how many real fourth roots does -1 have?

Step-by-step explanation:

[tex](3x + 2) + x = 180 \\ 3x + x = 180 - 2 \\ 4x = 178 \\ x = 44.5[/tex]

Answer:

x° = 44.5°

Step-by-step explanation:

x° and (3x + 2)° are supplementary angles, which means they add up to 180°.

Equation: x + 3x + 2 = 180

Step 1: Combine like terms.

[tex]\implies 4x + 2 = 180[/tex]

Step 2: Subtract 2 from both sides.

[tex]\implies 4x + 2 - 2 = 180 - 2[/tex]

[tex]\implies 4x = 178[/tex]

Step 3: Divide both sides by 4.

[tex]\implies \dfrac{4x}{4}=\dfrac{178}{4}[/tex]

[tex]\implies x = 44.5[/tex]

Step 4: Substitute 44.5 as the value of x in (3x + 2) to find its measure.

[tex]\implies 3(44.5)+2[/tex]

[tex]\implies 135.5[/tex]

Therefore, the measure of x° is 44.5°, and the measure of (3x + 2)° is 135.5°. Together, they add up to 180°.

The largest area of the rectangle is 6502.5 square feet.

Given that,

Using fence parallel to one of the rectangle's sides, a cattle rancher wants to surround a rectangular area and divide it into four pens (see the figure below). To finish the task, 510 feet of fencing are available.

We have to find what could the four pens' combined total area be.

We know that,

The rectangular shape's length is l and its width is b.

Total fencing= 2l + 5b=510 feet

2l +5b =510 feet

We can write as,

l=1/2(510-5b)

Total area of the rectangle is length into breath

A(b) = l × b

A(b) = 1/2(510-5b)×b

A(b)= 1/2(510b -5b²)

For maximum area

A'(b)=0

1/2(510b -5(2b))=0

b=51

We get l as

l = 1/2(510-5b)

l = 1/2(510-5(51))

l = 127.5

Total area of the rectangle is 127.5 × 51

Total area of the rectangle is 6502.5 square feet.

Therefore, The largest area of the rectangle is 6502.5 square feet.

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The area of the of the rectangle is 5.25square inch and the area of the square is 6.25square inch. Therefore the square has larger area.

The area of a shape is the “space enclosed within the perimeter or the boundary” of the given shape. We calculate the area for different shapes using formulas.

Area formula in rectangle is L× W and in square is L^2. This happened in square becos square has all it's sides equal. Where L and W are length and Width respectively

The area of rectangle with dimension 7inches by 3/4 inch is 7×3/4= 5.25 square inches

The area of the square with dimension 2 1/2 inches is( 5/2)^2= 25/4= 6.25m

Therefore the square has larger area

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Answer:

No

Step-by-step explanation:

Total money = €150

1 pair of sunglasses = €70

3 pairs of shorts = €15 × 3 = €45

then, Total = €70 + €45 + x

€150 = €115 + x

x = €150 - €115

x = €35

Which means Eddie got only €35 left on him which is not enough for him to buy the trainers

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Equation of a line:

y = 2x  - 3

y = 2 x 0 - 3 = -3

y = 2 - 3 = -1

y = 2 x 2 - 3 = 4 - 3 = 1

Table

x   0     1     2

y  -3    -1     1

The graph of the straight line is given below.

Thus,

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

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Answer:

domain: [tex](-\infty, \infty)[/tex]

range: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

You can put any real number into [tex]x[/tex] and get any real number out oft the function [tex]f(x)[/tex]

The value of m is 8.

The amount of times a number has been multiplied by itself is shown by its exponent. The result of multiplying 8 by itself n times is represented as follows:

8 x 8 x 8 x 8 x …..n times = [tex]8^n[/tex]

Given:

[tex]$(m-4)^4 = \left(\frac 1{16}\right)^{-1}$.[/tex]

Now, solving for m

[tex](m-4)^4[/tex] = 16

[tex](m-4)^4[/tex] = [tex]4^4[/tex]

Taking the quad root we have

m -4 = 4

m = 4+ 4

m = 8

Hence, the value of m is 8.

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Step-by-step explanation:

Range = Highest number - Lowest number

= 23 - 4

= 19

Step-by-step explanation:

uploading the picture is an excellent way to make sure we get the original problem definition.

but I just answered this (even without the picture). so, you need it again ?

