5. Find the distance between (-1, -1) and (1, 1). Round to the nearest tenth if needed.

A. 6
B. 2.9
C. 2.8
D. 31

The quadratic equation is x²+10x+26=0

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here: Complex root of a quadratic equation is 5+i

And we know that complex roots always occur in pairs.

Thus the other root must be its conjugate as 5+i

The sum of roots will be given by 5+i+5-i=10

and product of the roots is given by (5+i) (5-i)=25-(-1)

                                                                           =26

∴ The quadratic equation is x²+10x+26=0

Hence, The roots are 5+i , 5-i

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A semicircle with diameter AB is constructed inside the square ABCD which has side length 2. CE is a tangent of the semicircle that intercepts side AD. The length of CE is 2.5 unit.

Information available from the problem:

- ABCD is a square with side length of 2

- A semicircle with diameter AB is constructed inside the square

- The semicircle's tangent from C intersects AD at point E.

The situation can be depicted in the attached picture.

Refer to the attached picture,

FG = FB = radius of semicircle = 1

Since EC is a tangent of the semicircle, then.

∠CBF = ∠CGF = 90⁰

CF is a common sides of triangle CBF and triangle CGF.

Since there are 2 equal sides and 1 equal angle, using SAS rule, triangle CBF and triangle CGF are congruent.

Hence,

CG = CB = 2

FG² = CG x GE

1² = 2 x GE

Hence,

GE = 1/2

CE = CG + GE

CE = 2 + 1/2 = 2.5

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Answer:

D. x-7

Step-by-step explanation:

less than means subtract so julians height would be x-7

you got this <3

Answer

X-7

Step-by-step explanation:

X is a unknown variable which is her sisters hight.

We do not know Julian’s sisters hight so that is X

Julian sister=x

Julian is 7 inches shorter than his sister so that is the same as -7

So to find his hight do x-7.

The probability of each outcome is 1/12 or 0.083.

The probability of each outcome in the sample space can be calculated using the formula for permutations. The formula for permutations is nPk = n!/(n-k)!. In this case n is the number of gift cards (4) and k is the number of gift cards to be selected (2).  In this example, the sample space consists of 16 possible outcomes, and each outcome is equally likely. Thus, the probability of each outcome is 1/16. To calculate this, divide 1 by the total number of outcomes (16). This results in the probability of each outcome being 1/16.Therefore, nPk = 4P2 = 4!/2! = 12. Since each outcome is equally likely, the probability of each outcome is 1/12 or 0.083. This can be written as a fraction as 1/12 or as a decimal as 0.083.

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23 minutes she will be devoting to weightlifting in week 10.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Formula represent the sequential increase in weight lifting time is :

f (n) = 2n + 5

f (n) = 2n + 5

f (10-1) = 2(10-1) + 5

f(9) = 2(9)

f(9) = 18

f(9) = 23

Therefore,23 minutes she will be devoting to weightlifting in week 10.

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The probability is 1/10.

The equation x(x+5) = -n can be rewritten as x^2 + 5x + n = 0. To find the solutions of this equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 5, and c = n.

For there to be no real solutions, the discriminant (b^2 - 4ac) must be negative. The discriminant is 5^2 - 4(1)(n) = 25 - 4n. So for there to be no real solutions, 25 - 4n < 0, or n > 6.25.

Since the integer n is between 1 and 10 inclusive, the only value that would not have a real solution is n = 7. Therefore, the probability that for the randomly chosen n there exist no real solutions is 1/10.

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Step-by-step explanation:

yer lady friend come wait ♥️

ksks ovq fir

The best estimate of the system solution to the nearest integer values is (2,3).

The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis. A point's Cartesian coordinates (also known as rectangular coordinates) are a pair of integers (in two dimensions) or a triplet of numbers (in three dimensions) indicating signed distances from the coordinate axis. A point's coordinates are a pair of integers that define its precise location on a two-dimensional plane. Remember that the coordinate plane contains two axes that are perpendicular to each other, known as the x and y axes.

Here,

This question is asking us what the coordinates are for the point of intersection. Since the point is not directly on the grid lines, we must approximate.

The point is closest to the value "2" on the x axis.

The point is closest to the value "3" on the y axis.

This means the correct point is (2,3).

The best approximation of the solution to the system to the nearest integer values is (2,3).

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Therefore , the solution of the given problem of linear equation comes out to be  $105 is the total cost

A linear regression model is one that uses the equation y=mx+b. The slope is B, and the y-intercept is m. The preceding sentence is commonly referred to as a "math equation with two variables," despite the fact that both y and x are separate factors. The only variables in bivariate linear equations are two. In all circumstances, the solutions to linear equations' application domains are zero. Y=mx+b is the formula for a single linear equation.

