What is the ratio of tan θ?.

The value of x that makes both triangles congruent is x = -1 and x = 5

An equation is an expression showing the relationship between numbers and variables.

Two triangles are congruent if their corresponding sides are equal to each other and their angles are also equal.

Since triangle ABC is congruent to DEF, hence:

BC = EF

Substituting:

4x - 2 = x² - 7

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x + 1)(x - 5) = 0

x = -1 and x = 5

The value of x is x = -1 and x = 5

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Answer:

26 skittles are not red

Explenation:

35%of 40 is 14 because 40*0.35=14 red skittles

total number of skittles (40)-red skittles (14)=26

Answer:

26 skittles are not red

Step-by-step explanation:

Simplify the percentage.

35% = 35/100 = 0.35

Multiply 40 by 0.35.

40 x 0.35 = 14 (This is how many skittles are red.)

Now subtract the red skittles from the packet.

40 - 14 = 26

Hence, there are 26 skittles that are not red, and 14 skittles that are red.

The triangle with sides 56 , 55 and 43 is acute triangle

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ABC

Now , the base of the triangle is BC

The measure of BC = 43

The height of the triangle is AB

The measure of AB = 55

The hypotenuse of the triangle is AC

The measure of AC = 56

Now , if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

On simplifying the equation , we get

BC² + AB² > AC²

Substituting the values in the equation , we get

43² + 55² > 56²

1849 + 3025 > 3136

4874 > 3136

Hence , it is an acute triangle

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A collection of values for the variable that simultaneously satisfy each equation in a system of equations is referred to as the solution.

Typically, a system of linear equations consists of a pair of two-variable linear equations.

1. Examine substitution and elimination as two strategies for algebraically resolving systems of linear equations.

2. Use graphical representations of systems of linear equations to better grasp when these systems have a single solution, none at all, or an unlimited number of solutions.

3. Learn about algebraic techniques for counting the number of solutions to systems with two linear equations.

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The point that is equally spaced from a triangle's three vertices is known as the circumcenter.Triangle ABC's equilateral circumcenter is (-5, 2) .

The point that is equally spaced from a triangle's three vertices is known as the circumcenter.

The triangle's three vertices are all located at the center of the circle.We may insert the coordinate values for the triangle ABC's vertices A(-5,3), B(5,8), and C(-5.8) into the formulas above to determine its circumcenter.

x = (8 - 3) * (-5.8^2 + 3^2 - 5^2 - 8^2)

- (3 - 8) * (-5^2 + 3^

2 - (-5) (-5)

^2 -3^2) / 2 * (3 - (-5))

* (8 - 3) - (3 - 8) * (-5.8 - (-5))

x = (-5) (-5)

y = (3 - (-5.8))

* (-5^2 + 3^2 - (-5)^2 -3^2)

- (-5 - (-5))

* (3^2 + 3^2 - (-5.8) (-5.8)

^2 - 8^2)

/ 2 * (3 - 8) (3 - 8)

* (-5 - (-5))

- (3 - 8) * (3 - (-5.8))

y = 2

The circumcenter of triangle ABC is hence (-5, 2)

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Answer: To find the coordinates of P, we will use the part-to-whole ratio of 1 to 5. This means that the distance from A to P is 1/6 of the distance from A to B.

We can find the distance from A to B by using the distance formula:

d = √((x2-x1)² + (y2-y1)²)

where (x1, y1) and (x2, y2) are the coordinates of A and B, respectively.

So, the distance from A to B is:

d = √((1-(-9))² + (8-3)²) = √((10)² + (5)²) = √(100 + 25) = √125 = 5√5

Since P partitions AB with the ratio 1 to 5, the distance from A to P is 1/6 of the distance from A to B, which is (1/6) * (5√5) = √5

To find the coordinates of P, we will use this distance and the direction from A to B to find the coordinates of P.