Answer:

Option A

Step-by-step explanation:

→ Multiply both sides by 2

2s = a + b + c

→ Minus b and c from both sides

2s - b - c = a

There are 6188 ways are there to choose two dozen croissants with at least two of each kind.

A combination is the combination of two or more distinct things. Although it is not necessary to combine things in pairs, the term "combining" comes from the Latin word for "joining together two by two."Combination repetition is permitted.

There are six different varieties of croissants (n = 6), and we must select two dozen croissants (r = 12) with at least two of each type.

In combination, The order does not matter and repetition is allowed.

thus, according to combination,

[tex]C( n+ r - 1,r) = \frac{(n + r - 1 )!}{r! (n-1)!} \\\\C( 6+ 12 - 1,12) = \frac{(6 + 12 - 1 )!}{12! (6-1)!} \\\\ = \frac{17!}{12!5!} \\= 6188[/tex]

thus, there are 6188 ways possible to choose two dozen croissants with at least two of each kind.

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The the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is the function -

x = y

We have the function -

y = x

Now, we can define locus as -

A curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.

This equation -

y = x

is a straight line.

Refer to the graph attached.

The slope of the line is [m] = 1

The [y] intercept is at [c] = 0

Therefore, the the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.

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The graph of (y = 4x), which depicts the relationship between the quantity of tickets sold (x) and the sum of the proceeds from the sales (y), can be drawn by first formulating the linear equation and then using the transformation.

Which is the function's graph?

We have a piecewise function right here:

If x > 6, f(x) = 0.5*x - 2.

If x > 6, f(x) = -x - 1

Given:

Each ticket for the school play is $4.

There have been 'x' tickets sold in total.

The tickets generated 'y' in total revenue.

The graph showing the relationship between the quantity of tickets sold (x) and the sum of the ticket sales (y) can be drawn using the procedures below:

Form the linear equation in two variables as a first step.

y = 4x

The total revenue from the tickets is shown in the equation above.

Draw the graph of (y = x) in step two.

Step 3: In the graph of (y = x), multiply the x-axis by 4 units. The graph that is produced is (y = 4x).

You may find the graph for (y = 4x) below.

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Answer:

x < 1 and x > -4 (more down below)

Step-by-step explanation:

First we have to solve the algebra
|-2x - 3| + 2 < 7
|-2x - 3| < 5
1. -2x - 3 < -5                    2.  -2x -3 < 5
-2x < -2                           -2x < 8                        

x < 1                                x > -4 (switch the expression)
Now... The two answers are x < 1 and x > -4

The interval notation is a number line with circles on the two points (answers)
Sorry I can't exactly explain what that is you might have to search it up, but you need a number line like this, and you need to draw another line above the -5 and 1 with an open circle on -5 and 1

    O-----------------------O

<---5, -4, -3, -2, -1, 0, 1, 2-->

For graphing, make a graph with 5 points on each side with 4 quadrants or whatever reasonable size, and draw a vertical line that extends all the way above and below your graph above 1 on line x and a vertical line all the way above and below your graph above above -5 on x, then shade everything in between those two lines.

This helps you to know what value you plug in for X makes the inequality true (shaded region)

Answer:

[tex]\sqrt{2}[/tex] × [tex]\sqrt{8}[/tex]   And [tex]\sqrt{2}[/tex] ×[tex]\sqrt{3}[/tex]  

Step-by-step explanation:

3x9 are both whole numbers and 0x[tex]\sqrt{5}[/tex] has only one irrational number

Answer:

---------------------------

Answer: C. (2, 1)

Step-by-step explanation:

The numbers labeled are

(-5, -8)

(-2, 1)

(4, 0)

(2, 9)

Find coordinates by looking at each line. (x, y)

The x-axis is the horizontal line in the middle.

The y-axis is the vertical line going across.

The x-axis always goes first when plotting down coordinates, and y goes second.

So, the one NOT labeled is C (2, 1)

There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, then the probability that everyone in the group is a girl is 1/30

It is given that,

Total number of students = 10

Number of boys = 6

Number of girls = 4

Total number of ways to select 3 students from 10 students.

