To determine the fourth vertex of an isosceles trapezoid given three vertices, we use symmetry and properties of isosceles trapezoids, concluding the missing vertex is likely at (-1,3).
Explanation:To find the fourth vertex of an isosceles trapezoid given three vertices, we need to use the properties of isosceles trapezoids. The properties pertinent to solving this problem include parallel bases and non-parallel sides of equal length. Given vertices at (2,5), (6,5), and (9,3), we know the top base is parallel to the x-axis, as the y-coordinate is the same (5) for the first two points.
For the trapezoid to be isosceles, the fourth vertex must follow the pattern of equal non-parallel sides. Observing the pattern of the given points, and noting that the length of the non-parallel side from (9,3) should equal that of the side starting from (2,5), we conclude the missing point must maintain this equality in distance and form a right angle, mirroring the shape on the opposite side.
Without specific lengths, we apply symmetry principles. The height difference between the known base and the third vertex (3) indicates a 2-unit drop, suggesting the opposite side will mirror this. Thus, the fourth vertex should be 2 units below the other base vertex, at (2,5), making the y-coordinate 3. Given the distances in x are equal (4 units from each end vertex to their respective base vertex), the fourth vertex is at (-1,3).
Two sides of a triangle have the same length. The third side measures 4 m less than twice the common length. The perimeter of the triangle is 20 m. What are the lengths of the three sides?
The lengths of the sides of the triangle are 6 m, 6 m, and 8 m.
What is the perimeter of a triangle?The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.
Let the length of the first side and 2nd side are x,
Two sides of a triangle have the same length.
The third side measures 4 m less than twice the common length.
So the length of the third side = 2x - 4
Given that the perimeter of a triangle is 20 m
Since the perimeter of a triangle is the addition of the lengths of the triangle's three sides.
So the perimeter of a triangle = sum of all sides
⇒ x + x + 2x - 4 = 20
⇒ 4x = 24
⇒ x = 6
So the length of the third side = 2(6) - 4 = 8
Hence, the lengths of the sides of the triangle are 6 m, 6 m, and 8 m.
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Final answer:
To find the lengths of the triangle's sides, we establish a variable x for the two identical sides. The equation 4x - 4 = 20 is solved to give x = 6. Thus, the triangle has sides of 6 meters, 6 meters, and 8 meters.
Explanation:
The question is asking to determine the lengths of the three sides of a triangle when two of the sides have the same length, and the third side is 4 meters shorter than twice the length of the other two sides. Additionally, it is given that the perimeter of the triangle is 20 meters.
Let's denote the common length of the two sides as x meters. Hence, the length of the third side would be 2x - 4 meters. Since the perimeter of the triangle is the sum of its sides, we have the following equation:
x + x + (2x - 4) = 20
This simplifies to:
4x - 4 = 20
Adding 4 to both sides gives:
4x = 24
Dividing by 4 gives:
x = 6
Therefore, the lengths of the two identical sides of the triangle are 6 meters each, and the length of the third side is 2(6) - 4 = 8 meters.
What is the solution to the following equation?
х+11 = 24
А. x = 13
B.х = 35
C. х = 17
D. x = 29
Answer:
A. x=13
Step-by-step explanation:
[tex]x + 11 = 24 \\ x = 24 - 11 \\ x = 13[/tex]
Four times a number decreased by seven
Factor to solve each equation.
x2 - 7x+6=0
Answer:
x is 1 or -7
Step-by-step explanation:
x^2-7x+6=0 //we must find two numbers with multiple as -7 and sum as +6. numbers are -1 and 7.
(x-1)(x+7)=0
x-1=0 -»x=1
x+7=0 -»x= -7
If m varies directly with n.
and m = 20 when n = 5.
what is it m= 18?
For which equation is (4, 3) a solution?
y = x + 3
y = 3 x – 4
y = 2 x – 5
y = 2 x – 1
Answer:
y=3 x -4
Step-by-step explanation:
yes
The treasure map said to start at the old oak tree, walk 70 paces north, then 40 paces East, then dig. What is the straight-line distance (in paces) from the tree to the treasure?
Answer:
The straight-line distance (in paces) from the tree to the treasure is 80.62 paces
Step-by-step explanation:
Given:
Distance walked towards the north = 70 Paces
Distance walked towards the East = 40 Paces
To Find:
The straight line distance from the tree to the treasure =?
