

Now, is this a function?

Yes, it is a function, because each input is mapped into only one output.

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Answer:

5500 is correct Answer.

Please mark me as brainlist answer.

The probability that a randomly selected person doesn't get a shave and doesn't get a haircut is 0.250.

The probability that a randomly selected person gets a shave, given that they get a haircut is 0.606.

The probability that a person selected at random would not get a shave or a haircut can be found as:

= 1 - (Prob. of haircut + Prob. of shave - Prob. of both)

= 1 - (0.66 + 0.49 - .40)

= 0.250

The probability that a random person would get a shave given they have gotten a haircut is:

= Probability of both / Probability of getting a haircut

= 0.40 / 0.66

= 0.606

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Answer:

x=8

Step-by-step explanation:

-x-6=-14

-x=6-14

x=14-6

x=8