Here,

The first company's equation is y = 10.5x.

Additionally, the second company's equation is y = 7.5x + 30.

Where

number of T-shirts equals x.

y = overall cost

For the overall cost to be the same for both businesses, we have to:

=> 10.5x = 7.5x + 30

=> 10.5 x - 7.5 x = 30

=> 3 x = 30

=> x = 30/3

=> x = 10

To make the T-shirts' prices equal, the volleyball team must purchase 10 from each vendor.

Total for each business:

=> 10.5x = 10.5 (10) = $ 105

OR

Totals for each company are calculated as follows:

=> 7.5x + 30 = 7.5(10) + 30 = 75 + 30

=> $105

Therefore , the solution of the given problem of linear equation comes out to be  $105 is the total cost.

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the difference in volume between the two boxes is 1432.842 cubic inches.

In mathematics, volume is the space taken by an object.

here, we have,

A cereal box has dimensions of 12 inches, (7)3/4 inches, and 2 inches.

A pastry box has a dimensions of (3)2/3 inches, (3)1/2 inches, and (2)1/3 inches.

To find the volume of the cereal box, we multiply the length, width, and height:

12 inches * 7 and 3/4 inches * 2 inches = 96 inches * 7.75 inches * 2 inches = 1458 cubic inches

To find the volume of the pastry box, we multiply the length, width, and height:

3 and 2/3 inches * 3 and 1/2 inches * 2 and 1/3 inches = 3.666 inches * 3.5 inches * 2.333 inches = 25.158 cubic inches

To find the difference in volume between the two boxes, we subtract the volume of the pastry box from the volume of the cereal box:

1458 cubic inches - 25.158 cubic inches = 1432.842 cubic inches

hence, the difference in volume between the two boxes is 1432.842 cubic inches.

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Answer:

Step-by-step explanation:

the difference in volume between the two boxes is 1432.842 cubic inches.

On solving the provided question, we can say that Area of square = SxS=846 and perimeter of square = 4xS= 846/4=S= 211.5=Side.

A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.

Area of square = SxS=846

Perimeter of square = 4xS= 846/4=S= 211.5=Side.

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The correct question is -

A parking lot is shaped like a trapezoid as shown. If the area of the parking lot is 846 square meters, what is the perimeter? (Hint: The formula for the area of a trapezoid is (A=h2(b1+b2)

The completed table specifying the values obtained from the proportional relationship between the time in minutes and the number of cages cleaned is presented as follows;

Minutes; [tex]{}[/tex]             15         30       60          90

Cages cleaned;  [tex]{}[/tex]2           4          8           12  

Please find attached the graph of the above table created with MS Excel.

A proportional relationship is one in which the values of the output variable is a constant multiple of the input variable.

The time it takes the owner of Paradise Pets to clean the 2 hamster cages = 15 minutes

The table of values obtained from a similar question is presented as follows;

Minutes; [tex]{}[/tex]               15     30            90

Cages cleaned; [tex]{}[/tex]   2                8            

The relationship between the number of cages cleaned and the time it takes, taken as a proportional relationship, indicates that we get;

Cages cleaned = k × Minutes

Where;

k = The constant of proportionality

k = Cages cleaned ÷ Minutes

The number of cages cleaned in 15 minutes = 2 cages, therefore;

k = 2 ÷ 15 = 2/15

The number of cages cleaned in 30 minutes is therefore;

Cages cleaned = (2/15) × 30 = 4

The cages cleaned in 30 minutes = 4 cages

The time it takes to clean 8 cages is found as follows;

Minutes = Cages cleaned ÷ k

Minutes to clean 8 cages = 8 ÷ (2/15) = 60

The time it takes to clean 8 cages = 60 minutes

The number of cages cleaned in 90 minutes = (2/15) × 90 = 12

The number of cages cleaned in 90 minutes = 12 cages

The completed table is therefore;

Minutes; [tex]{}[/tex]             15           30        60      90

Cages cleaned; [tex]{}[/tex]  2           4           8        12  

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The total number of boys is 8 and that of girls is 22.

Let x be the number of boy members in the math club. According to the problem, the number of girl members is 2 less than 3 times the number of boy members, so we can write the equation:

G = 3*B - 2

We also know that the total number of club members is 30, so we can write the equation:

B + G = 30

We can substitute the first equation into the second equation to eliminate "G":

B + (3*B - 2) = 30

Combining like terms:

4*B - 2 = 30

⇒ 4*B = 30 + 2

⇒ 4B = 32

Dividing by 4:

∴ B = 34/4

⇒ B = 8

So there are 8 boy members in the math club. To find the number of girl members, we can substitute this value back into the first equation:

G = 3*8 - 2 = 22

So there are 22 girl members in the math club.