The direction from A to B is:

(1 - (-9))/(8 - 3) = 10/5 = 2

So, the slope of line AB is 2. Therefore, the slope of line AP is -1/2 (perpendicular to AB)

We know that A = (-9, 3) and the slope of line AP = -1/2. We can use this to find the equation of the line AP:

y - 3 = -1/2(x + 9)

y = -1/2x - 3/2 + 3

y = -1/2x + 3/2

Since the point A is on the line, we can substitute the coordinates of A into the equation:

3 = -1/2*(-9) + 3/2

3 = 4.5

This is not true, so we can say that the equation is wrong.

To find the equation of line AP, we can use the point-slope form of a line:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

So, the equation of line AP is:

y - 3 = -1/2(x + 9)

Now we know that the point P is on the line AP and the distance from A to P is √5.

We can use this information to find the coordinates of P by moving along the line AP by √5 units in the direction of P.

To move in the direction of P, we need to move parallel to the line, which means we need to keep the slope of the line same.

So we can move

Step-by-step explanation:

It is called an isosceles right angle triangle.

In a right angle triangle there is one right angle present.

In an isosceles triangle two sides are equal to each other.

But in isosceles right angle triangle both the conditions got fullfield i.e., there is one right angle with other two sides are equal to each other.

Properties of isosceles right angle triangle:

1. The two sides are equal to each other i.e. the base of the triangle is equal to the perpendicular of the triangle.

2. There is only one right angle and other two angles must be equal to each other.

3. The other two angles in isosceles right angle triangle must be 45 degree each.

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Answer:

10

Step-by-step explanation:

Since 3/3 = 1, then:

3/3 × 10 = 1 × 10 = 10

(a) FIFO: The oldest unit would be the one purchased on April 27 for $231. Therefore, the gross profit for April would be the difference between the selling price and the cost of the unit sold, which is not provided in the information given. The ending inventory on April 30 would be zero, as all units were sold.

(b) LIFO: The newest unit would be the one purchased on April 27 for $231. Therefore, the gross profit for April would be the difference between the selling price and the cost of the unit sold, which is not provided in the information given. The ending inventory on April 30 would be one unit, as one unit was not sold.

(c) Weighted Average Cost: The cost of the unit sold would be the average cost of all units purchased, which is $231. Therefore, the gross profit for April would be the difference between the selling price and the average cost of all units, which is not provided in the information given. The ending inventory on April 30 would be zero, as all units were sold.

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The newest unit would be the one purchased on April 27 for $231. Therefore, the gross profit for April would be the difference between the selling price and the cost of the unit sold, which is not provided in the information given. The ending inventory on April 30 would be one unit, as one unit was not sold.

If  DE=8 and EF=3 then the length of DF is 8.54 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

DEF is a given triangle.

DE is the opposite side of the triangle.

EF is the adjacent side of the triangle.

DF is hypotenuse.

By using pythagoras theorem we find the DF.

DE²+EF²=DF²

8²+3²=DF²

64+9=DF²

73=DF²

Take square root on both sides

DF=√73=8.54

Hence, the length of DF is 8.54 units.

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To solve complex numbers using steps:

A complicated equation is one that requires the use of complex numbers to solve. A number with both a real element and an imaginary part is referred to as a complex number. It is written as follows: A and B in the previous equation both denote numerical values. A complex number is, as an illustration, <4+3i>.

In order to accomplish vaguely defined goals that cannot be attained through normal behaviors, complex issue solving is a set of self-regulated psychological processes and activities. A wide range of tactics and inventive knowledge combinations are required.

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The set of values that satisfy a given set of equations or inequalities is known as a solution set in mathematics.

The solution set, for instance, is the subset of a set of polynomials over a ring on which all of the polynomials formal disappear (evaluate to 0).

Plug in each value from the replacement set and evaluate both sides of the equation to determine the solution set from the replacement set. The value is a solution to the equation if the two sides are equal. One example: From the replacement set, choose the set with the solution 11 - 5w = 1.

