Pythagorean Theorem
Find the length of the third side, write in simplest radical form if needed.

A graph which represents the solutions to this quadratic equation (x² + 8x = -20) is: B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8).

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve.

In conclusion, we can reasonably infer and logically deduce that the given quadratic equation is modeled by an upward parabola with its vertex at (-4, 4) as shown in the graph attached below.

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The simple interest formula is:

A = P(1 + rt)

where A is the final amount, P is the princiapal, r is the annual interest rate (as a decimal), and t is time in years.

Substituting with A = $4,440, P = $3,000, and r = 0.12 (= 12/100), we get:

Let's use the variable x to represent the number of pizzas Ms. Ruggiero can buy.

If each pizza is $8.75, the wings are $4.25, the tax is 9.25% and the tip is 15%, and all this needs to be lesser than or equal 50, we have the inequality:

So Ms. Ruggiero can buy 4 pizzas with $50.

We are given the following system of equations:

To solve the system we will add equations (1) and (2):

Adding like terms:

Now we multiply equation (2) by -2:

Now we add this equation to equation (3):

Adding like terms:

Now we add equations (4) and (5):

Adding like terms:

Dividing both sides by -2:

Now we replace this value of "x" in equation (4):

Subtracting 1 to both sides:

Now we replace the values of "x" and "y" in equation (1):

Adding like terms:

Subtracting 5 to both sides:

Therefore, the solution of the system is:

Right Triangles

A right triangle is identified because it has an interior angle of 90° (right angle). The other two angles must be acute and add up to 90°.

In the special case that both acute angles have a measure of 45°, then we have an isosceles triangle, that is, both legs have the same length.

We can see one of the legs measures

Being this an isosceles triangle, the other leg (the base of the triangle) also measures L, thus you should drag

To the box at the bottom.

The other unknown length is the hypotenuse H. According to the Pythagorean's Theorem:

Substituting:

You should drag the length 10 to the hypotenuse.

We can get equation B from equation A by Adding the same quantity to both sides. The equations are equivalent and have the same solution.

The equations are:

A : 4x+2 = 6-x

B : 5x+2 = 6

(1) We can get equation B from equation A by adding x to both sides of the equation.

We can verify this.

Add x to both sides of the equation A,

⇒ 4x+2 +x = 6-x+x

⇒ 5x+2 = 6

This is equation B.

So Add the same quantity to both sides of equation A to get equation B.

(2) We just added a same quantity on both sides of equation A. This will not change the equations. So equation A and equation B are equivalent. Also they have same solution.

Equation A: 4x+2=6-x

⇒ 4x+x = 6-2

⇒ 5x = 4

⇒ x = 4/5

Equation B: 5x+2 = 6

⇒ 5x = 6-2

⇒ 5x = 4

⇒ x = 4/5

So both have same solution.

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Answer

Yes

Step-by-step explanation

Given the expression:

Combining similar terms:

Multiplying:

Using Volume formula, the height of the square pyramid is 5 cm.

If the side of the square base of the pyramid is b and height of the pyramid be h

Volume of the square pyramid , V is given by the below formula.

V = 1/3(b²h)

Given

Volume of the square pyramid, V = 60 cm³

base side is given , b = 6 cm

let Height of the square pyramid be h

⇒ V =  1/3(b²h)

⇒ 3V = b²h

⇒3V/b² = h

⇒ 3(60)/ 6² = h

⇒ h = 180/36 = 5

Therefore, the height of the given square pyramid id 5 cm.

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An inverse variation is represented as:

To find the missing value we need to find k first. Using the first pair we have:

Now, we plug the value of k and use the second pair to find y:

Therefore, y=24/5.

Answer:

14/5 or, 2 4/5.

Step-by-step explanation:

4/5 + 3/5 = 7/5, 7/5 + 7/5 = 14/5

14/5 as a mixed number is 2 4/5.

I think you're talking about fractions so.

We know that 30% of the members are in 6th grade, and add up to 12 members.

Lets X be the total members.

Then 0.3*X are in 6th grade, and this is equivalent to 12 members.

NOTE: 0.3 is the decimal form of 30%.

We can write:

Answer: there are 40 members in the Debate Club.

7. Tan A = opposite/adjecent

Therefore Tan A = 24/7

• Option number (2) is correct .

8. Cos Q = adjacent/hypotaneus

where hypotaneus side : r^2 = x^2+y^2

r^2 = 12^2 +5^2= 169

r =√169 = 13

Now Cos Q = 12/13

• Option 4 is correct .

The given inequality is expressed as

Exponents and powers are terms that occasionally get used interchangeably, which can be confusing.

Mathematics uses expressions called powers, where n is the exponent and x is the base. When a number or variable is multiplied repeatedly, it is referred to as a power. The exponent of power tells us how many times to multiply the base by itself.

You can interpret the term as "x to the power." The exponent (n) is written smaller and at the head of the line using superscript, whereas the base (x) is printed in full size (if you are typing it on a computer). For instance, it is written as x squared or x to the second power, which in reality means that the value of x is multiplied by an amount equal to the exponent's value.

If the base is a number: In this situation, all you have to do to discover the solution is multiply the base by itself as many times as the exponent's value.

If the base is a variable, you must first replace the variable with a value before continuing.

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Here, we want to find the function h(x)

From the question, we can see that the function f(x) is a composite function that was obtained by fitting g(x) into h(x)

What can we notice about g(x) and f(x)?

What we can see is that f(x) is the square of g(x)

Thus, what this mean is that h(x) = x^2

Answer:

Angle 3 = 95° (vertically opposite angles)

Angle 2 and 4 = 180 - 95

= 85° (adjacent angles on straight line)

Angle 5 = 180 - 144

= 36° (adjacent angles on straight line)

Angle 6 = 180 - angle 3 - angle 5

= 180 - 95 - 36

= 49° (sum of angles in triangle=180)

Angle 1 = 180 - 90 - angle 6

= 180 - 90 - 49

= 41° (sum of angles in triangle=180)

Angle 7 = 180 - 38 - angle 5

= 180 - 38 - 36

= 106° (sum of angles in triangle=180)

Explanation:

Since L is the midpoint of JM, then JL = LM.

Therefore,

Statement: JL = LM

Reason: L is the midpoint of JM

The lines JK and NM are parrallel; therefore, by the alternate interior angles theorem,

Furthermore, since ∠JLK and ∠MLN are vertical angles,

Now since ∠JLK = ∠MLN, ∠LJK = ∠LMN, and JL = LM, then by ASA postulate

Hence, our proof is complete!

The figure represents : Line

What is a Line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.

from the figure we have to find that  whether its a line, line segment, vertex or ray

Line: A line is a perfectly straight, one-dimensional shape that extends infinitely in both directions and has no thickness. Sometimes a line is referred to as a straight line or, more formally, a right line.

Line segment: In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters or conventional measures like feet or inches.

Ray: A ray is a vector from a point to another point when seen as a vector. A ray is typically viewed in geometry as a half-infinite line, or half-line, with one of the two points and assumed to be at infinity.

Vertex: A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.

The figure represents a Line

Hence,  The dashers part of the figure represent a Line

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Simple interest is a clear and simple method for computing financial interest. Simple Interest is the amount returned for using the borrowed funds over a predetermined amount of time.

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

Simple Interest is the amount returned for using the borrowed funds over a predetermined amount of time.

A = P(1 + rt)

Simple interest is a method for figuring out how much interest was paid on a sum of money during a specific time period at a specific rate. Simple interest has a constant principle amount. Simple interest is a clear and simple method for computing financial interest.

Therefore, the correct answer is option D. $715.15.

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Answer:

y=-4/3x

Step-by-step explanation:

There is no b because it starts at the origin.