Therefore,

The number of boys = B = 8

The number of girls = G = 22

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The measure of ∠ ​ABC is 112°

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a shape with its angles.

Triangle BCD is an equilateral triangle. So all the angles are equal, that is 60° each.

∠ ​ADB = 64° (base angle of an isosceles triangle are equal)

∠ ​ABD = 180° - 64° - 64° (sum of angles in a triangle is 180°)

∠ ​ABD = 52°

∠ ​ABC = ∠ ​ABD + ∠ ​CBD

∠ ​ABC = 52° + 60°

∠ ​ABC = 112°

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Answer: in a triangle if all its angle measure less than 90 degree is called an acute triangle.

Step-by-step explanation: In equilateral triangle all of its 3 angle measure equally and are less than 90 degree thus making it an acute triangle.

1. The area of the shaded part = 95π

2. The area of the half circle = 12.5π

3. the distance of the bicycle = 0.0675/π inches

4. The diameter of the circle = 9 unit

radius = 4.5

area = 20.25π unit²

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

The area of a circle = πr²

1. Area of the shaded part = area of big circle - area of small circle

= 12²π - 7²π

= 144π - 49π

= 95π

2. area of semi circle = 1/2πr²

= 1/2×5²× π

= 25π/2

= 12.5π unit²

3. The distance moved by the biycle =

S = tetha/r

tetha = 2π×100 = 200π

S = 200π/13.5

S = 14.8π inches

4. c = πd

c = 9π

d = 9

r =d/2 = 9/2 = 4.5

Area = 4.5²π

A = 20.25π unit²

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3 ice cream machines will make a total of 480 gallons for the same length of time and 4 ice cream machines will make a total of 640 gallons for the same length of time.

For the quantity 3 ice cream machines will make.

2 ice cream machines produce a total of 320 gallons in a certain amount of time.

If 2 ice cream machines can make a total of 320 gallons. Then,

3 ice cream machines will produce a total of x gallons in the same amount of time

x = (320 × 3)/2

x = 480 gallons

Hence, 3 ice cream machines will produce a total of 480 gallons.

For the quantity 4 ice cream machines will make.

If 2 ice cream machines can make a total of 320 gallons. Then,

4 ice cream machines will produce a total of y gallons in the same amount of time

y = (320 × 4)/2

y = 640 gallons

Hence, 4 ice cream machines will produce a total of 640 gallons.

--The given question is incomplete, the complete question is

"Two ice cream machines make a total of 320 gallons in a certain amount of time. Working together for the same length of time, how many gallons of ice cream can each number of machines make?

3 ice cream machines

4 ice cream machines"--

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The probability to find the spin projection along the x-axis to be 1 is 0.5. The operator corresponding to the spin projection along the x-axis is X, and the expectation value of X in this state is 0.

This result is a consequence of the fact that operator X is a Hermitian operator, which means that its eigenvalues are real. The eigenvalues of X are ±1, so the probability of measuring a spin projection of 1 is ½. This is because the eigenstate corresponding to the eigenvalue 1 is |+⟩, which is a superposition of |0⟩ and |1⟩.

Similarly, the eigenstate corresponding to the eigenvalue -1 is |-⟩, which is also a superposition of |0⟩ and |1⟩. Thus, the qubit is equally likely to be found in either the |+⟩ or the |-⟩ state, and so the probability of measuring a spin projection of 1 is 0.5.

In summary, since the qubit is in a superposition of the two computational basis states, the expectation value of any Hermitian operator is 0, and the probability of measuring a spin projection of 1 is 0.5.

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Answer:

Jennifer

Step-by-step explanation:

The domain of a function is the set of x-values that result in defined and real values for that function.

In this case the requirement was to plot a graph so that the domain is between -4 and 5 inclusive

We can represent this mathematically as -4 ≤ x ≤ 5

If you look at both graphs, Ashton's graph on the left has a minimum
x-value of -4 and a maximum x-value of 5. So his graph is correct

Carlie's graph on the right does have a minimum x-value of -4 but its maximum x-value is between 2 and 3. So this graph is incorrect

Therefore Jennifer's statement is correct

Answer: Jennifer

The word "and" in probability implies that we use the Multiplication rule.

The correct option is Option D.

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

The relationship between two events is explained by the probability multiplication rule.