Solution:
We we track the trail we can find a right triangle formed where the two sides are 70 pace and 40 pace each. The straight line distance is the hypotenuse of the triangle(Refer the figure below
Now we can find the length of the hypotenuse by Pythagorean theorem
[tex]a^2 =b^2 +c^2[/tex]
where b and c are the sides of the triangle
and a is the hypotenuse
[tex]a^2 = 70^2 +40^2[/tex]
[tex]a^2 =4900 + 1600[/tex]
[tex]a = \sqrt{4900 + 1600}[/tex]
[tex]a =\sqrt{6500}[/tex]
a = 80.62
Find the slope of the line passing through the points (3,4) and (8, -3)
Answer:
1.5
Step-by-step explanation:
y2 - y1 ÷ x2 - x1
(3,4) (8, -3)
(x1,y1) (x2,y2)
Included side between
Answer:
side WA
Step-by-step explanation:
i put sw which was wrong its (side WA) 100% ☺☺☺
HELP PLS OR IM DEAD......
Answer: OPTION C.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Whrere "m" is the slope and "b" is the y-intercept.
The line intersects the y-axis when [tex]x=0[/tex], therefore, you can identify from the given table that "b" is:
[tex]b=3[/tex]
Now, in order to find the slope of that line, you can follow these steps:
1. Substitute the value of "b" and the coordinates of any point from the table and into [tex]y=mx+b[/tex]
2. Solve for "m".
Then, choosing the point (1,1), you get:
[tex]1=m(1)+3\\\\1-3=m\\\\m=-2[/tex]
Therefore, you can determine that the equation of that line in Slope-Intercept form, is:
[tex]y=-2x+3[/tex]
its c are you already dead??
Find the additive inverse or opposite of –4
Final answer:
The additive inverse of – 4 is 4 because when – 4 is added to 4, the result is 0. This demonstrates the concept of additive inverses in algebra, where each number has a counterpart that sums to zero.
Explanation:
The question is asking to find the additive inverse or opposite of – 4. The additive inverse of a number is the number that, when added to the original number, results in a sum of zero. This is a fundamental concept in algebra and mathematics in general. To find the additive inverse of – 4, you simply need to find a number that, when added to – 4, equals 0.
The additive inverse of – 4 is 4. This is because – 4 + 4 = 0. When you add – 4 and its additive inverse together, their sum is 0, which means 4 is the correct answer. The concept of the additive inverse is crucial in equations solving and other algebraic manipulations, assisting in understanding how to balance equations and solve for unknowns.
solve for
please help!!
Answer:
x = 76°
Step-by-step explanation:
At point I
to get angle JID
angle JID + 107° = 180°. (angle on a straight line)
angle JID = 180° - 107°
angle JID = 73°
for Triangle JiD
angle DJI + 31° + 73° = 180° (Sum of angles in a triangle)
angle DJI = 180 - 104 = 76°
angle FJI = 31 + 73 =104°. ( Sum of two interior angles in a triangle is equal to one exterior angle)
Hence,
x° + 104° = 180° (angle on a straight line)
x = 76°
help me please-------------------------
Answer:
Based on the answers I can see, it'd be all of them.
Step-by-step explanation:
When rounding to the nearest hundred, you round down if the tens are 49 or smaller (e.g. 401 to 400). If the tens are 50 or bigger, you round up (e.g. 351 to 400). I hope that helps you.
3/10 + 62/100 =
WILL YOU PLEASE GIVE STEPS TO FIND THE SUM ON THE PROBLEM ABOVE?
3/10 = 30/100 after multiplying top and bottom by 10
so we have 30/100 + 62/100 = (30+62)/100 = 92/100
Reduce this fraction
92/100 = (23*4)/(25*4) = 23/25
Therefore, 3/10+62/100 = 23/25
Karen gave an equal amount of m and m's to herself and four friends. Each person receives m and m's equivalent to the largest one digit number. How many m and m's did Karen have?
Answer:
Karen had 45 m and m's candy.
Step-by-step explanation:
Let the number of m and m's candy be 'x'.
Now given:
Karen gave an equal amount of m and m's to herself and four friends.
So we can say that;
Number of people m and m's candy distributed equally = 5
Also Given:
Each person receives m and m's equivalent to the largest one digit number.
Now we know that;
Largest one digit number is 9.
So we can say that;
Each person receives m and m's = 9
We need to find number of m and m's Karen have.
Solution:
So we can say that;
Total number of m and m's Karen have is equal to Number of people m and m's candy distributed equally multiplied by number of m and m's can each person receives.
framing in equation form we get;
Total number of m and m's Karen had = [tex]9\times5 = 45[/tex]
Hence Karen had 45 m and m's candy.
The Ramy family bought 4 sandwiches and 3 salads. They spent $24. Let x be the cost of a sandwich and y be the cost of a salad.
If each sandwich costs $3.75, how much did each salad cost?
The core of calculus in mathematics are functions. The unique varieties of relations are the functions.
The cost of 1 salad exists $3.
What is meant by function?A function is a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.
A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain.
Let, the cost of 1 sandwich be 'x' and the cost of 1 salad is 'y'.
4 sandwiches = 4x
3 salads = 3y
total spent = $24
From the given equation, we get
4x + 3y = 24
If each sandwich costs $3.75,
⇒ 4(3.75) + 3y = 24
simplifying the above equation, we get
⇒ 15 + 3y = 24
⇒ 3y = 24 - 15
⇒ 3y = 9
⇒ y = 9/3
⇒ y = 3
Therefore, the cost of 1 salad exists $3.
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Interest earned: $3250 principal: $5000 Interest rate: ? Time: 10 years Please HELP ME! :0 20 points
Answer: Interest rate = 0.065
Step-by-step explanation:
I=PRT
3250=5000r*10
Divide by 10 on both sides
325=5000r
r=0.065
(4x²+9x-7) - (-7x²+5x-1)
Answer:
11 x^2 + 4x -6
Step-by-step explanation:
combine like terms but be careful with the minus sign in front of the second set of parentheses.
4x^2 + 9x -7 + 7x^2 -5x +1
Answer: [tex]-3x^2+4x-6\\[/tex]
Step-by-step explanation:
4x^2 +9x-7 does not need distributive propery
-(7x^2+5x-1) does with that negitive in front of parentheses
It then becomes -7x^2-5x+1
Add it all together
[tex]-3x^2+4x-6[/tex]
:
Select all that apply.
40 is what percent of 25.
A
160%
B
62.5%
C
1600%
D
625/1000
E
160/100
F
1600/100
Answer:
The answer is A 160% and E [tex]\frac{160}{100}[/tex].
Step-by-step explanation:
To find what percentage 40 is of 25, you first need to find what 1% of 25 is. To solve you do 25 ÷ 100 which is equal to 0.25. You then need to divide 40 by 0.25, which would be the same as multiplying 40 by 4. 40 ÷ 0.25 = 160. Therefore, 40 is 160% of 25. 160% is the same as saying [tex]\frac{160}{100}[/tex] or 160 out of 100 or you could say 160 ÷ 100 = 1.6, which would mean 25 × 1.6 = 40.
40 as a percentage of 25 can be applied such that the percentage would be:
A. 160%E. 160/100How to find the percentages ?To find what percent 40 is of 25, you would use the formula:
= (Part / Whole) * 100%
So here, 40 is the part and 25 is the whole:
= (40 / 25) * 100%
= 160%
40 is 160 % of 25.
160 / 100 is also 160 %. The rest of the options are incorrect leaving options A and E.
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Jamahl Jones earned $20.50 cutting grass, $16.50 babysitting, and $4.95 selling two baseball cards. He puts
all but $10.00 in his checking account. What is his total deposit?
a. $41.95
c. $31.95
h $31.50
d. $30.00
Can someone answer this?
Apply the product rule by raising each term by the power outside powers.
Then divide and simplify to get the second choice:
40w + (1.5)(8)(w) =780
Answer: w = 15
Original Question: 40w + (1.5)(8)(w) =780
Step-by-step explanation:
1) 40w + 1.5 x 8w = 780
2) 40w + 12w = 780
3) 52w = 780
4) 52w/52 = 780/52
w = 15
What are the solutions of the polynomial 4x^2-4x+10 4 x 2 − 4 x + 10? Write the answer in complex, a+bi a + b i form.
x=____+____i,x=____-____i
The solutions of the polynomial are [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
Step-by-step explanation:
The solutions of a polynomial is the value of x when the polynomial equal to zero
The formula of quadratic polynomial is [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}[/tex] , where
a is the coefficient of x²b is the coefficient of xc is the numerical term∵ The polynomial is 4x² - 4x + 10
- Equate it by zero to find its solutions
∴ 4x² - 4x + 10 = 0
∵ The coefficient of x² is 4
∴ a = 4
∵ The coefficient of x is -4
∴ b = -4
∵ The numerical term is 10
∴ c = 10
- Use the formula to find the values of x
∵ [tex]x=\frac{(-4)(+/-)\sqrt{(-4)^{2}-4(4)(10)}}{2(4)}[/tex]
∴ [tex]x=\frac{-4(+/-)\sqrt{16-160}}{8}[/tex]
∴ [tex]x=\frac{-4(+/-)\sqrt{-144}}{8}[/tex]
∵ [tex]\sqrt{-144}=12\sqrt{-1}[/tex]
- Substitute [tex]\sqrt{-1}[/tex] by i
∴ [tex]12\sqrt{-1}=12i[/tex]
∴ [tex]x=\frac{-4(+/-)12i}{8}[/tex]
- Divide up and down by 4 to simplify the fraction
∴ [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
The solutions of the polynomial are [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
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Let f(x) = 2x + 5. The graph of f(x) is transformed into the graph of g(x) by a vertical
stretch of 3 and a translation of 4 units down. What is the equation for g(x)? Show
and explain your work.
