Use the distance formula do to determine what type of triangle DEF is if it has coordinates D(2, 1), E(3, 5), F(6, 2). Just write the number you get under the square root symbols in the blank below in order.1. What is the length of DE2. What is the length of EF3. What is the length of DFList your answers for the above length of sides the name what type of triangle is DEF
Answers
Step 1
Draw the triangle DEF
Step 2
State the formula for the distance between two points
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)}^2[/tex]Step 3
Find the length of DE
[tex]\begin{gathered} DE=\sqrt[]{(3-2)^2+(5-1)^2} \\ DE=\sqrt[]{1^2+4^2} \\ DE=\sqrt[]{1+16} \\ DE=\sqrt[]{17} \end{gathered}[/tex]Step 3
Find the length of EF
[tex]\begin{gathered} EF=\sqrt[]{(6-3)^2+(2-5)^2} \\ EF=\sqrt[]{3^2+(-3)^2} \\ EF=\sqrt[]{9+9} \\ EF=\sqrt[]{18} \end{gathered}[/tex]Step 4
Find the length of DF
[tex]\begin{gathered} DF=\sqrt[]{(6-2)^2+(2-1)^2} \\ DF=\sqrt[]{4^2+1^2} \\ DF=\sqrt[]{16+1} \\ DF=\sqrt[]{17} \end{gathered}[/tex]Step 5
Find out what type of triangle it is.
An isosceles triangle is a triangle that has two sides of equal length.
Since triangle DEF has lines DF and DE to be equal in length, we can conclude that triangle DEF is an Isosceles triangle
Related Questions
Help mee pleasee!!
thank you <3
Answers
The linear equation that models the average price of a new home in terms of the year x is given by y = -5600x + 294000 and the average price of a new home would be $238000 in 2014.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The line must pass through points (0, 294000) and (7, 288400) which is given in the question.
We have to determine the slope of the line :
m = (y₂ - y₁)/(x₂ -x₁ )
m = (288400- 294000)/(7 -0)
m = -5600
This represents new home per year
So with your y-intercept of 294000, your equation becomes
y = -5600x + 294000
Using this equation to predict the average price of a new home in 2014.
Let y be the average price of a new home in the year x, where x = 0 represents the year 2004.
Substitute the value of x = 10 for the year 2014
y = -5600(10) + 294000
y = -56000 + 294000
y = 238000
Hence, the average price of a new home would be $238000 in 2014.
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Write the ratio as a ratio of whole numbers in lowest terms $2.00 to $0.80
Answers
Ratio given is $2.00 : .80
To simplify, you can move your decimal point over 2 to the right to remove the decimals and then simplify
2.00 ➡️ 200
.80 ➡️ 80
200:80 divide both by 40
5:2 is your simplified ratio
Scott is 72 inches tall and Chris is 185 centimeters tall. Who is taller? Show your work. How do we convert this?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Scott is 72 inches tall and Chris is 185 centimeters tall.
Who is taller? Show your work.
Step 2:
Scott is 72 inches tall
and
Chris is 185 centimeters tall
Converting cm to inches, we have that:
[tex]\begin{gathered} 1\operatorname{cm}\text{ = }0.393701\text{ inch} \\ 185\text{ cm = 185 x 0.393701 = }72.\text{ 834685 }\approx\text{ 72. 8 inch} \end{gathered}[/tex]CONCLUSION:
Since Chris' height = 72.8 inch tall and Scott's height = 72 inch tall
Hence, Chris is taller.
If (ax + 3)(bx + 4) = 6x 2+ cx + 12 for all values of x, and a + b = 5, what are the two possible values for c ?
Answers
Answers: c = 17 and c = 18
==================================================
Explanation:
Let's expand out the left hand side and rearrange terms like shown in the steps below.
(ax + 3)(bx + 4) = 6x^2 + cx + 12
ax(bx + 4)+3(bx + 4) = 6x^2 + cx + 12
abx^2 + 4ax+3bx + 12 = 6x^2 + cx + 12
abx^2 + (4a+3b)x + 12 = 6x^2 + cx + 12
Then equate the corresponding coefficients
ab = 6 .... x^2 terms4a+3b = c .... x termsWe'll use the fact that a+b = 5. Solving for 'a' gets us a = 5-b
Plug this into the equation dealing with the x^2 coefficients.
ab = 6
(5-b)b = 6
5b-b^2 = 6
0 = b^2-5b+6
b^2-5b+6 = 0
(b-3)(b-2) = 0
b-3 = 0 or b-2 = 0
b = 3 or b = 2
If b = 3, then a = 5-b = 5-3 = 2
If b = 2, then a = 5-b = 5-2 = 3
Therefore, the solutions to this system of equations
[tex]\begin{cases}a+b = 5\\ab = 6\end{cases}[/tex]
are (a,b) = (2,3) and (a,b) = (3,2)
In other words, the answer to the question "what two numbers multiply to 6 and add to 5?" is "2 and 3". The order doesn't matter which is why we can flip the 'a' and b values.
---------------------------------
Go back to 4a+3b = c which was us equating the x coefficients.
This is the same as c = 4a+3b
Plug in a = 2 and b = 3
c = 4a+3b
c = 4*2+3*3
c = 8 + 9
c = 17 is one possible value of c.
Now let's plug in a = 3 and b = 2
c = 4a+3b
c = 4*3+3*2
c = 12 + 6
c = 18 is the other possible value of c.
The amount of $In each The amount of $ Total
Answers
Let Lydia invest $x
Half of her stock pays 11% dividend.
So mathematically the amount will be
[tex]\frac{x}{2}\times\frac{11}{100}=\frac{11x}{200}[/tex]With the other half, she pays stocks in 14% interest
So mathematically
[tex]\frac{x}{2}\times\frac{14}{100}=\frac{14x}{200}[/tex]Her total annual interest is $420
So
[tex]\frac{11x}{200}+\frac{14x}{200}=420\Rightarrow25x=84000\Rightarrow x=3360[/tex]She invested $3360 in total
And $1680 in each.
Miguel bought snacks for his team's practice. He bought a bag of popcorn for $3.33 and a 20-pack of juice bottles. The total cost before tax was $23.33. How much was each bottle of juice?
Answers
The cost of each bottle is $[tex]1[/tex]
Given:
A bag of popcorn costs $[tex]3.33[/tex]Miguel bought [tex]20[/tex]packs of juice bottlesThe total cost before tax was $[tex]23.33[/tex]To find: Cost of each bottle of juice?
It is given that Miguel bought snacks for his team's practice which includes a bag of popcorn, and [tex]20[/tex] packs of juice bottles out of which the bag of popcorn cost him $[tex]3.33[/tex] , and the total cost before tax of all the items costs him $[tex]23.33[/tex]
Now we have to find that how much each bottle of juice costs him as asked in the given question.
Let the bag of popcorn's amount be x and the pack of bottle juice is y
Now according to the linear equation in two variable
[tex]x*1+y*20=23.33[/tex]........(1)
where 1 is the total pack of popcorn bag and [tex]20[/tex] the amount of bottle juice packs
As we know that [tex]x=3.33[/tex] since a bag of popcorn costs him $[tex]3.33[/tex]
Now put the value of x in (1) hence,
[tex]3.33*1+y*20=23.33[/tex]
On further solving we get,
[tex]20y=20[/tex]
On further solving we get,
[tex]y=1[/tex] as the price of every juice of bottle.
Hence a bottle of juice costs him $[tex]1[/tex]
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Solve using the fractions 5/8 and 1 2/7
Answers
107/56 is the solution of fractions .
What do math fractions mean?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.The given fractions are 5/8 and 1 2/7.
We need to find the sum of given fractions.
Now, we can write 1 2/7 as 9/7.
So, 5/8 + 9/7
Here, LCM of 8 and 7 is 56
Then, 35/56 + 72/56
=(35+72)/56
=107/56
Therefore, the sum of the two given fractions is 107/56.
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ALGEBRA - 30 POINTS
In a volatile housing market, the overall value of a home can be modeled by V(x) = 210x2 – 4400x + 125000, where V represents the value of the home and x represents each year after 2020. Find the vertex and interpret what the vertex of this function means in terms of the value of the home. Show the work you completed to determine the vertex.
Answers
Answer: the vertex is 157x4
Step-by-step explanation:
In the diagram, CD 1 AC, BE 1 AC, AE = 17, BE = 8, and CD = 32. Find DE. 32 D В E 8 17 A 45 51 O 68 O 35 Question 3 1 pts a HE
Answers
Input data
AE = 17
BE = 8
CD = 32
Procedure
[tex]\begin{gathered} \frac{AD}{AE}=\frac{CD}{BE} \\ \frac{AD}{17}=\frac{32}{8} \\ AD=17\cdot\frac{32}{8} \\ AD=68 \end{gathered}[/tex]
Now for DE
[tex]\begin{gathered} AE+DE=AD \\ DE=AD-AE \\ DE=68-17 \\ DE=51 \end{gathered}[/tex]The answer would be DE=51
I need help with my work
Answers
In order to determine the price per orange, calculate the quotient in between 3.78 and 14:
3.78/14 = 0.27
Hence, one orange costs $0.27
Which equation that gives the rule for this table.x: 3, 4, 5, 6y: 10, 11, 12, 13A: Y= -x + 7B: Y = x + 7C:Y = 6x + 7OrD: Y= -6 + 7
Answers
To solve this problem we can evaluate te terms in the table in each equation so:
For A) y = -x + 7
we replace (3,10)
[tex]\begin{gathered} 10=-3+7 \\ 10=4 \end{gathered}[/tex]So A is incorrect.
For B) y = x + 7
we replace (3,10), (4,11), (5,12) and (6,13)
[tex]\begin{gathered} 10=3+7=10 \\ 11=4+7=11 \\ 12=5+7=12 \\ 13=6+7=13 \end{gathered}[/tex]So B is the correct answer
In a study of bluetits 12 birds were trapped and their masses and wing spans were measured. The data collected are shown in this table. Calculate the estimated standard deviation for the mass of the bluetits, showing your answer to 3 significant figures.
Answers
The standard deviation of the mass of the bluetits to 3 significant figures is 1.30.
What is the standard deviation?Standard deviation is used to determine the variation of a dataset. Standard deviation is the spread of a data from the mean of the dataset. The higher the value of the standard deviation, the greater the spread of the dataset.
In order to determine the standard deviation, take the following steps:
Determine the mean of the mass : (9.9 + 9.8 + 12.2 + 13.3 + 11.8 + 10.2 + 12. 3 + 12.9 + 9.2 + 10.3 + 10.7 + 12.1) / 12 = 11.225
Determine the difference between each value and the mean and then square the result and then find the square root. The answer gotten is the standard deviation. 1.30
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Determine whether the relation {(6, –3),
(4, 1), (7, –2), (–3, 1)} is a function. Explain.
Answers
Answer:
A ifs it's not right sorry
A wire of length 22cm is bent in the shape of a circle . find the area of the circle. if the same wire is recent in the form of a square, find it's area which figure encloses more area
Answers
The circle is found to have the more area as compered to the square.
What is termed as the perimeter?A perimeter is a loop that encompasses, encircles, or outlines a two-dimensional shape or length. The circumference of a circle or perhaps an ellipse is its perimeter.For the given question;
The length of the wire is given as 22 cm.
The wire is bent in the circle.
Then, the perimeter of the circle is 22 cm.
Perimeter = 2πr = 22 cm.
Where, π = 3.14 and r is the radius of the circle.
2πr = 22 cm.
r = 11/π 11/3.14
The area of the circle is found as;
Area = πr²
Put the values.
Area = 3.14(11/3.14)²
Area = 38.53 cm².
For the square.
Perimeter = 4 side
22 = 4 side
side = 22/4 = 11/2 = 5.5
Area of square = side²
Area of square = 5.5²
Area of square = 30.25 cm².
Thus, the circle is found to have the more area as compered to the square.
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i dont know how to do these please help
Answers
Answer:
Step-by-step explanation:
the formula for this is PV= nRT
where, P=Pressure, V= Volume, n = Number of moles, R= Molar gas constant, T=Temperature
for this question, P AT S.T.P= 101325 Nm^-2, V= ?, n= 1.35 mol, R= 8.31,
T= 273k
fixing the values into the formula we have,
[101325][V]=[1.35][8.31][273]
make V the subject of formula
V= [1.35][8.31][273]/101325
V= 3062.65/101325
V= 0.03 cm^3
solve for y = x + 8 for x
Answers
x = y - 8
(Score for Question 1: of 3 points) 1 1. Mahala is standing and fishing on a dock that is 2 - feet above the surface of the water in the pond. Her baited hook is 1.5 feet below the surface of the water. The surface of the water is represented by the 4 rational number 0. Use the number line to graph the distance the dock, point D. is above the water and the hook, point H, is below the water. Make sure you label each point appropriately. Answer: 3 2 -1 0 1 2 3
Answers
graphing the distance of the dock, point D. is above the water and the hook, point H, is below the water.
See the diagram below :
Point D , is above the water =highlited in yellow.
Point H, the hook, is below the water = shown by colour green.
What are the correct answers the drop down both say negative or positive
Answers
Given the data set:
(-8,-10) (6, -1), (-5,-7),(3, -2) (10, 0) (4,-3) (-3,-6) , (9, 1)
We will graph the points to find the slope of the line of best fit for the data
The graph will be as shown in the following figure:-
As shown, the given points are the dots of blue color
The line of best fit is the dashed red line
As shown, the line has a positive slope and a negative y-intercept
So, the answer will be:
The line of best fit for the data will have a positive slope and a negative y-intercept value.
Drag each tile to the correct box Arrange the cylinders in order from least volume to greatest volume. agindur math a diameter of 28 un and a test of 18 units acide with a radius of 13 units and a height of 17 units a cyinder with a diameter of 30 pts and a hught of 14 units onder with a radius of 12 units and a hot 20 units
Answers
Answer:
Explanation:
The volume of a cylinder is given by
[tex]V=\pi r^2h[/tex]Now, to correct the order of the cylinders from least to greatest, we have to calculate the volume of each.
(a). A cylinder with a diameter of 28 units and a height of 18 units.
Diameter is 2 times radius; therefore, r = 14 and the volume is
[tex]V=\pi(14)^2\times18[/tex][tex]V=3529\pi[/tex](b). A cylinder with a radius of 13 units and a height of 17 units.
The volume is
[tex]V=\pi(13)^2\cdot17[/tex][tex]V=2873\pi[/tex](c). A cylinder with a diameter of 30 units and a height of 14 units.
The radius is 15 units; therefore, the volume is
[tex]V=\pi(15)^2\cdot14[/tex][tex]V=3150\pi[/tex](d). A cylinder with a radius of 12 units and a height of 20 units.
The volume is
[tex]V=\pi(12)^2\cdot20[/tex][tex]V=2880\pi[/tex]Hence, from least volume to greatest volume the order is
[tex](b)<(d)<(c)<(a)[/tex]What's the next term in the sequence of 1, 8, 27, 81, 243?
Answers
The next term in the sequence of 1, 8, 27, 81, 243 is 729.
What is a sequence?
Sequences are ordered collections of numbers, often known as "terms," such as 2,5,8. There are some sequences that adhere to a particular pattern that allows for endless extension. For instance, 2,5,8 adheres to the "add 3" pattern, thus we may now continue the process. There are formulas for sequences that show us where to find any given term.
It might be good to separate each phrase into its component parts to solve this problem:
1, or 3^0, is a factor of 1.
8 is 2^3
27 is 3^3
81 is 3^4
243 is 3^5
The likelihood of the following phrase is 3^6, or 729.
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solve for y 10x+8y=4
Answers
Solve the equation.
[tex]\begin{gathered} 10x+8y=4 \\ 8y=-10x+4 \\ y=-\frac{10}{8}x+\frac{4}{8} \\ =-\frac{5}{4}x+\frac{1}{2} \end{gathered}[/tex]So y = -5/4 x +1/2.
Find the least common multiple (LCM) of 12 and 18
Answers
Answer:
0.0[infinitely reprating] 1 is the smallest
Answer:
36
Step-by-step explanation:
LCM of 12 and 18 is the smallest number among all common multiples of 12 and 18. The first few multiples of 12 and 18 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (18, 36, 54, 72, . . . ) respectively
After 4 months of a new nutrition program rashid has lost 16% of his original weight he lost 36lb what was rashids original weight?