10C3= 10!/ 3!7!= 120

Total number of ways to select 3 students from 4 girls

4C3 = 4!/ 3!=4

The probability that everyone in the group is a girls is

P = 4/120

  = 1/30

Hence ,  the probability that everyone in the group is a girl is 1/30

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The 20 and 21 unit leg lengths of the right triangles ΔACD and ΔBCD formed by the altitude CD indicates, by using Pythagorean theorem that the length of BC is 29 units

A right triangle is a triangle that has two perpendicular sides. The altitude of a triangle is perpendicular to the base of the triangle, forming two right triangles in acute triangle.

Angle ∠A = 45°

The length of the segment the altitude CD divides AB into = 20 and 21 units

Please find attached a drawing created using MS Word based on the question parameters.

[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]

AD = 20

Therefore;

[tex]tan(45^{\circ}) = \dfrac{CD}{20}[/tex]

CD = 20 × tan(45) = 20

Pythagorean theorem applied to right triangle ΔCBD, indicates that;

[tex]\overline{BC}^2[/tex] = [tex]\overline{CD}^2[/tex] + [tex]\overline{DB}^2[/tex]

DB = 21 units, which gives;

[tex]\overline{BC}^2[/tex] = 20² + 21² = 841

BC = √(841) = 29

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Line a and line b are parallel to each other, and c is neither parallel nor perpendicular.

Line a passes through (2, 10) and (4, 13).

Line b passes through (4, 9) and (6, 12).

Line c passes through (2, 10) and (4, 9).

If a line passes through two points, then the slope of the line is

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Line a passes through (2, 10) and (4, 13).  So, the slope of this line is

[tex]m_{a}=\frac{13-10}{4-2}=\frac{3}{2}[/tex]

Line b passes through (4, 9) and (6, 12).  So, the slope of this line is

[tex]m_{b}=\frac{12-9}{6-4}=\frac{3}{2}[/tex]

Line c passes through (2, 10) and (4,9).  So, the slope of this line is

[tex]m_{c}=\frac{9-10}{4-2}=\frac{1}{2}[/tex]

The product of slopes of perpendicular lines is -1.

and if the slope of 2 lines is equal then those lines are parallel

so, line a and line b are parallel to each other, and c is neither parallel nor perpendicular.

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ANSWER: 137

Step-by-step explanation:

This can be rewritten as:

18 × 7 - (-1)² -(-9)

Using BODMAS

firstly open the brackets using the negative sign, we have;

18 × 7 +1² + 9

Now you can apply your BODMAS.

126 + 1 + 9

ANS = 137

Answer:

-1/4 * x + 2

Step-by-step explanation:

first figure out the slope. You can easily read the point where the graph is crossing the y axis. From there, more right and read how much the graph goes up wor down. You see the graph goes down, so you know the slope must be a negative value. To get the full value of the slope, you need to work out how much the graph goes down if you go 1 right. So when you move 1 right from the point 2 on the y axis, you can't easily read how much it went down. But you can see that the graph passes the pont of x = 4 and y = 1. So it went 4 right and 1 down. To only got 1 down you divide y/x -> 1/4
So the slope is -1/4
and because the graph hits the y axis at 2 and not at 0, you need to add +2 to the equation.

Answer: The volunteers are unaware of which surgery they receive.

Step-by-step explanation:

The 27.4 m² of carpet is needed for three bedrooms.

Firstly we will calculate the area of each room.

Area of bedroom a = 3.1 × 3.1

Area of bedroom a = 9.61 m²

Area of bedroom b = 2.9 × 3.2

Performing multiplication on Right Hand Side of the equation

Area of bedroom b = 9.29 m²

Area of bedroom c = 2.5 × 3.4

Area of bedroom c = 8.5 m²

Total area of all the rooms = 9.61 + 9.29 + 8.5

Performing addition on Right Hand Side of the equation

Total area of all the rooms = 27.4 m²

Hence, 27.4 m² carpet is required for three bedrooms.

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Using the concepts of the hypothesis test, it is found that the p-value is of 0.0007 corresponding to  ten students who  were surveyed and asked how many hours they spent playing video games.

At the null hypothesis, we test if the mean is still the same, that is, of 10.2 hours per week, thus:

H[tex]_o[/tex] = μ=10.2

At the alternative hypothesis, we test if the mean has increased, that is, if it is greater than 10.2 hours per week, thus:

H₁=μ> 10.2

Ten students were surveyed, so there are 9 df. The test statistic is t = 0.45, and it is a one-tailed test, as we are testing if the mean is greater than a value.

