What is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial?

The scale factor when AABC is a dilation of ADEF with center (0, 0) is 1/3.

A scale factor is a number that scales, or multiplies, some quantity. In the context of geometry, a scale factor is a ratio that describes how the dimensions of one geometric figure are related to the dimensions of another similar figure. Similarly, if a two-dimensional shape is scaled up or down by a factor of k, then all of its linear dimensions (such as length, width, and height) are multiplied by k, and its area is multiplied by k².

Here,

In triangle ABC,

AB=6 units

In triangle DEF,

DE=2 units

Scale factor=DE/AB

=2/6

=1/3

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The value of this approximation will be 3.7678.

To approximate the integral of 4 1 (2x2 1) dx using a midpoint Riemann sum with 3 equal subintervals, the following calculations can be used:

Start by finding the width of each subinterval (w). Using the given bounds of integration, this can be calculated as: w = (b-a)/n, where n is the number of subintervals. In this case, w = (2-1)/3 = 0.3333.

Next, calculate the midpoint of each subinterval. This can be done by taking the average of the lower and upper bounds of each subinterval. In this case, the midpoints are 1.1667, 1.5, and 1.8333.

Finally, calculate the value of the midpoint Riemann sum by adding the product of the function evaluated at each midpoint and the width of each subinterval. This can be expressed as:

Sum = 0.3333 * [4(1.1667)2 -1] + 0.3333 * [4(1.5)2 -1] + 0.3333 * [4(1.8333)2 -1]

This gives a value for the midpoint Riemann sum of 3.7678.

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Answer:

x=-3 and y=1

Step-by-step explanation:

-4x+5y=17 ---------(i)

4x+6y=-6 ----------(ii)

Using elimination method;

Adding both equation:

-4x+4x+5y+6y=17+(-6)

11y= 17-6

11y=11

y=11/11

y=1

substitute y into equation (i) or (ii);

4x+6(1)=-6

4x+6=-6

4x=-6-6

4x=-12

x=-12/4

x=-3

Answer: [tex]\sqrt{41}[/tex]

Step-by-step explanation:

Using the distance formula: D = √(2 - 7)2 + (-6 - -2)2

= √(-5)2 + (-4)2

= √41

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ M(\stackrel{x_1}{7}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{2}~,~\stackrel{y_2}{-6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ MA=\sqrt{(~~2 - 7~~)^2 + (~~-6 - (-2)~~)^2} \implies MA=\sqrt{(2 -7)^2 + (-6 +2)^2} \\\\\\ MA=\sqrt{( -5 )^2 + ( -4 )^2} \implies MA=\sqrt{ 25 + 16 } \implies MA=\sqrt{ 41 }[/tex]

mind  you that the distance equation comes directly from the pythagorean theorem.

The solution of this mathematical expression (12 - x) . 5 when x = 2 is equal to: C. 50.

In Mathematics, a mathematical expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

In order to evaluate the given mathematical expression, we would substitute the value of x into the mathematical expression and then open the bracket as follows;

(12 - x) . 5

When the variable x = 2, the mathematical expression becomes;

Mathematical expression = (12 - 2) × 5

Mathematical expression = 10 × 5

Mathematical expression = 50

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The required number of ways the 6 medals can be distributed among boys and girls is 14400 ways.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
10 boys and 11 girls are competing, Number different ways, the six medals possibly be given out is,
= 10C3 × 10C3
= 14400

The required number of ways the 6 medals can be distributed among boys and girls is 14400 ways.

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1. ∠AHB and ∠AHG are vertical angles False

When two lines intersect, the angles that face each other are called vertical angles. Instead of referring to them as being up-down, "vertical" in this context denotes that they share a vertex (corner point).

2.∠EHF and ∠DHE are adjacent angles True

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have the same vertex and side, they can be a complimentary angle or supplemental angle.

3. The measure of ∠FHG is equal to the measure ∠DHF  True

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The full question and image are attached.

In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.

Answer:

move 5 blocks to the west.

Step-by-step explanation:

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The location of Katha after she walked west is -5 on the number line.

To find out what percent 567 is of 448, we can use the following formula:

What does math mean by percent?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

percent = (part / whole) x 100

where "part" is the value we are trying to find the percentage of (in this case, 567), "whole" is the total value (in this case, 448), and "percent" is the final answer.