Answers
Rashids original weight based on the information illustrated is 225lb.
What was the original weight?From the information given, after the nutrition program rashid has lost 16% of his original weight he lost 36lb.
Let the original weight be given as x.
Therefore, 16% × x = 36
0.16x = 36
Divide through by 0.16
0.16x / 0.16 = 36 / 16
x = 36/0.16
x = 225lb
The weight is 225lb.
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What is the point-slope form of equation of the line that passes through the point (-1, -4) and has a slope of 3?
Answers
Answer:
y - (-4) = 3(x - (-1)
Step-by-step explanation:
Answer:
y−4=−3(x+1)
Step-by-step explanation:
ANGLES what is x,need quick please
Answers
Answer: x = 68
Step-by-step explanation:
Because the 22 degrees and x make up a complementary angle (add up to 90 degrees) we can subtract 22 from 90 to get x.
90-22 = 68
Find the exact value using a half angle identity: cos 7 pi/8
Answers
Answer:
[tex]\cos \frac{7\pi}{8}=-\frac{1}{2}\sqrt[]{2+\sqrt[]{2}}[/tex]Explanation:
Given
[tex]\cos \frac{7\pi}{8}[/tex]Using the identity:
[tex]\begin{gathered} \cos (\frac{7\pi}{2\times4})=\pm\sqrt[]{\frac{1+\cos\frac{7\pi}{4}}{2}} \\ \\ =-\sqrt[]{\frac{1+\frac{1}{\sqrt[]{2}}}{2}} \\ \\ =-\sqrt[]{\frac{2+\sqrt[]{2}}{4}} \\ \\ =-\frac{1}{2}\sqrt[]{2+\sqrt[]{2}} \end{gathered}[/tex]Homework 3.4: Compound InequalitiesScore: 10.38/1811/18 answeredQuestion 6<>04Give the interval that describes the set of values shown above.
Answers
Give the interval that describes the set of values shown above
The interval marked in blue has the following features:
* Starts with a filled blue dot at x=2
* Ends with a filled blued dot at x=4
* Runs from x=2 to x=4 with a blue line
The filled dots indicate that the endpoints are included in the interval
The line indicates that all the values in between the interval are included in the interval
There are two basic forms to indicate an interval with included endpoints:
* A pair of values (the endpoints) comma-separated included in a pair of brackets:
Interval: [2,4]
* The closed interval indicated by inequalities signs:
[tex]2\leq x\leq4[/tex]Select the correct answer.
What is the completely factored form of this polynomial?
x² + 12x²+32
OA.
O B. (x²+4)(x² + 8)
(x + 4)(X + 8)
O C.
O D.
(x²+4)(x + 2)(x + 4)
(x + 2)(x-2)(x² + 8)
G
Reset
Answers
Factor form of the polynomial (x+8)(x+4)
What is Polynomial?
A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
Given polynomial,
x² + 12x+32
x² + 4x + 8x +32
x(x+4) + 8(x+4)
(x+8)(x+4)
Hence, The completely factored form of this polynomial is (x+8)(x+4)
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11x+4<15 or 12x-7>25
Answers
Answer:
Step-by-step explanation:
11x + 4 < 15 or 12x - 7 > 25
-4 -4 +7 +7
11x < 11 or 12x > 32
11 (divide) 11 | 12 (divide) 12
x < 1 or x > 2.7
hope this is right!
hurry help DUE TONIGHT Based on the figure, which equation is true? Show your work.
Answers
Okay, here we have this:
Considering the provided figure, that we know an angle, the leg opposite a is an angle and we want to know the hypotenuse, we can use the trigonometric ratios since it is a right triangle, so we obtain the following:
The trigonometric ratio that relates an angle, its opposite leg and the hypotenuse is the sine, therefore that is the one we will use, so we have:
[tex]\begin{gathered} \sin (\vartheta)=\frac{Opp}{Hyp} \\ \sin (32)=\frac{8.5}{x} \end{gathered}[/tex]Finally we obtain that the correct answer is the first option (A).