Thus, using a t-distribution calculator, the p-value of the test is of 0.0007.

Hence, when the ten students were surveyed and asked how many hours they spent playing video games and the test statistics is equal to 0.45,then the p-value is 0.0007

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The equation of the line in slope - intercept form will be -

y = (4/5)x + 5

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

At [c] = 0 -

y = mx

We have a directly proportional relation.

The general equation of a straight line is -

[y] = [m]x + [c]

At [c] = 0, y = mx

m = y/x

where [m] acts as a constant of proportionality.

So -

y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.

Therefore, y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.

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The area of the parallelogram shown in this problem is of:

A = 432 units squared.

The area of a parallelogram of base b and height h is given by the multiplication of these two dimensions, as presented as follows:

A = b x h.

In this problem, these dimensions are given as follows:

(the height is perpendicular to the sides of the parallelogram, forming an angle of 90º, as is the case in this problem).

Hence the area of the parallelogram, applying the multiplication of the obtained base and height, is calculated by the multiplication of the base and of the height given as follows:

A = 27 x 16 = 432 units squared.

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Answer:

432

Step-by-step explanation:

The area of a parallelogram is the product of a side length (the base) and the perpendicular distance between that side and the opposite side (the height). In this case, we can use (line)DC as a base and (line)EG as the matching height, so the area is equal to

(DC) ∙ (EG) = 27 ∙ 16 = 432.

The probability that Roger Federer wins at least 2 Grand Slam titles is 60.82%

Given data:

To calculate the probability that Roger wins at least 2 Grand Slam titles out of the 20 competitions during the 5-year period, we can use the binomial distribution.

The binomial distribution calculates the probability of obtaining a certain number of successes (in this case, Roger winning a Grand Slam) in a fixed number of independent trials (the 20 competitions), given the probability of success in a single trial (0.1).

We need to calculate the probability of Roger winning 2, 3, 4, ..., up to 20 Grand Slam titles and then sum those probabilities to find the overall probability of winning at least 2 titles.

Using a binomial probability formula, the probability of getting exactly k successes in n trials is given by:

[tex]P(X = k) = C(n, k) * p^k * (1 - p)^{(n - k)}[/tex]

Where:

C(n, k) is the binomial coefficient (n choose k)

p is the probability of success in a single trial (0.1)

n is the number of trials (20)

To find the probability of winning at least 2 Grand Slam titles, we calculate the probabilities for k = 2, 3, 4, ..., 20, and sum them up:

P(X ≥  2) = P(X = 2) + P(X = 3) + ... + P(X = 20)

P(X ≥  2) = Σ(P(X = k)) from k = 2 to 20

Calculating each individual probability P(X = k) and summing them up can be tedious. However, use complementary probability to simplify the calculation:

P(X ≥  2) = 1 - P(X = 0) - P(X = 1)

[tex]P(X = 0) = C(20, 0) * 0.1^0 * (1 - 0.1)^{(20 - 0) }[/tex]

[tex]=(1 - 0.1)^{20}[/tex]

= 0.12157

[tex]P(X = 1) = C(20, 1) * 0.1^1 * (1 - 0.1)^{(20 - 1) }[/tex]

[tex]= 20 * 0.1 * (1 - 0.1)^{19 }[/tex]

= 0.27017

P(X ≥  2) = 1 - 0.1074 - 0.2684

P(X ≥ 2 ) = 0.60826 (approximately)

Hence, the probability that Roger Federer wins at least 2 Grand Slam titles out of the 20 competitions is approximately 0.60826, or 60.82%.

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The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

When two triangles ΔABC and ΔXYZ are similar then

                    AB/XY = BC/YZ = AC/XZ

Here we have

ΔABC and ΔOPQ which are similar and right-angled triangles

As we know in a right-angled triangle

=>  Hyp² = side² + side²  

From ΔABC,

AB² = AC² + BC²  

=> AB² = 6² + 4²

=> AB² = 100 = 10²

=> AB = 10 units

Since  ΔABC and ΔOPQ are similar

=>  AB/OP = BC/OQ = AC/PQ  

=>  10/OP = 4/ f = 6/ 6

Take 10/OP = 6/ 6  

=>  6(10) = 6(OP)

=>  OP = 10 units  

4/ f = 6/ 6  

=> f = 4 units    

Therefore,

The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units

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