The set of values that satisfy a given inequality is called a solution set. This indicates that the inequality will be satisfied by every value in the solution set and by no other value. Example: 2x + 3  7, where x is a natural number, is the solution.

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The value of x is 1.

On comparison, when two or more triangles have some common relations with respect to their sides or measure of internal angles, they are said to be similar.

To find the value of x, compare the corresponding sides of the two triangles.

To have;

7x/ 9x = (8x - 1)/ (10x + 1)

9x (8x - 1) = 7x(10x + 1)

72x^2 - 9x = 70x^2 + 7x

collect like terms

72x^2 - 70x^2 - 9x + 7x = 0

2x^2 -2x = 0

2x(x - 1) = 0

2x = 0 or x - 1 = 0

x = 0. or x = 1

Therefore,

x = 1

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Answer:

Step-by-step explanation:

ur mom ur mommy

27.5% percent of the men surveyed shop online.

When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage.

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. (Value/Total Value)100% is the formula used to calculate percentages.

The simplest way to use percentages is to compare two numbers, with the second number being rebased to 100. Consider that we are curious about the proportion of employed women who are female.

A % is a number or ratio stated as a fraction of 100 in mathematics (from the Latin per centum, "by a hundred"). The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed.

Store = 37 women

Total women:  37/49 = 0.75%

Men: shop equals 52

Total men: 11 /40 = 27.5%

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30-60-90 and 45-45-90 triangles are called special right triangles because they have specific ratios of their side lengths.

A 30-60-90 triangle is a special right triangle in which the angles measure 30 degrees, 60 degrees and 90 degrees, and the side length ratio is 1: √3: 2.

where the hypotenuse is twice the length . 45-45-90 triangle is a special right triangle in which the angles measure 45 degrees, 45 degrees and 90 degrees, and the side length ratio is 1:1: √2, where the hypotenuse is the square root of 2 times the length of each leg.

These ratios are unique and special among right triangles, which makes these triangles special. They are also easy to remember and use in various mathematical calculations. Because of this property, they are widely used in trigonometry and geometry and are very useful in solving problems related to the right triangles in general.

Additionally, these triangles have certain symmetry and specific relationships between the legs and hypotenuse, which makes it easy to calculate unknown sides or angles in a triangle. This makes them very useful in real-world applications such as construction, engineering, and design.

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Yes, the square root of 64 is a rational number.

and Square root of 64 is 8

Now, According to the question:

Square numbers are those numbers that are produced by multiplying an integer to itself. If n is an integer, then n2 is the square of n.

What are the examples of square numbers?

The examples for square numbers are:

[tex]6^2[/tex] = 36

[tex]10^2[/tex] = 10 x 10 = 100

[tex]15^2[/tex] = 15 x 15 = 225

[tex]12^2[/tex] = 12 x 12 = 144

Hence, Yes, the square root of 64 is a rational number. As we know that √64 = 8, a rational number.

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Functions y = A sin(Bx + C) and y = A cos(Bx + C) have periods of 2 /|B| radians each. A function's frequency is equal to the reciprocal of its period.

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The law of Sines is used to find the length of the third side of an obtuse triangle. The value of a i.e., third side length is equals to 6.065 units.

In geometry, obtuse triangles are defined as the triangles with an obtuse angle, which is an angle measuring greater than 90°. According to the law of sines of triangles if a triangle has sides a, b, and c, and angles A, B, and C, where side a has opposite angle A, side b has opposite angle B, and c has opposite angle C, then

sinA/a = sinB/b = sinC/c

The sum of all interior angles of a triangle is 180°. If we have two of the sides of an obtuse triangle, and two of the angles of an obtuse triangle, then we can use the law of sines to determine the third side of the obtuse triangle. Let's consider an obtuse triangle ABC present in above figure. We want to find the length of side a. We have, AB = 8 units , AC = 5 units, BC = a units.