So, we can plug in the values and get:

percent = (567 / 448) x 100

To get the percentage we need to multiply the fraction by 100

percent = 126.58%

So 567 is 126.58% of 448.

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Answer: A- 0.035

Step-by-step explanation:

The bicycle travels 2198 cm or about 21.98 meters for 10 complete revolutions of the tires.

What is the circumference of the circle?

The distance traveled by bicycle each time the tires make one complete revolution is equal to the circumference of the tire. The circumference is given by the formula:

C = 2 * π * r

Where C is the circumference, π is approximately 3.14, and r is the radius of the tire. Since the diameter of the tire is 70 cm, the radius is half the diameter, which is 70/2 = 35 cm. So we can substitute that value into the formula to find the circumference:

C = 2 * 3.14 * 35 = 219.8 cm

So the bicycle travels 219.8 cm each time the tire makes one complete revolution. To find out how far the bicycle travels each time the tires make 10 complete revolutions, we simply multiply the distance per revolution by 10:

distance = 219.8 cm * 10 = 2198 cm

Hence, the bicycle travels 2198 cm or about 21.98 meters for 10 complete revolutions of the tires.

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If one of the roots of the given quadratic equation is -7/5 then the value of k is -7.

Given: - We are having the quadratic equation 5m² + 2m + k = 0 and also one of the roots of the equation an given as -7/5

To find: - The value of K.

Now we find the value of k: -

∵ one root is given to us = -7/5

∴ m = -7/5 is one solution of the quadratic equation

i.e, m = -7/5 will satisfy the above equation

So, we put the value of m and we get,

5 (-7/5)² +2 (-7/5) + k = 0

49/5 - 14/5 + k = 0

∴ 35/5 +k = 0

⇒ 7 + k = 0

⇒ k = -7

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In a triangle, the measures of those two angles are, 80° and 90°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A triangle has an angle that measures 10°.

And, The other two angles are in a ratio of 8 : 9.

Since, The other two angles are in a ratio of 8:9.

So, The value of those two angles are 8x and 9x.

We know that;

The sum of all three interior angles in a triangle is 180°.

So, We can formulate;

⇒ 10° + 8x + 9x = 180°

⇒ 10° + 17x = 180°

⇒ 17x = 180 - 10

⇒ 17x = 170

⇒ x = 170 / 17

⇒ x = 10

Thus, The value of those two angles are,

⇒ 8x = 8 × x = 80°

⇒ 9x = 9 × x = 90°

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C. Obtuse Angle measures more than 90 degrees but less than 180 degrees.

An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. It is greater than a right angle (which measures exactly 90 degrees) but less than a straight angle (which measures exactly 180 degrees). Obtuse angles are often referred to as "greater than a right angle."

A Right angle is an angle which measures exactly 90 degrees.

An Acute angle is an angle which measures less than 90 degrees.

A Reflex angle is an angle which measures greater than 180 degrees but less than 360 degrees.

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The exponential equation is [tex]y=ab^x[/tex]. Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = [tex]ab^{x}[/tex] . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = [tex]ab^{x}[/tex] . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = [tex]ab^{x}[/tex]

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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The length of the side [tex]\overline{BC}[/tex], and [tex]\overline{AB}[/tex], found using Pythagorean Theorem, and the measures of the angle ∠B in the right triangle ΔABC are;

The Pythagorean Theorem defines the relationship between the legs and the length of the hypotenuse side of a right triangle.

According to Pythagorean Theorem, the sum of the squares of the legs of a right triangle is the same magnitude as the square of the of the length of the hypotenuse side.

The parameters of the right triangle are;

∠A = 45°

[tex]\overline{AC}[/tex] = 14 km

∠C = 90°

The angle sum property can be used to find the measure of the angle ∠B as follows;

m∠A + m∠B + m∠C = 180° (Angle sum property of a triangle)

45° + m∠B + 90° = 180°

m∠B = 180° - (90° + 45°) = 45°

Two angles in the triangle ΔABC are congruent, therefore, the triangle is an isosceles right triangle and the legs, [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex] are congruent.

[tex]\overline{AC}[/tex] = [tex]\overline{BC}[/tex] (definition of congruency)

[tex]\overline{BC}[/tex] = [tex]\overline{AC}[/tex] = 14 kilometers

The hypotenuse side of the right triangle = [tex]\overline{AB}[/tex]

The legs of the right triangle are; [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex]

Pythagorean Theorem, states that we get;

Therefore;

[tex]\overline{AB}[/tex]² = 14² + 14² = 14² × (1 + 1) = 14² × 2

[tex]\overline{AB}[/tex] = √((14)²×2) = 14·√2

The correct option is option c.

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Answer:

ur answer is :

78

Step-by-step explanation:

On solving the provided question, we can say that from provided graphs we say  [tex]x^2 = 4y + 7[/tex] =.> [tex]x^2 = 15 = > x = \sqrt{15}[/tex]

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

from provided graphs we say

[tex]x^2 = 4y + 7[/tex]

y = 2

[tex]x^2 = 15 \\x = \sqrt{15}[/tex]

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Logarithm and Natural Log are abbreviated as Log and Ln, respectively. Natural logarithms are distinct from regular logarithms.

Ln essentially refers to a base-e logarithm. This is also referred to as a basic logarithm. A natural logarithm is another name for this.

Logarithm and Natural Log are abbreviated as Log and Ln, respectively. When an unknown variable appears in an equation as the exponent of another quantity, logarithms are crucial for solving the problem.

Different from ordinary logarithms are natural logarithms. A natural logarithm's base is the special number e, whereas a common logarithm's base is 10. This appears to be a variable, but it actually represents a fixed, irrational number roughly equivalent to 2.718281828459.

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Correct option is C, Both have fixed initial rate and payment amount.

A balloon mortgage is similar to an adjustable rate mortgage (ARM) in other ways, with an initial rate period that is equal to the balloon duration. For instance, a 7-year balloon is frequently contrasted with a 7-year ARM. For 7 years, both have a set rate; after that, the rate will change.

A balloon mortgage starts off with set payments for a set amount of time and comes to a finish with a single, large payment. Because it is substantially greater than the initial instalments, the one-time payment is known as a balloon payment. According to the definition of a balloon loan, the final payment is at least twice as much as the average monthly payment on the mortgage. Balloon payments typically cost tens of thousands of dollars.

Variable-rate mortgages (VRMs), commonly referred to as adjustable-rate mortgages (ARMs), feature an interest rate that may fluctuate on a regular basis based on changes in the appropriate financial index linked to the loan. Generally speaking, if the index rate rises or falls, your monthly payment will too.

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Answer:

Both have fixed initial rate and payment amount

Step-by-step explanation:

Answer: Nicole had 3x = 3*24 = 72 coupons in total.

Let x be the number of coupons Wong had at the beginning.

Nicole had x coupons at the beginning because they both had an equal number of coupons.

When Wong gave Nicole 24 coupons, Nicole had x+24 coupons in total.

Nicole had 3 times as many coupons as Wong, so x+24 = 3x

x = 24

Nicole had 3x = 3*24 = 72 coupons in total.

Step-by-step explanation:

hope this helps

The temperature of the ice when it is 2 ⅓ inches thick is - 7 degrees Fahrenheit

The equation y = -3 x means that the temperature of the ice is directly related to the thickness of the ice.

Given the thickness of the ice, the temperature of the ice would be negative three times the temperature.

This means that when the thickness is 2 ⅓ inches thick, then the temperature is:

y = - 3 x

y = - 3 x 2 ⅓ inches

y = - 7 degrees Fahrenheit

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a. The amount in the account at the end this year after the interest is paid will be 1.04x

b. The amount in the account at the end this year after the interest is paid will be 1.08x.

c. The expression for the amount in the account after N years will be x + 0.04xn

From the information, Mybankaccount pays 4% interest at the end of each year. The person had $x in the bank account at the start of this year. The amount in the account at the end this year after the interest is paid will be:

= x + (x × 0.04 × 1)

= x + 0.04x

= 1.04x

The amount in the account at the end of 2 years after the interest is paid will be:

= x + (x × 0.04 × 2)

= x + 0.08x

= 1.08x

The expression for the amount in the account after N years will be:

x + (x × 0.04 × n)

x + 0.04xn

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The average speed of the trip will be 1.60 miles/mins and 96.64 miles/hrs.

What is an average?

An average of a list of data is a mathematical expression for the center value of a set of data. It is defined mathematically as the ratio of the total of all the data to the number of units in the list. In statistics, the average of a particular collection of numerical data is also known as the mean.

e.g.