Set A∩B represents the events in which both events A and B have occurred for two events A and B related to a sample space S. Consequently, (A∩B) indicates that occurrences A and B happened at the same time. You can write the event A∩B as AB. Using the characteristics of conditional probability, the likelihood of event AB is calculated.

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Answer:

14/3

Step-by-step explanation:

Cross Multiply 6/7 by 4

6/7 x 4/1

= 28/6

Simplify

=14/3

Make a linear function that, after t minutes, returns the circle's radius in inches. The circle's radius will have increased by inches, hence the radius increases by inches [3 points]. Create a linear function that returns the circle's radius.

The slope-intercept form of a linear function equation. As a result, it is written as f(x) = mx + b, where m is the slope & b is the y-intercept of a line.

Therefore, the distance to the safe zone is 24 * 4 + 70, which is 166.

The formula should be D=166-24t. She needs to go 166 meters, and since she is approaching the safe place at 24 meters per second, her distance to the safe zone is decreasing by 24 meters per second, making the calculation -24 meters per second rather than 24 meters per second.

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The consecutive integers for the two roots are:

17) 14 < √214 < 15

18) 7 < ∛441 < 8

17) First, we want to find two consecutive integers such that √214 lies between them.

To do so, we just need to find two consecutive integers such that when we square them, one is smaller than 214, and the other is larger than 214.

For example:

13*13 = 169

14*14 = 196

15*15 = 225

Now we can see that:

14² < 214 < 15²

If we apply the square root we get:

14 < √214 < 15

Thes are the two integers.

18) Now we want to do the same thing, but this time with:

∛441

This time we need to cube our numbers.

7*7*7 = 343

8*8*8 = 512

These are the two integers such that:

343 < 441 < 512

Now we can apply the cube root to get:

∛343 <∛ 441 < ∛512

7 < ∛441 < 8

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The minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of miles per hour is 4.8708 seconds.

We can solve this problem easily by using the Pythagorean Theorem. This is because the distances from the cop car to the road form two legs of a right triangle. This makes the total length of this zone the hypotenuse of this triangle and thus, this problem can be solved using the Pythagoras theorem.

= (150)^2 + (200)^2 = h^2

= 62500 = h^2

= h = 250

Our distance is in feet, but our speed is in miles per hour. Let's convert this distance into miles as well.

= 250 feet × 1 mile/5280 feet = 0.04735 miles

Then, when we use the formula  d = rt

= 0.04735 = 35t

= 0.04735/ 35 ≈ 0.001353

Since our speed was in miles per hour, this time is also in hours. We need to convert this to seconds before we can state our final answer.

= 0.001353 hours × 60 minutes/1 hour × 60 seconds/1 minute = 4.8708 sec

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The inverse function of tangent (tan^-1) is also known as arctangent. The domain of arctangent function is all real numbers and its range is (-π/2, π/2).

The tangent function, tan(x), is defined for all real numbers x, but it's not defined when x = (nπ + π/2), where n is an integer. So the domain of the tangent function is all real numbers except (nπ + π/2), where n is an integer.

When we take the inverse of a function, we switch the roles of the domain and range, so the domain of the tangent function becomes the range of the inverse function and the range of the tangent function becomes the domain of the inverse function. The range of the tangent function is all real numbers, but it is not defined for (nπ + π/2), where n is an integer. So the domain of the arctangent function is all real numbers except (nπ + π/2), where n is an integer.

The range of arctangent function is (-π/2, π/2) because the range of arctangent function is the set of all possible values of the input of tangent function for which it is defined.

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The air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second is 1011.5 millibars.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

In a hurricane,

the mean sustained wind velocity v (in meters per second) can be modeled by v(p) = 6.3/(1013-p)

The mean sustained wind velocity = 54.5 M/s

To find the air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second:

That means,

the equation

54.5 = 6.3/(1013-p)

63 = (1013 - p)54.5

63 = 55208.5 - p54.5

p = 55145.5 / 54.5

p = 1011.844

Therefore, the air pressure is 1011.844 millibars.

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The inequality that shows the distance ran is 3x ≥ 4y

An equation is a expression that shows the relationship between numbers and variables.

Inequalities are used for the non equal comparison of numbers and variables.

Lena ran 3 miles each day for x days. Ivan ran 4 miles each day for y days.

Total number of miles that Lena ran = 3x

Total number of miles that Ivan ran = 4y

The total number of miles that Lena ran is at least the total number of miles that Ivan ran, hence:

3x ≥ 4y

The inequality is 3x ≥ 4y

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Answer: -2/5 is the answer.

Step-by-step explanation: