In a football game, Team A defeated Team B by a score of 31 to 14. The total points scored came from a combination of touchdowns, extra-point kicks, and field goals, worth 6, 1, and 3
points, respectively. The numbers of touchdowns and extra-point kicks were equal. There were six times as many touchdowns as field goals. Find the number of touchdowns, extra-point
kicks, and field goals scored.

Answers

Answer 1

The number of touchdowns is 4.

The number of extra-point kicks is 4.

and the number of field goals is 2.

What are linear equations in three variables?

If a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables.

How to solve the system of linear equations in three variables?

Select two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. then, solve the system of the two newly obtained equations using the Addition/Subtraction method.

Let the number of touchdowns be "x", the number of extra-point kicks be "y", and the number of field goals is "z".

Total points scored in game = 20+14 =34

Now,

According to the given question,

                                6x + y + 3z = 34 -----------(I)

                                x = y ----------(II)

                                x = 2z

                                z = [tex]\frac{x}{2}[/tex] -----------(III)

Putting the values of "y" and "z" in equation (I), we get

                              6x + x + 3×[tex]\frac{x}{2}[/tex] = 34

                               [tex]\frac{17x}{2}[/tex] = 34

                               x = 4

Now, putting the value of "x" in equations (II) and (III), we get

                               y = 4.

                               z = 2.

Hence, The number of touchdowns is 4. The number of extra-point kicks is 4, and the number of field goals is 2.

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Related Questions

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.

x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36

Answers

The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

What is Equation of Circle?

The location of a circle in the Cartesian plane is represented by a circle equation. We can write the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.

The standard equation of a circle with center at

(a, b) and radius is r.

So, the standard equation circle is

(x -a)² + (y- b)² = r²

Given:

As, we know the standard form for equation of a circle is

(x-a)² + (y-b)² = b =r²

where (a, b) is the center of the circle and r is the radius of the circle.

We have

diameter = 12 units

radius = 12/2 = 6 units

So, the center will be at (0, 3)

Thus, the equation of circle

(x-0)² + (y-3)² = 6²

x²+ (y-3)² = 36

Hence, the Equation of Circle is x²+ (y-3)² = 36.

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0°F; drops 15° what’s the new temperature

Answers

The new temperature is given as -15°F.

What is a Measurement unit?

A measurement unit is a unit to measure certain quantities.

For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.

To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

Given that,

The present temperature is 0°F.

And, the drop in the temperature is 15°.

The new temperature after the drop can be found by subtracting the amount of drop from the initial temperature as follows,

0 - 15°F

=  -15°F

Hence, the new temperature after the drop is  -15°F.

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step by step explanation to-4x = -x + 3

Answers

The value of x is -1 for equation -4x = -x + 3

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given equation is -4x = -x + 3

In the given equation minus four times of x equal to minus x plus three

x is the variable

Plus and minus are operators

-4x = -x + 3

Take the variables to one sides

Add +x on both sides

-4x+x=-x+x+3

-3x=3

Divide both sides by -3

x=-1

Hence, the value of x is -1 for equation -4x = -x + 3

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2. Write each of the following as a power function in the form f(x) = kx^p.
f(x) = -3/2x^5

Answers

The simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .

What is power function ?

A function having a single term that is the sum of a real number, a coefficient, and a variable raised to a fixed real number is called a power function. Consider functions for area or volume as examples (a number that multiplies a variable raised to an exponent is known as a coefficient). A power function is a function where y = x n, where n is any real constant number. In reality, many of our parent functions, including linear and quadratic functions, are power functions.

Here ,

a) f(x) = [tex]\frac{-3}{2x^5}[/tex]

To write in the form of f(x)= [tex]kx^p[/tex]

=> f(x) = [tex]\frac{-3}{2}* \frac{1}{x^5}[/tex]

=> f(x) = [tex]\frac{-3}{2} x^-5[/tex]

b) g(x) = 5[tex]\sqrt[3]{x}[/tex]

Here we know that [tex]\sqrt[n]{a} = a^\frac{1}{n}[/tex] , then

=>g(x)=5[tex]x^\frac{1}{3}[/tex]

Hence the simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .

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Show that the terms of the series ∑n=1log 5r are in AP. Hence, find the sum of the first twenty terms of the series and also the least value of n for which the sum to n terms exceeds 400

Answers

The required sum of the first twenty terms of the series ∑n=1log 5r are in AP will be 32.37.

What are the properties of logarithms?

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

We have been given that the terms of the series ∑n=1log 5r are in AP.

As per the given question,

∑n(log(5r)) = log(5·1)+log(5·2)+log(5·3)+...+log(5·n)

n = 20

∑log(5r) = log(5·1)+log(5·2)+log(5·3)+...+log(5·20)

Using the property of logarithmic logₐ(xy) = logₐx + logₐy,

∑log(5r) = (log(5)+log(1)) + (log(5)+ log(2))+(10g(5)+Log(3))+ ...(10g(5)+Log(20))

∑log(5r) = (log(5)+log(5)+log(5)+...+log(5)

∑log(5r) = 20·1og(5)+((log(1)+log(2)+log(3)+...+log(20)

Using property of logarithmic logₐ(xy) = logₐx + logₐy,

∑log(Sr)=20·1og(5)+log(1×2×3×...20)

∑log(5r) = 20-log(5)+log(201)

∑log(5r) = 32.365524703598

Rounded to the nearest hundredth decimal,

∑log(5r) = 32.37

Thus, the required sum of the first twenty terms of the series ∑n=1log 5r in AP will be 32.37.

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On an architect's blueprint, 1 inch corresponds to 4 feet. Find the length of a wall represented by a line 1 inches long on the blueprint​

Answers

The length of wall in real life is 4 feet.

Given that on an architect's blueprint, 1 inch corresponds to 4 feet.

In this architect's plan, a wall represented by a line 1 inches long on the blue print.

So, the length of wall in real life is = 4 feet.

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Answer:

4ft

Step-by-step explanation:

If 1 inch corresponds to 4 ft on the blueprint. The ratio is 1 inch on the blue print for every 4 ft in real life.

Which of the following is NOT true about the body mass index? A. uses statistical data of weight and height across the population B. measures the percentage of one's body fat directly C. relies on a correlation between weight and body fat D. does not account for one's body frame size or muscle content Please select the best answer from the choices provided. A B C D Mark this and return

Answers

The statement that is not true about body mass index is B. measures the percentage of one's body fat directly

What is Body mass index?

The Body Mass Index (BMI) calculates a person's weight in relation to their height. It is not a precise assessment of a person's total body fat, more of an indicative.

The majority of the time, total body fat and BMI are correlated.

The Body mass index (BMI) formula

= weight in kilograms / square of height in meters

BMI Categories values are classified below

Underweight  ≤ 18.5

Normal weight = 18.5–24.9

Overweight = 25–29.9

Obesity = BMI of 30 or greater

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Answer:B

Step-by-step explanation:

126=2×3×3×k
Solve for k

Answers

The answer for k is 7

[tex]{ \huge{ \boxed{ \red{ \sf{x = 7}}}}}[/tex]

Step-by-step explanation:-

[tex]{ \sf{126 = 2 \times 3 \times 3 \times k}}[/tex]

[tex]{ \sf{126 = 6 \times 3 \times k}}[/tex]

[tex]{ \sf{126 = 18 \times k}}[/tex]

[tex]{ \sf{126 = 18k}}[/tex]

Divide both the sides by 18 in order to find the value of k. Then,

[tex]{ \sf{ \frac{126}{18} = \frac{18}{18} k}}[/tex]

[tex]{ \boxed{ \boxed{ \purple{ \sf{x = 7}}}}}[/tex]

Please help 25 points

Answers

Answer: 6x - 4 = 68

Step-by-step explanation:

           Vertical angles are congruent to each other. The two angles given, 6x - 4 and 68, are vertical angles. This means we can set them equal to each other for our equation. Using this logic, the answer is;

                         6x - 4 = 68

Michel is taking 4 credit hours of courses at his local community college. Each credit hour costs $110.50. He is also to pay three technology fees of $19.25. Determine the total amount that he will pay in tuition.

Answers

Total: 499.75

Step-by-step explanation:

4 × 110.5 = 442

3 × 19.25 = 57.75

442 + 57.75 = 499.75

) Nike deposits N5,000.00 in a savings bank account. If she is paid an interest rate of 5% per annum for 2 years, how much is the simple interest? NOO. O​

Answers

The simple interest that Nike will receive after 2 years is $500.

The principal amount =$5000

Rate = 5% = 0.05

Time = 2 years

Now simple interest = PRT = 5000 × 0.05 × 2 = 500

Hence the simple interest earned by Nike is $500

Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest.

Simple interest does not change the principal amount in the same way as compound interest, which adds the interest of one year's principal to the next year's principal to calculate interest.

A loan is a sum of money that a person obtains from a bank or another type of financial institution in order to pay bills. A few types of loans are personal, student, auto, and mortgage loans.

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ERROR ANALYSIS Describe and correct the error in finding m/1. X 115° +39° + m/1 = 360° 154° +m1 = 360° m1= 206​

Answers

That’s correct I hope I helped

-1/2u+3/5=1/6 What is u?

Answers

Hello, there today we will be solving your problem

_____________________

[tex]\huge\blue{\mid{\fbox{\tt{Answer}}\mid}}[/tex]

[tex]u=\frac{13}{15}[/tex]

[tex]\huge\blue{\mid{\fbox{\tt{Explanation}}\mid}}[/tex]

Definitions

Multiplication - Multiplication, otherwise known as the inverse of division repeats a certain number's value into what it has been multiplied by. Ex. [tex]4\cdot4=16[/tex]

Fraction - A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.

Algebra - Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all mathematics

Reciprocal - In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by [tex]\frac{1}x[/tex] or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction [tex]\frac{a}b[/tex] is [tex]\frac{b}a[/tex]. For the multiplicative inverse of a real number, divide 1 by the number.

_____________________

Now we can solve this equationStep one - Subtract:   [tex]-\frac{1}{2} u=\frac{1}{6}-\frac{3}{5}[/tex]Step two - Simplify: [tex]-\frac{1}{2} u=-\frac{13}{30}[/tex]Step three - Multiply by the reciprocal of [tex]-\frac{1}2[/tex]: [tex]-\frac{1}{2}u\cdot -\frac{2}{1}=-\frac{13}{30}\cdot -\frac{2}{1}[/tex]Step four- Simplify: [tex]u=\frac{13}{15}[/tex]Your answer is  [tex]u=\frac{13}{15}[/tex]

What are the solutions to the equation 3k² + k-3=0?
Approximate the value of both solutions. Round each answer to two decimal places. Enter your answers as
a list of numbers, separated with commas. Example: 3.25,4.16
k=

Answers

The answer will be 0.33 using quadratic equation.

What is quadratic equation

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation given 3k² + k -3=0

(3k-1)(k+3)=0

k =1/3

k=0.33

Hence the value of k is 0.33.

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Solve for x.
-8x+14 ≥ 60 OR - 4x + 50 < 58
Choose 1 answer:
(A
E
x≤-
x≤
-
23
4
23
4
x>-2
or x>-2
There are no solutions
All values of a are solutions

Answers

Answer:

[tex]x\leq -7 or x > -2[/tex]

Step-by-step explanation:

-8x+14 ≥ 60 or - 4x + 50 < 58
     -8x ≥ 56 or         - 4x < 8
        [tex]x \leq -7[/tex] or            [tex]x > -2[/tex]

The equation for line t can be written as y+3= 1/2(x–7). Line u, which is perpendicular to line t, includes the point (3,3). What is the equation of line u?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answers

The equation of a line u perpendicular to line t and passes through (3, -3) is  y = -2x + 3

How to represent the slope of a line?

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

m = slopeb = y-intercept

Line t has equation as y + 3 = 1 / 2 (x - 7).

Line u is perpendicular to line t and it passes through (3, -3).

The products of the slope of perpendicular lines is equals to negative 1.

Therefore,

m₁ m₂ = -1

1 / 2 m₂ = -1

m₂ = -2

Therefore,  the equation of the line have a slope of -2.

let's find the y-intercept using (3, -3)

-3 = -2(3) + b

b = -3 + 6

b = 3

Therefore, the equation in slope intercept form is y = -2x + 3.

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What other congruence is needed to prove that △QRP≅△QFP by ASA?
QR≅QF
∠R≅∠F
∠QPR≅∠QPF
PR≅PF

Answers

The requirements for two triangles to be congruent by ASA are: a congruent side must be between two congruent and corresponding angles.

To prove that the two triangles are congruent by ASA, you need angles QPR and QPF to be congruent.

Answer = angle QPR congruent to angle QPF

Day
(t) No. of Calories
Burned
C(t)
2 314
4 356
6 370
8 386
10 405
12 442
14 516
Amanda goes to the gym every day and cross–trains. Based on a chart at the gym showing the calories expended for various activities, Amanda has kept track of the number of calories she has burned over the last two weeks. She wants to find the rate at which she burned calories on day 8. That is, she needs to find C'(8). Estimate the value.

A.
8.00 calories per day
B.
8.75 calories per day
C.
17.50 calories per day
D.
17.75 calories per day

Answer: In photo below

You're Welcome :)

Answers

If she wants to find the rate at which she burned calories on day 8. C'(8) is: B. 8.75 calories per day

How to find the calories per day?

First step is to find the upper and lower values for the burned calories on day 8.

Upper value (C'(8) =  405 - 386 /2

Upper value C'(8) = 19/2

Upper value C'(8) = 9.5

Lower value C'(8) = 386 -370/2

Lower value C'(8) = 16/2

Lower value C'(8) = 8

Now let find C'(8)

C'(8) = 9.5+8/2

C'(8) = 17.5/2

C'(8) = 8.75 calories per day

Therefore the correct option is B.

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I need help with solving problem.

Answers

Answer:

i can help but first what the questions and where are the options?

Step-by-step explanation:

-353.92 - (-283.56) -131.29

Answers

-353.92-(-283.56)-131.29= -20,165

y=-2x^2+20x-2 what is the maximum or minimum value of the function

Answers

The Minimum value is y(min) = 48 , x = 5 and The maximum value is   [tex]y = -2(x -5)^2+48[/tex]

Given,

In the question:

The given Function is :

[tex]y = -2x^2 + 20x -2[/tex]

To find the maximum or minimum value of the function:

Now, According to the question:

For maximum value:

The given Function is :

[tex]y = -2x^2 + 20x -2[/tex]

Take out the leading coefficient is :

[tex]y = -2(x^2 + 10x) -2[/tex]

Complete the square:

[tex]y = -2(x^2 + (2(-5))x +(-5)^2+(-2-(-2).(-5)^2)[/tex]

Express the function in vertex form:

[tex]y = -2(x -5)^2+48[/tex]

For Minimum Value:

y(min) = 48

x = 5

Hence, The Minimum value is y(min) = 48 , x = 5 and The maximum value is   [tex]y = -2(x -5)^2+48[/tex].

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8 (a) Write 0.000089 in standard form.

Answers

Answer: 0.000089

Step-by-step explanation: 0.000089 is already in standard form, if you want 0.000089 in the scientific form then that would be...

8.9 x 10⁻⁵

Find the values of x and y​

Answers

X= 20 & Y= 70 in right-angled triangle .

What is right angle triangle?

A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The longest of the three sides, known as the hypotenuse, is the third side.

2X + 140 = 180

2X = 40°

   X = 20°

X + Y = 90°

   Y = 70°

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Apples cost 1.85 per kilogram
Work out the cost of 1.6 kilogram of apples
for 20 points

Answers

Answer:

1.6 kg = $2.96

Step-by-step explanation:

The given statement is,

→ 1 kg of apple = $1.85

→ a = 1.85

Now the cost of 1.6 kg of apple is,

→ 1.6 × a

→ 1.6 × 1.85

→ $2.96

Hence, 1.6 kg of apple is $2.96.

Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72. Which of the following are still outstanding?

Answers

The amount that is outstanding when Brett tallies up the transactions in his check.is $9.19.

How to calculate the value?

From the information, Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72.

The amount that is outstanding will be the difference between the amount given. This will be:

= Bank statement - Total balance

= $257.72 - $248.53

= $9.19

This is the outstanding amount.

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Suppose the government has a balanced budget and wants to increase spending without changing tax rates. The government enters the loanable funds market to borrow $150 billion for economic stimulus spending. How much money is available for private investment after this action has shifted the demand curve as shown in the figure?

Answers

The money available for private investment is $250 billion dollar

What is demand curve ?

The demand curve is a graphical representation of the connection between the cost of a commodity or service and the amount that is demanded over time. The price will often be shown on the left vertical axis in a representation, and the amount needed will typically be shown on the horizontal axis.

Refer to the attachment for graph:

Once investments and government borrowing are added together, the total is = $400

if borrowing from the government is= $150

private investment

=( investment and and government borrowing) - (government borrowing )

= $400 - $150 = $250

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2 step equation:12. Amy wants to start taking gymnastics. There is a one-time fee of $35 to sign up, then it costs $85 per month. If Amy saves up $225, how many months of gymnastics can she take?​

Answers

The number of months Amy can take the Gymnastic = 2 months.

Amy wants to start taking gymnastics.

The fee structure of the gymnastics is divided into two parts.

There is a one time fee payment of 35$ and there is a monthly payment that costs 85$ per month.

So the first month fee of the gymnastics = 35 + 85 = 120$

Savings of Amy = 225$

If Amy pays the 1st month fee ,

then the she will be left with the savings  = 225$ - 120$ = 105 $

It means Amy can join the gymnastics for one more month .

Hence the number of months Amy can take the Gymnastic = 2 months .

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Drag each tile to the correct box. Not all tiles will be used.
Find the equations with unit rates greater than the unit rate of the graph. Then arrange these equations in order from least to greatest unit rate.

Answers

The equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x

How to determine the equations with unit rates greater than the unit rate of the graph?

On a graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:

Slope = y2-y1 / x2-x1  

Thus, we can any two convenient points on the graph and use it calculate the slope:

Let's pick points (5, 10) and (12, 25)

This implies x1 = 5, y1 = 10 and  x2 = 12, y2 = 25

Slope = y2-y1 / x2-x1

Slope = 25-10 / 12-5 = 15/7

Thus,  the unit rate of the graph is 15/7 = 2.143

Find the equations with unit rates greater than the unit rate of the graph:

y = 19/8x: unit rate = 19/8 =  2.375

y = 27/13x: unit rate = 27/13 = 2.077

y = 21/9x: unit rate = 21/9 = 2.333

y = 11/5x: unit rate = 11/5 = 2.200

y = 15/17x: unit rate = 15/17 = 0.882

y = 31/15x: unit rate = 31/15 = 2.067

y = 13/6x: unit rate = 13/6 = 2.167

The equations with unit rates greater than the unit rate of the graph are y = 19/8x, y = 21/9x, y = 11/5x and y = 13/6x

Therefore, the equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x. Drag each tile to the correct box accordingly

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A straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form. 8 in. 5 in. 5 in.

Answers

The length of the straw fitted in the box is 10.67 inches.

What is cuboid?

A cuboid is a solid three-dimensional object which has six faces that are rectangular with eight vertices, and twelve edges.

Given that, a straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner,

Diagonal of a cuboid  = √ l² + w² + h²

Therefore, diagonal of the box = √ 5² + 5² + 8² = 10.67 in

Hence, The length of the straw fitted in the box is 10.67 inches.

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Please help asap!! Please please please

Answers

Yes, I agree with Jorge.

Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.

Jorge could improve his proof by stating his explanation in terms of mathematics.

He could have used the SAS similarity to show that the given triangles are similar.

What is the similarity test of two triangles?

If the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal, the two triangles are similar.

In the given figures,  the length of side AB is equal to the length of side DE.

                        Side AB = Side DE ----------(I)

Similarly, the length of side BC is equal to the length of side EF.

                        Side BC = Side EF ----------(II)

And the measure of angle  ABC is equal to the measure of angle DEF.

                              ∠ ABC = ∠ DEF -------(III)

From (I), (II), and (III), and by using the SAS test we can say that

                               ΔABC ~ ΔDEF    ----------- SAS test

Hence,

Yes, I agree with Jorge.

Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.

Jorge could improve his proof by stating his explanation in terms of mathematics.

He could have used the SAS similarity to show that the given triangles are similar.

To learn more about the SAS test for the similarity of triangles, visit:

https://brainly.com/question/22472034

#SPJ1

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