The average of 2, 3, and 4 equals (2+3+4)/3 = 9/3 = 3. As a result, the central value of 2,3, and 4 is 3. Thus, the definition of average is to determine the mean value of a set of data.

Average speed:-

The formula for average speed is found by calculating the ratio of the total distance traveled by the body to the time taken to cover that distance.

average speed = total distance / total time

Now,

As given

Total distance covered = 16+185+145

                         =346 miles

Total time taken=20 + 120 + 75

                  =215 minute  (3.58 hours)

Average speed=346/215

                         =1.60 miles/mins

Average speed=346/3.58

                            =96.64 miles/hrs

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A collection of numbers, variables, and mathematical operations is referred to as an expression. When g = 10 and h = 6, the result of the expression (2/5)g + 3h - 6 is 16.

What is an Expression?

An expression in mathematics is a group of numbers, variables, and mathematical operations created in accordance with context-dependent rules.

The value of the equation with g = 10 and h = 6 is, given the expression (2/5)g + 3h - 6,

(2/5)g + 3h - 6

= (2/5)(10) + 3(6) - 6

= 4 + 18 - 6

= 16

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The full question:

Evaluate 2/5g + 3h - 6 when g = 10 and h = 6

The coordinates for the other endpoint of the line segment will be (-4,-9).

What are coordinates of a line segment?

The location of a line segment on the coordinate plane is defined by two endpoints whose coordinates are known. The line links the two endpoints but does not extend beyond them. It is a segment (piece) of a line.

This is the same as the definition of a line segment in ordinary plane geometry, the only difference being that we know the coordinates of the points involved.

Coordinates - Coordinates are the components of an ordered pair. In an ordered pair, the first number is called the x-coordinate and the second number is called the y-coordinate.

Now

Given,

One endpoint (x2,y2) having coordinates= (8,-5)

Let other endpoint be = (x1,y1)

Midpoint (x, y) = (2,-7)

Therefore,

x=(x1+x2)/2 and y=(y1+y2)/2

x1=2x-x2             y1=2y-y2

x1=4-8                 y1=-14+5

x1=-4                   y1=-9

Hence, other endpoint is (4,-9).

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The centroid of the region enclosed by y = ex, y = 0, x = 0 and x = 5 is at the point ( (5e^5 - 5) / (e^5 - 1) , (e^10 - 1) / 2(e^5 - 1) ).

To find the centroid of a region, we need to first find the area of the region and the coordinates of the center of mass of the region.

The region enclosed by y = e^x, y = 0, x = 0 and x = 5 can be represented by the definite integral of the function y = ex between the limits of x = 0 and x = 5. The area of this region is given by the definite integral:

∫[0,5] e^x dx

The definite integral of ex is e^x, so the area of the region is e^5 - e^0 = e^5 - 1.

To find the x-coordinate of the centroid, we need to find the integral of

x e^x from 0 to 5, divided by the area.

= ∫[0,5] xe^x dx / (e^5 - 1)

The integral of xe^x is

= (xe^x - ∫e^x dx)

= (xe^x - e^x)

So the x-coordinate of the centroid is

= ∫[0,5] xe^x dx / (e^5 - 1)

= (4e^5 + 1) / (e^5 - 1)

To find the y-coordinate of the centroid we need to find the integral of

ye^x from 0 to 5, divided by the area.

∫[0,5] (e^x * e^x) dx / (e^5 - 1)

∫[0,5] (e^(2x)) dx / (e^5 - 1)

The integral of e^(2x) is (1/2)e^(2x)

So the y-coordinate of the centroid is

∫[0,5] e^(2x) dx / (e^5 - 1) = (1/2) * (e^10 - e^0) / (e^5 - 1)

= (1/2) * (e^10 - 1) / (e^5 - 1)

= (e^10 - 1) / 2(e^5 - 1)

So the centroid of the region enclosed by y = ex, y = 0, x = 0 and x = 5 is at the point ( (5e^5 - 5) / (e^5 - 1) , (e^10 - 1) / 2(e^5 - 1) ).

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When Martina has $80 in a savings account earning 10% interest compounded annually, she will have $106.48 in three years.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 = 2. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

Initial amount=$80

rate=10% compounded annually

time=3 year

A=P(1+r/n)^(nt)

Year 0 $80.00

Year 1 $88.00

Year 2 $96.80

Year 3 $106.48

Martina will have $106.48 in 3 years when she has $80 in a savings account that earns 10% interest, compounded annually.

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