Answer:

-4/3x is the correct answer as provided by IceJadeKitsune

I am merely providing an explanation in case you are curious

Step-by-step explanation:

The equation for a line in slope-intercept form is

y = mx + b

where m is the slope and b the y-intercept

The slope of a line, m can be determined by what is called the rise/run ratio

The process is as follows

From the graph choose points origin (0, 0)  which is one point where the line crosses the y axis

From the graph we see that another distinct point where the line passes is at x = -3, y = 4 or the point(-3, 4)

Having got these two points we calculate
rise = 4 - 0 = 4
run = -3 - 0 = -3
Slope m = -4/3

Slope is negative because as y increases, x decreases

So the equation is y = -4/3x + b

Looking at the graph, we see that b = 0 since the graph passes through the origin as correctly stated by  IceJadeKitsune


Therefore the equation of the line is [tex]\boxed{\bold{y = -\dfrac{4}{3}x}}[/tex]

To be able to get the enlarged dimensions, we will multiply the dimension of the poster by the given scale factor 5/2.

We get,

Therefore, the enlarged dimension of the poster will be 7.5 ft. x 30 ft.

Solution:

Amount needed (P): $9,350

Time in years (n): 3

Interest (r): 5%

Compounded: semiannually

To find the Amount (A).

we have the formula A, we get,

The present value is $10,843.133

Conditional equations - Mischa's dives take her 6.5 meter

What are conditional equations?

An equation that holds true for one or more values of the variable but holds false for other values of the variable is known as a conditional equation.

Explain the airthematic mathematical operations.

it deals with the study and use of numbers in all other branches of mathematics.  Basic operations include +,-, x, and /.

We frequently employ these fundamental mathematical operations in our daily lives: +, -,x, and, /. For every such area of our lives, we apply mathematical operations, whether it be to figure out the annual budget or distribute things evenly to a lot of people.

Mischa dives from a platform that is 5 meters above the water.

Her dive take her 1.7 meters below the surface of the water.

The total distance of Mischa's dive take her will be,

5+1.7meters

=6.7 meter

thus Mischa's dives take her 6.5 meters far.

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Let:

A = (-4,3)

B = (-1,3)

C = (-1,1)

after a 90 clockwise rotation:

A = (-4,3)--------->(y,-x)------->(3,4)

B = (-1,3)----------->(y,-x)------>(3,1)

C = (-1,1)------------>(y,-x)------>(1,1)

After a translation 3 units down and 2 units left:

(3,4)------>(x-2,y-3)------->(1,1)

(3,1)------>(x-2,y-3)------->(1,-2)

(1,1)------>(x-2,y-3)------->(-1,-2)

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

Therefore, the answer is D

The given vector is

The formula to find the direction angle is

Replacing each coordinate, we have

The amount of jumping packs in 1 minute is 21

From the question, the given parameters are:

Number of jumping packs in a row = 84 packs

Number of minutes = 4 minutes

The amount of jumping packs in 1 minute is the quotient of the number of jumping packs in a row and the number of minutes

This is represented as

Jumping packs in 1 minute = Number of jumping packs in a row /Number of minutes

Substitute the known values in the above equation

Jumping packs in 1 minute = 84/4

Evaluate

Jumping packs in 1 minute = 21

Hence, the jumping packs in 1 minute is 21

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The record holder makes 21 jumping jacks in 1 minute which is the ratio of the number of jumping jacks performed in a row to the total number of minutes.

A ratio is a relationship between two amounts that is represented by the division of one by the other.

The ratio of the total number of jumping jacks performed in a row to the total number of minutes determines how many jumping jacks should be performed in a minute.

No. of jumping packs in a row = 84 packs

No. of minutes = 4 minutes

So jumping packs in 1 minute = 84/4

Apply the division operation to get

Jumping packs in 1 minute = 21

Therefore, 21 jumping jacks should be performed in 1 minute.

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Let's use the following formula:

where:

Ao= Initial amount

t = time

h = half-life

solve for t:

Answer:

1 = yes

2 = no

3 = no

4 = yes

5 = yes

6 = no

7 = no

8 = no