Four thousand two hundred carnations were reserved for use on thge float. If this was 7/10 of the flowers needed, how many glowers would be on the float

Answers

Answer 1

The flowers on the float would be 6.000 flowers. The result is obtained by using fraction multiplication.

How to count a set of objects using fractions?

Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.

For example:

1/4 (one-fourth)2/5 (two-fifth)

It means one of four parts and two of five parts.

We have four thousand two hundred carnations on the float. It was 7/10 of flowers needed. Find the whole flowers on the float!

The carnations of a set of flowers is 7/10. It is 4200 carnations.

The carnations part is 7 and the whole part of flowers is 10.

Using fraction, the whole flowers would be

= 10/7 × 4200

= 6.000 flowers

Hence, the number of flowers needed to be on the float is 6.000 flowers.

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Related Questions

HELP !!!
write days in May and days in a year as a ratio

Answers

Answer: 31 to 365 or 31:365 or 31/365

The ratio of days in May and days in a year is 31 to 365 or 31:365

What is the ratio?

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We need to find the days in May and days in a year as a ratio

Therefore, Days in may = 31

Days in a year = 365

Thus, the expected ratio = 31/365

Or

31:365

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4. Clare is paid $90 for 5 hours of work. At this rate, how many seconds does it take care to earn 25 cents?
5. A car that travels 20 miles in 1/2 hour at consent speed travels at the same rate as a car that travels 30 miles in 3/4 hour at a constant speed.
6. Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. complete the diagram to show smaller and larger batches that would taste the same as lin's favorite blend.

Answers

The first answer is 50 seconds.
And If you see this please help me answer this question!

Multiply = 4/7 x 5 1/4
please help me

Answers

Answer:

3

Step-by-step explanation:

[tex]\displaystyle \frac{4}{7}*5\frac{1}{4}=\frac{4}{7}*\frac{21}{4}=\frac{21}{7}=3[/tex]

Which polynomial is prime?
x3 + 3x2 -2x - 6
x° - 2x2 + 3x 6
4x4 + 4x3 - 2x - 2
D 2x + x3 -x +2

Answers

The final equation is a polynomial of primes  [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored. Variables are sometimes known as indeterminate in mathematics.

what is polynomial ?

 An essential component of the "language" of mathematics and algebra are polynomials. They are used to express numbers that are the result of mathematical operations in almost every area of mathematics. Other types of mathematical expressions, such as rational expressions, also use polynomials as "building blocks."

given

Is a base form of a polynomial in other words is a polynomial that can't be factored.

so we have

[tex]A ) x^{3} +3x^{2} - 2x - 6 = ( x +3 ) ( x^{2} - 2 )\\B) x^{3} -2x^{2} +3x - 6 = ( x- 2 ) (x^{2} + 3)\\C)4x^{4} +4x^{3} - 2x - 2 = 2( x +1 )(2x^{2} - 1)\\D) 2x^{4} +x^{3} -x + 2[/tex]

hence, the final equation is a polynomial of primes  [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored.

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Maisie walked for 4 hours at an average speed of
1.6 miles per hour (mph).
How many miles did Maisie walk?
If your answer is a decimal, give it to 1 d.p.

Answers

Answer: Maisie walked 6.4 miles.

Step-by-step explanation:

Since Maisie is walking at a constant pace of 1.6 miles per hour we can set up the following equation:

y = 1.6(x)

In this equation, Y is the number of miles Maisie walked in total and X is the number of hours she walked. All we have to do is plug in 4 hours as x and solve.

y = 1.6(4)

y = 6.4 miles.

What is the rule for quadrant 4?

Answers

All points in Quadrant IV have a positive x-coordinate and a negative y-coordinate.

The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant. The x-axis in this quadrant has positive values, whereas the y-axis has negative numbers.

A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from first to fourth.

A quarter of a circle; a 90° arc. the region enclosed by an arc and two radii are drawn one to each extreme. As a mechanical component, anything is shaped like a quarter of a circle.

All Quadrant I points have two positive coordinates.

Quadrant II points all have a negative x-coordinate and a positive y-coordinate.

All Quadrant III locations have two negative coordinates.

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Help me with this problem - find y

[tex]y + 25 = 625 \div 25[/tex]

Answers

Answer:

[tex]y=0[/tex]

Step-by-step explanation:

[tex]y+25=25 \\ \\ y=25-25 \\ \\ y=0[/tex]

Answer:

[tex] \sf \: y = 0[/tex]

Step-by-step explanation:

Given equation,

→ y + 25 = 625 ÷ 25

Now the value of y will be,

→ y + 25 = 625 ÷ 25

→ y + 25 = 25

→ y = 25 - 25

→ [ y = 0 ]

Hence, the value of y is 0.

Big Ideas:
Explain your reasoning.

Answers

Answer:

Stretch the graph of f(x) = x + 3 vertically by a factor of 2.

The "same" transformations result in f(x) = 2x + 5

The "different" transformation results in f(x) = 2x + 6

Step-by-step explanation:

Transformation Rules

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

Carry out the given transformations.

Given function:

[tex]f(x) = 2x + 3[/tex]  

Translation of 2 units up:

[tex]\begin{aligned}\implies f(x) + 2&= 2x + 3 + 2\\&=2x+5\end{aligned}[/tex]

Given function:

[tex]f(x) =x + 3[/tex]

Vertical stretch by a factor of 2:

[tex]\begin{aligned}\implies 2f(x)&=2(x+3)\\&=2x+6\end{aligned}[/tex]

Given function:

[tex]f(x) = x + 5[/tex]

Horizontal shrink by a factor of 1/2:

[tex]\implies f\left(\dfrac{1}{\frac{1}{2}}x\right)=f(2x)=2x+5[/tex]

Given function:

[tex]f(x) = 2x + 3[/tex]

Translation of 1 unit left:

[tex]\begin{aligned}\implies f(x+1) &= 2(x+1) + 3\\&=2x+5\end{aligned}[/tex]

Three of the transformations result in the same function f(x) = 2 + 5.

Therefore, the transformation that does not belong with the other three is:

Stretch the graph of f(x) = x + 3 vertically by a factor of 2.

Calculate the area of a rectangle with the base of 12 feet and height of 3 feet.

(I need the answer as fast as possible so if anybody could help that would be greatly appreciated)

A: 9 square feet
B: 15 square feet
C: 30 square feet
D: 36 square feet

Answers

Rectangle equation for area is BH, so 12x3 is 36

It ha been etimated that about 15% of frozen chicken contain enough almonella bacteria to caue illne if improperly cooked. Suppoe that a upermarket buy 1000 frozen chicken from a upplier. Find an approximate 68% interval (remember empirical rule: approx. 68% of data within 1 tand. Deviation of mean) for the number of frozen chicken that may be contaminated

Answers

approximate 68% interval (remember empirical rule: approx. 68% of data within 1 tand. Deviation of mean) for the number of frozen chicken that may be contaminated is (271.02, 328.98) = (271, 329)

Suppose number of trials, n = 1000

And number of defective chickens is within 1 standard deviation of the mean :

Mean = np ; p = 0.3

Mean = 1000 * 0.3 = 300

Standard deviation (s) : sqrt(np(1-p))

s = sqrt(1000 * 0.3 * 0.7)

s = sqrt(210)

s = 14.49

2 standard deviations of the mean: and interval

Mean ± 2s

Lower bound : 300 - 2(14.49) = 271.02

Upper bound : 300 + 2(14.49) = 328.98

(271.02, 328.98) = (271, 329)

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Nathan had 58 pieces of gum that he wants to make last six days how much can he chew each day so that the gum last him six days between what two whole numbers does your answer lie

Answers

Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Nathan had 58 pieces of gum that he wants to make last six days.

Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,

= (58/6).

= 9.66 chewing gums but it should be a whole number.

So, Nathan can chew between 9 to 10 chewing gums each day.