The equation of g(x) is g(x) = 6x + 11
Step-by-step explanation:
Let us revise some transformation
A vertical stretching is the stretching of the graph away from the x-axis, If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by kIf the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k∵ f(x) = 2x + 5
∵ The graph of f(x) is stretched vertically by scale factor 3
- That means multiply f(x) by 3
∴ The equation of the new graph is 3(2x + 5)
∵ The new graph is translated 4 units down
- That means subtract 4 from 3(2x + 5)
∴ The equation of g(x) is g(x) = 3(2x + 5) - 4
- Simplify the equation of g(x)
∴ g(x) = 3(2x) + 3(5) - 4
∴ g(x) = 6x + 15 - 4
- Add the like terms in the right hand side
∴ g(x) = 6x + 11
The equation of g(x) is g(x) = 6x + 11
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three sets of the sum of a number and four are added to the sum of seven times the same number and thirteen
The algebraic expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)
Solution:
Given the statement:
Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen
Let us first understand the given statement,
Let the number be "x"
" sum of a number and four" means x + 4
"Three sets of a sum of a number and four" translated to 3(x + 4)
"sum of seven times the same number and thirteen" means 7x + 13
Thus the algebraic expression for given statement is:
[tex]3(x+4)+(7x + 13)[/tex]
Using distributive property in above expression
[tex]a(b+c) = ab + bc[/tex]
Therefore,
[tex]3(x+4)+(7x + 13) = 3x + 12 + 7x + 13[/tex]
Combine the like terms
[tex]3(x+4)+(7x + 13) = 10x+25[/tex]
Thus the required expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)
Given the line below.
Write the equation of the line, in point-slope form. Identify the point (-2, -2) as (x1, y1). Use the box provided to submit all of your calculations and final answer.
Answer:
[tex]y+2=(x+2)[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(-2,-2) and (2,2)
substitute the values
[tex]m=\frac{2+2}{2+2}=1[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=1\\(x1,y1)=(-2,-2)[/tex]
substitute
[tex]y-(-2)=(1)(x-(-2))[/tex]
[tex]y+2=(x+2)[/tex]
Suppose you and some friends are going to the movies. The amount of
money you spend for tickets varies directly with the number of people buying
tickets. If you spend $28 for four tickets, what is the constant of variation?
Answers:
1
4
7
28
Answer:
money spent = number of people * price of 1 ticket (direst variation)
28 = 4 * price of a ticket
so price of one ticket = 28/4 = 7
Constant of variation is 7
we might write it as m = 7n
Step-by-step explanation:
The angle of elevation of the top of a house from a point on the horizontal line 45m away from the foot of the house is 30 degree,find the height of house
The height of the house, given the angle of elevation and the distance of the point is 25. 98 meters.
How to find the height ?
You can use the tangent function because it relates the angle of elevation to the opposite side and the adjacent side (the horizontal distance).
The tangent of the angle of elevation is equal to the ratio of the height to the horizontal distance:
tan(30 degrees) = h / 45 meters
Solve for "h" by multiplying both sides by 45 meters:
h = 45 meters x tan(30 degrees)
You can calculate the value of tan(30 degrees):
tan(30 degrees) = 0.5774
Multiply:
h = 45 meters x 0.5774
= 25.98 meters
Evaluate the expression when n=4.
n^2+6n-6
Answer:
34
Step-by-step explanation:
when n=4.
n^2+6n-6 = (4)^2+6(4)-6 = 16 + 24 - 6 = 10 + 24 = 34
axb= 0.24. how many possible values for a and b are there?
Answer:
There are infinite possible values for a and b there.Step-by-step explanation:
[tex]a \times b = 0.24\\b = \frac{0.24}{a} or, a = \frac{0.24}{b}[/tex].
In the above equation the proper values can not be found only when the denominator will be 0.
As for example, if a = 2, then b = 0.12.
If a = 0.12, then b = 2.
If a = 1, b = 0.24 or b = 1, a = 0.24.
Thus, a or b can be any real number rather than 0.