∠A = 32° , ∠B =40° , ∠C = obtuse angle

=>∠C = 180°-∠A - ∠B = 180°- 32°- 40° = 108°

From above formula, sinA/a = sinB/b= sinC/c

=> sin 32°/5 = sin 40°/a = sin 108°/8

=> a = 5 sin 40°/ sin 32°

=> a = 5×0.6428/0.5299

=> a = 6.06529533874

=> a ≈ 6.065

Therefore, the length of third side is 6.065 units.

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Answer:

C

Step-by-step explanation:

It can't be a or d because 15.75x needs to be greater than 145, so in c the how many he sells would represent the x value.

It would cost $224 to buy 56 party favors.

A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation. It is a mathematical problem expressed entirely in words typically used as an educational tool.

Word problems are regarded as an important aspect of the basic curriculum because they require students to apply their understanding of various concepts to real-life settings.

If the packages cost $4 each then 56 packages will cost 56 * 4 dollars.

we get, 56 * 4 = $224

Thus, it would cost $224 to buy 56 party favors.

Complete question: Football party favors come in packages like the one shown. How much would it cost to buy 56 party favors? Think about how you can model with math to help solve the problem. It's $4 per package.

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The angle measures that are correct include:

m2 = 125°

m8 = 55°

m14 = 100°

m16 = 80°

An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

Here, the measurement of the angles are as follows;

m3 = 55°

m8 = 55°

m12 = 100°

m14 = 100°

m16 = 80°

m9 = 80°

m12 = 80° (opposite angles)

m10 = m11 = 100°  ( 180° - 100°)

m13 = m16 = 80°

m14 = m15  = 100°

m14 = 100°  

m16 = 80°

m5 = m8 = 55°

m2 = m3 = 125°

m2 = 180° - 55° = 125°

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Lines e and f are parallel. The m9 = 80° and m5 = 55°. Which angle measures are correct? Check all that apply. m2 = 125° m3 = 55° m8 = 55° m12 = 100° m14 = 100° m16 = 80°

The equation for a line that passes through the points (-5, 3) and (3, -3) is y=-3/4(x+1)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope of line that passes through the points (-5, 3) and (3, -3)

m=-3-3/3+5

m=-6/8=-3/4

Now let us find y intercept.

3=-3/4(-5)+b

3=15/4+b

b=3-15/4

b=-3/4

So the slope intercept form is y=-3/4x-3/4

Hence, the equation for a line that passes through the points (-5, 3) and (3, -3) is y=-3/4(x+1)

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Y form is the slope-intercept form of a straight line.

Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.

The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.

To find the equation of the straight line, we use the slope-intercept form, y = mx + b, where m is the slope of the line, b is the y-intercept of the line.

We can find the equation of a line in the form of y = mx + b, if the coordinates of points forming the line are known to us.

Thus, Y form is the slope-intercept form of a straight line.

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Examples of the rules followed while applying multiplication are :

1. 0 × 9 = 0

2. 1 × 7 = 7

3. 12 × 10 = 120 , 12 × 100 = 1200.

4. 11 ×12 = 12 ×11

As given in the question,

Examples of the multiplication rules are :

1. Multiply any number by zero result is zero.

Example : 0 × 9 = 0

2. Multiply  One  to any real number result is the number itself.

Example : 1 × 7 = 7

3. Multiply any real numbers with 10 , 100 you have just add number of zero present.

Example : 12× 10 =120

12× 100 =1200

4.Order of the multiplication does not affect the result.

Example : 11 × 12 = 12 × 11

Therefore, the examples of multiplication rule  are :

1. 0 × 9 = 0

2. 1 × 7 = 7

3. 12 × 10 = 120 , 12 × 100 = 1200.

4. 11 ×12 = 12 ×11

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The probability that a randomly chosen college student exercises in the morning or afternoon is 0.76

We have given that the M be the event that the student exercises in the morning and A be the event that the student exercises in the afternoon.

To find : The probability that a randomly chosen college student exercises in the morning or afternoon

P(M) = 0.25+0.37 = 0.62

P(A) = 0.14+0.37 = 0.51

P(M and A) = 0.37

Now,

P(M or A) = P(M) + P(A) - P(M and A)

                = 0.62 + 0.51 - 0.37

                = 0.76

Hence, Option last 0.76 is the correct choice.

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Answer:

28+24 can be written as a product of two factors using the GCF and the distributive property as: (12 x 2) + (12 x 2) = 12 x (2+2) = 12 x 4 = 48

Answer:

No

Step-by-step explanation:

Notice when x increases by 1, y increases by $6?

When x goes from 1.5 to 2.5 gigabytes ( increase by 1 ), y increases from $65 to $71. That's a $6 increase for x increasing by 1 gigabyte.

In addition, when x goes from 2.5 to 3.5 gigabytes ( increase by 1), y increases from $71 to $77. This is also a $6 increase for x increasing by 1 gigabyte.

Yet...

65 / 1.5 doesn't equal 71 / 2.5

65 / 1.5 = 43 1/3

71 / 2.5 = 28.4

43 1/3 [tex]\neq[/tex] 28.4, so there is no proportion

Answer: No.

Step-by-step explanation:

      In a proportion relationship, y = kx. In other words, x times the constant of proportionality will equal y. Without a given constant of proportionality, we can use k =[tex]\frac{y}{x}[/tex]. In all instances, y divided by x should equal the same value (k). We will see if this stands true for all the given values.

      65 / 1.5 = 43.33333

      71 / 2.5 = 28.4

      74 / 3 = 24.66667

      77 / 3.5 = 22

      No. The x and y values do not have a proportional relationship.

A correct description of the transformation include the following: D. translation 10 units left and 4 units down.

In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.

On the other hand, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

By translating the pre-image of triangle ABC vertically down by 4 units and horizontally left by 10 unit, the coordinates of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 10, y - 4)

Coordinate A = (5, 2)   →    Coordinate A' (5 - 10, 2 - 4) = (-5, -2)

Coordinate B = (6, 1)   →    Coordinate B' = (6 - 10, 1 - 4) = (-4, -3)

Coordinate C = (4, 5)   →     Coordinate C' = (4 - 10, 5 - 4) = (-6, 1)

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Complete Question:

The table below shows the coordinates of a figure that was transformed.

Pre-Image Image

A(5,2) A'(-5,-2)

B(6,1) B'(-4,-3)

C(4,5) C'(-6, 1)

Which is a correct description of the transformation?

Question 4 options: Rotation 180° clockwise B. Reflection over the x-axis. Translation 5 units left and 2 units down. Translation 10 units left and 4 units down.

Answer: 16%

Step-by-step explanation: If 80% of customers purchased regular gas and 10% of those who purchased regular gas paid in cash, then 8% paid in cash. If 100-80=20% of customers purchased something other than regular gas and 40% of those who did paid in cash, than another 8% paid in cash. 8+8=16, so (c 16 is the answer.

There are 4 friends in the group.

Poker: In poker, the number of each card in the deck is important. A standard deck of poker cards has 52 cards, with 13 cards in each of the four suits (hearts, diamonds, clubs, spades). Each suit has cards numbered 2-10, plus a jack, queen, king and ace. This allows for the calculation of odds and probability in the game.

If each person received 12 trading cards and 48 cards in the package, you can use division to find how many people are in the group.

We know that:

48 trading cards / 12 trading cards per person = 4 people

Therefore, there are 4 friends in the group.

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You can use division to determine the number of people in the group if each person got 12 trading cards and there were 48 total cards in the package.

12 trading cards per individual times 48 trading cards equals four people.

As a result, the company consists of 4 friends.