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A jar contains $1.70 in ckels, dimes and quarter. There are twenty coins in all with twice as amny nickels as dimes. How many nickels are there in the jar

Answers

American nickels are issued as currency. A value of $1.70 is equal to 10 nickels and 12 dimes ($0.50 + $1.20).

How to find the calculation?

A dime is worth ten cents and a nickel five cents. In other words, one dime is equivalent to two nickels.

In light of this, we might state that a nickel is worth half what a dime is worth.

Despite having a higher value than a nickel, the dime is smaller.

n + d = 22 <— d = 22-n

Amount in pennies: 5n + 10d = 170

5n + 10(22 - n) = 170

5n + 220 - 10n = 170

220 - 5n = 170

220 - 170 - 5n = 0

50 - 5n = 0

50 = 5n

n = 10

A value of $1.70 is equal to 10 nickels and 12 dimes ($0.50 + $1.20).

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Find the area of the circle shown. Use 3.14 as an approximation for T. Round your answer to the nearest tenth. ​

Answers

Here the exact values of circle is not given.so in general .Area of Circle = πr² or πd2/4 in square units, where (Pi) π = 22/7 or 3.14.

How to find the Area of Circle?

The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r2, where r is the circle's radius, is the formula for c

Area of Circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of circumference to diameter of any circle. It is a special mathematical constant.

Area of Circle:

[tex]\pi[/tex]×r²

Where [tex]\pi[/tex]=3.14

But Here we need correct values to find the area of the circle.

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If a student scored 75 points on a test where the mean score was 83. 5 and the standard deviation was 6. 1. The student's z score is ________. Round to 2 decimal places

Answers

The z score of the student is -1.39. The value z score is rounded to 2 decimal places.

What is mean?

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

The formula for the z-score is

z = (x - μ)/σ

x = standard value

μ = mean

σ = standard deviation

Given that the scored 75 points. The mean score of the student was 83.5 and the standard deviation was 6. 1.

Putting x = 75, μ = 83.5 and σ = 6.1

z = (75 -  83.5)/6.1

z = -1.3934

z ≈ -1.39

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X
-1
0
2
f(x)
MKB6223
18
가 2
What is the decay factor of the exponential function
represented by the table?
이를
이를
○ 2
○6

Answers

Here, 1/3 is halfway between 0 and 1. The exponential function supplied has a decay factor of 1/3 as a result.

How do you find the decay factor of an exponential function?

An exponential function's basic form is:

[tex]$$y=a b^x$$[/tex]

Where an is the starting value, b>1 is the growth factor, and 0b1 is the decay factor.

the point through which the exponential function passes (0,6). In I if x=0 and y=6, we obtain

[tex]$$\begin{aligned}& 6=a b^0 \\& 6=a(1) \\& 6=a\end{aligned}$$[/tex]

the point through which the exponential function passes (1,2). Substituting [tex]$x=1, y=2, a=6$[/tex] in (i), we get

[tex]$$\begin{aligned}2 & =6(b)^1 \\2 & =6 b \\\frac{2}{6} & =b \\\frac{1}{3} & =b\end{aligned}$$[/tex]

Here, [tex]$^{b=\frac{1}{3}}$[/tex] between 0 and 1 is located. The provided exponential function's decay factor is thus [tex]$\frac{1}{3}$[/tex].

Therefore the correct answer is 1/3 .

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Find the measure of the missing angle? please help :)

Answers

The measure of the angle ∠SUT will be 30°. Then the correct option is C.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.

The measure of the angle ∠SUT is calculated as,

∠SUT + ∠UTS = ∠JST

∠SUT + 80° = 110°

∠SUT = 110° - 80°

∠SUT = 30°

The measure of the angle ∠SUT will be 30°. Then the correct option is C.

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Melissa wants to check the accuracy of the finance charge on her loan. She has a $6,000, 4-year loan at an APR of 3.11%. What is her monthly payment? Round to the nearest cent.

Answers

Answer: $133.10.

Step-by-step explanation:

Answer:

To calculate the monthly payment for a loan, you can use the following formula:

Monthly payment = (APR/12) * loan amount / (1 - (1 + APR/12)^(-number of payments))

In this case, the loan amount is $6,000, the APR is 3.11%, and the loan is for 4 years, or 48 months. Plugging these values into the formula, we have:

Monthly payment = (0.0311/12) * $6,000 / (1 - (1 + 0.0311/12)^(-48))

Calculating, we find that the monthly payment is approximately $147.26. Rounded to the nearest cent, the monthly payment is $147.26.

Step-by-step explanation:

Can 123 make a triangle?

Answers

No, 1, 2, and 3 are not valid side lengths for a triangle. So 1, 2 and 3 cannot make a triangle.                                                                      

In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.                                                              

3 + 2 = 5 > 1

3 + 1 = 4 > 2

1 + 2 = 3 not greater than 3

So as 1 + 2 not greater than 3, these set of side lengths does not follow the theorem. Thus a triangle cannot be formed with sides of length 1, 2, and 3.

--The question is incomplete, answering to the question below--

" Can 1, 2 and 3 make the sides of a triangle?"

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please help: Can a triangle have side lengths with the given lengths? Explain. 8m, 10m, 19m​

Answers

Answer:

no

Step-by-step explanation:

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

8+10 is 18

which is less than 19

Albert is a marine biologist studying the bluefin tuna population in Caro Bay. When he first started monitoring the population, there were about 1,550 bluefin tuna in the bay. One year later, he estimated that the population of bluefin tuna had decreased to about 1,488. Albert expects the population of bluefin tuna to continue decreasing each year.


Write an exponential equation in the form y=a(b)x that can model the population of bluefin tuna in Caro Bay, y, x years after Albert began monitoring it.
Use whole numbers, decimals, or simplified fractions for the values of a and b.

Answers

The exponential function that models the population of bluefin tuna after x years is given as follows:

y = 1550(0.96)^x.

The parameters of the exponential function are given as follows:

a = 1550.b = 0.96.

How to define the exponential function?

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

a is the initial value.b is the rate of change.

When he first started monitoring the population, there were about 1,550 bluefin tuna in the bay, meaning that the parameter a is given as follows:

a = 1550.

One year later, he estimated that the population of bluefin tuna had decreased to about 1,488, hence the parameter b is obtained as follows:

b = 1488/1550 = 0.96.

Hence the function is defined as follows:

y = 1550(0.96)^x.

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Choose the best answer.
A general guideline for the amount that is withheld for contribution to an employee's pension fund
is
O 6.0%
© 6.5%
O 7.5%
O 7.0%

Answer is 6.5

Answers

Answer: Yes, the answer is 6.5%. The percentage of employee's salary that is withheld for contribution to their pension fund can vary depending on the company or organization, but generally it is around 6-7%. 6.5% is a common percentage used by employers as a guideline for the amount that is withheld for the employee's pension fund.

Step-by-step explanation:

Is 5x 3y a linear equation in two variables?

Answers

Yes, 5x - 3y = 7 is a linear equation in two variables (x and y)

A linear equation in two variables is an equation in the form ax + by = c, where a, b, and c are real numbers and a and b are not both 0. In this equation, 5x 3y, the coefficients of the variables are 5 and 3, respectively, so a = 5 and b = 3. Therefore, 5x 3y is a linear equation in two variables.

A linear equation in two variables (x and y) is an equation that can be written in the form ax + by = c, where a and b are real numbers and a and b are not both 0. This means that any equation that has two variables with real coefficients will be a linear equation. For example, 5x 3y is a linear equation in two variables because the coefficients of the variables x and y are 5 and 3, respectively. Therefore, 5x 3y is a linear equation in two variables.

the complete question is : Is 5x-3y=7 a linear equation in one variable?

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The day before Gerardo returned from a two-week trip, he wondered if he left his plants inside his apartment or outside
on his deck. He knows these facts:
• If his plants are indoors, he must water them at least once a week or they will die.
• If he leaves his plants outdoors and it rains, then he does not have to water them. Otherwise, he must water them at
least once a week or they will die.
. It has not rained in his town for 2 weeks.
When Gerardo returns, will his plants be dead? Explain your reasoning.

Answers

If his plants are indoors, he must water them at least once a week or they will die.

What would you say about an indoor plant?A houseplant is an attractive plant that is cultivated indoors. It is sometimes referred to as a potted plant, potted plant, or an indoor plant. As a result, they are typically seen for ornamental reasons in settings like homes and businesses.Not only do indoor plants improve a room's overall beauty, but studies have also shown that they improve emotions, promote creativity, lower stress levels, and remove air pollutants, all of which contribute to a happier and healthier you. Indoor plants may improve our mood in addition to improving their appearance.If his plants are indoors, he must water them at least once a week or they will die.

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Set builder notation integers between 7 and 50

Answers

Answer:

[tex]\{x|x\in \mathbb{Z}, 7 < x < 50\}[/tex]

Step-by-step explanation:

Basically, the above answer tells us that the set of all x such that x belongs to Z, the set of integers, and x is between 7 and 50.

If m= 2, n=3, and p= -1, then find the value of : 2mn4 – 15m2n + p
In Full Details!! As Soon As Possible

Answers

Answer:

-131

Step-by-step explanation:

2×2×3×4-15×2×2×3+-1

48-179

=-131

It’s actually -133!
Because 2x2x3x4=48
And -15x2x2x3=-180.
48-180+(-1)=-133

What are the 3 parts of a quadratic equation?

Answers

The 3 parts of a quadratic equation are standard form, factored form and vertex form.

A quadratic equation is a polynomial equation of degree two in one variable of type f(x) = ax² + bx + c where a, b, c, ∈ R and a ≠ 0.

There are three forms of quadratic equations

Standard form of quadratic equation y = ax² + bx + c

factored form of quadratic equation y = a(x − r₁)(x − r₂​)

Vertex form of quadratic equation y = a(x − h)² + k

Each of the above quadratic forms looks unique, allowing the different problems to be more easily solved in one form than another.

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What is the solution of the equation 2x y 4 and 3x 2y =- 1?

Answers

The solution of the equation 2x+y=4 and 3x-2y=-1 is the value of x = 1, while the value of y = 2

We have, the sets of equations as:

2x+y=4 and 3x-2y=-1?

As here, let 2x+y = 4 ----(i) and 3x-2y = -1 ----(ii)

As here to solve the value of x and y we will first equalise the co-efficient of x.

Here, the co-efficient of x in the first equation is 2, while in the second equation it is 3

So, for equalising, we will first multiply the first equation by 3 and the second by 2,

Thus, we will get it as:

6x+3y=12 ----(iii)

6x-4y=-2----(iv)

Now subtracting (iv) from (iii)

We will get,

7y = 14

=>y=2

Putting the value of y in (i),

2x=4-y = 4-2 =2

=>x = (2/2)=1

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The complete question may be like:

What is the solution of the equations 2x+y=4 and 3x-2y=-1?​

Which one of the following solids can produce this two dimensional shape when sliced vertically ​

Answers

The solid that can produce the given two-dimensional shape when sliced vertically is option 2.

What is vertical alignment?

When we examine anything vertically, we see it from top to bottom. When something is standing, it is referred to as the alignment.

What is horizontal alignment?

When we examine objects horizontally, we do it from left to right. When anything is in the sleeping posture, it is known as the alignment.

The given shape is a rectangle. When the rectangular prism is sliced in a vertical manner the solid will represent the given shape that is a rectangle.

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In Duck Creek, a bicycle license plate consists of one letter followed by one digit; for example, $Q7$ or $J1$. How many different license plates are possible

Answers

On solving the provided question, we can say that by permutation 26 possible letters  x  10 possible digits  = 260 possible plates

what is permutation?

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of

26 possible letters  x  10 possible digits  =

26 x 10   =

260 possible plates

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This is a two part question and it would really help me if you could solve both! :)

Answers

[tex]\displaystyle\\Answer:\ none \ of\ these\ (m=-\frac{5}{3} );\ isosceles,\ right[/tex]

Step-by-step explanation:

1.

a) find the midpoint G of the side DE:

[tex]x_D=-2\ \ \ \ x_E=3\ \ \ \ y_D=-2\ \ \ \ y_E=1[/tex]

[tex]\displaystyle\\x_G=\frac{x_D+x_E}{2} \\\\x_G=\frac{-2+3}{2}\\\\x_G=\frac{1}{2}\\\\x_G=0.5[/tex]

[tex]\displaystyle\\y_G=\frac{y_D+y_E}{2}\\\\y_G=\frac{-2+1}{2} \\\\y_G=\frac{-1}{2} \\\\y_G=-0.5\\\\Thus,\ G(0.5,-0.5)[/tex]

b) find the midpoint I of the side DF:

[tex]x_D=-2\ \ \ \ x_F=6\ \ \ \ y_D=-2\ \ \ \ y_F=-4[/tex]

[tex]\displaystyle\\x_I=\frac{x_D+x_F}{2} \\\\x_I=\frac{-2+6}{2} \\\\x_I=\frac{4}{2} \\\\x_I=2[/tex]

[tex]\displaystyle\\y_I=\frac{y_D+y_F}{2}\\\\y_I=\frac{-2+(-4)}{2}\\\\y_I=\frac{-6}{2} \\\\y_I=-3\\\\Thus,\ I(2,-3)[/tex]

c) the slope of GI:

[tex]x_G=0.5\ \ \ \ x_I=2\ \ \ \ y_G=-0.5\ \ \ \ y_I=-3[/tex]

[tex]\displaystyle\\m_{GI}=\frac{y_I-y_G}{x_I-x_G} \\\\m_{GI}=\frac{-3-(-0.5)}{2-0.5} \\\\m_{GI}=\frac{-3+0.5}{1.5} \\\\m_{GI}=\frac{-2.5}{1.5} \\\\m_{GI}=\frac{-2.5(2)}{1.5(2)} \\\\m_{GI}=-\frac{5}{3}[/tex]

2.

Type of Δ DEF:

a) find the length of the side DE:

[tex]|DE|=\sqrt{(3-(-2)^2+(1-(-2)^2}\\\\|DE|=\sqrt{(3+2)^2+(1+2)^2} \\\\|DE|=\sqrt{5^2+3^2}\\\\|DE|=\sqrt{25+9} \\\\|DE|=\sqrt{34} \ units[/tex]

b) find the length of the side EF:

[tex]|EF|=\sqrt{(6-3)^2+(-4-1)^2}\\\\|EF|=\sqrt{3^2+(-5)^2}\\\\ |EF|=\sqrt{9+25} \\\\|EF|=\sqrt{34}\ units[/tex]

Hence, DE=EF

c)  find the m∠DEF:

[tex]\displaystyle\\cos \angle E=\frac{\overrightarrow {DE}+\overrightarrow {EF}}{|DE|*|EF|} \\\\[/tex]

Find the coordinates of the vector by the coordinates of its beginning and end points:

[tex]\displaystyle\\\overrightarrow {DE}=(x_E-x_D,y_E-y_D)\\\\\overrightarrow {DE}=(3-(-2),1-(-2))\\\\\overrightarrow {DE}=(5,3)\\\\\overrightarrow {EF}=(x_F-x_E,y_F-y_E)\\\\\overrightarrow {EF}=(6-3),-5-1)\\\\\overrightarrow {EF}=(3,-5)\\Hence,\\\\cos\angle E=\frac{5*3+3*(-5)}{\sqrt{34}*\sqrt{34} } \\\\cos\angle E=\frac{15-15}{34 }\\\\cos\angle E=\frac{0}{34 }\\\\cos\angle E=0\\\\m\angle E=90^0[/tex]

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