Find the length of the midsegment of the trapezoid with the vertices S(0, 0), 7(2, 7), U(6, 10), V(8, 6).
The length of the midsegment is
Answers
Answer:
7.5
Step-by-step explanation:
A trapezoid is a quadrilateral where the bases are parallel, but the legs are not parallel.
Given vertices of trapezoid STUV:
S = (0, 0)T = (2, 7)U = (6, 10)V = (8, 6)The parallel bases of the trapezoid are TU and SV.
Find the lengths of TU and SV using the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}TU&=\sqrt{(x_U-x_T)^2+(y_U-y_T)^2}\\&=\sqrt{(6-2)^2+(10-7)^2}\\&=\sqrt{(4)^2+(3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}SV&=\sqrt{(x_V-x_S)^2+(y_V-y_S)^2}\\&=\sqrt{(8-0)^2+(6-0)^2}\\&=\sqrt{(8)^2+(6)^2}\\&=\sqrt{64+36}\\&=\sqrt{100}\\&=10\end{aligned}[/tex]
The midsegment of a trapezoid is the segment parallel to the bases that connects the midpoints of the legs.
[tex]\boxed{\begin{minipage}{6.5cm}\underline{Midsegment of a Trapezoid}\\\\$M=\dfrac{b_1+b_2}{2}$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the length of the midsegment. \\\phantom{ww}$\bullet$ $b_1$ and $b_2$ are the parallel bases. \\\end{minipage}}[/tex]
Substitute the found lengths of the bases into the midsegment formula:
[tex]\implies M=\dfrac{5+10}{2}[/tex]
[tex]\implies M=\dfrac{15}{2}[/tex]
[tex]\implies M=7.5[/tex]
The length of the midsegment is 7.5.
Related Questions
How many real solutions does the equation have?
g² +42 = 0
Answers
Answer:
The equation g² + 42 = 0 has two real solutions.
To solve this equation, we can start by subtracting 42 from both sides to get g² = -42. Then, we can take the square root of both sides to get |g| = √42. Since the square root of a number is positive, this means that g = √42 or g = -√42. These are the two solutions to the equation.
g²=0-42
g²=-42
Now, we can take the square root of both sides to cancel out the g²:
±√g²=±√-42
We have a problem here: negative roots do not exist. This is because no two same-signed values multiply together to get -42. View this example: a²=a•a and a²=-a•-a. A positive multiplied to a positive value produces a positive value, and a negative multiplied by a negative produces a positive value. By the definition of exponents, a number multiplied to itself can only be the same-sign as its base. Therefore, we have two imaginary solutions. The rule for complex numbers is: i=√-1 and i²=-1.
So, let’s simplify the equation into the proper complex numbers:
g=±√42•-1
Notice how the 42 is factored into 42•-1. This is because √-1=i.
g=±i√42
Thus, the equation has no real solutions.
HELP ASAP PLEASE will give branlist what is the slope of the linear relationship
1/4
-4/1
4/1
-1/4
Answers
Answer:
-1/4
Step-by-step explanation:
the slope is going down by a rate of -1/4
The diagram shows a isosceles right triangle, follow the steps to explore relationships between Saint triangles, measure the length of each leg and hypotenuse
Answers
The length of the sides are given by the 45°–45°–90° triangle theorem.
Correct responses:
AB = 1
AC = 1
BC = √2
How to find the length of an Isosceles Triangle?The 45°–45°–90° triangle theorem is one that states that the ratio of the lengths of the sides of triangles having interior angles of 45°, 45°, 90° is expressed as 1 : 1 : √2
We know that the lengths of the legs of an isosceles triangle are equal. Now, the legs of the given isosceles right triangle in the attached file are AB and AC.
Thus, we can say that, AB = AC
If the length of AB s 1 unit, then we have;
AB = AC = 1
Using Pythagoras theorem, we have;
BC² = AB² + AC²
Which gives; BC = √2
Therefore, by plugging in the length of AB = AC = 1, we have;
AB = 1
AC = 1
BC = √2 ≈ 1.414
The above values are in the ratio 1 : 1 : √2, which now corresponds with the 45°-45°-90° triangle theorem.
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divide
6x^4-2x^3- 13x-7 by 3x plus 8
Answers
Answer:
700 the answer is 700.
Step-by-step explanation:
the answer is 700
Shady Grove Middle School is having an outdoor activity day. Each grade can have several teams, but the size of the team must be the same for each grade. There are 108 seventh graders and 102 eighth graders. How many students can be on each team?
Answers
108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 54, 108
102: 1, 2, 3, 6, 17, 34, 51, 102
Both has the GCF of 6 (if that’s how you word it)
Your answer would be 6 students on each team. And I have no idea if it’s called GCF for both numbers. Probably is, but eh.
If m∠b is 32°, what is the m∠d?
58⁰
64⁰
148⁰
32⁰
Answers
Answer:
I guess it's 58° fr apparently
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. If necessary, round to the nearest tenth. A(-2,4), B(4,-3);3to2
Answers
The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2 is the ordered pair (4.2, -0.2).
How to determine the coordinates of point P?In this exercise, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.
Mathematically, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(3(4) + 2(-2))/(3 + 2)], [(3(-3) + 2(4))/(3 + 2)]
P(x, y) = [(27 - 4)/(5)], [(-9 + 8)/5]
P(x, y) = [21/5], [-1/5]
P(x, y) = [4.2, -0.2]
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PLEASE HELP ME! URGENT!
Answers
The numeric values for each expression in this problem are given as follows:
a. g(g(g(1))) = 1.
b. f(f(f(2)) = 1.
c. f(f(g(2))) = 2.
d. g(f(g(4))) = 2.
How to obtain the numeric value for each expression?The numeric value for each expression is obtained using the compositions, and also the numeric values given from the tabke,
As an example, from the table, we have that when x = 1, g(x) = 4, hence:
g(1) = 4.
Hence:
g(g(g(1))) = g(g(4)) = g(3) = 1.
The circle symbol represents composition, meaning that the expressions are similar to item a.
Thus the numeric value in item b is obtained as follows:
f(f(f(2)) = f(f(4)) = f(5) = 1.
The numeric value in item c is obtained as follows:
f(f(g(2))) = f(f(5)) = f(1) = 2.
The numeric value in item d is obtained as follows:
g(f(g(4))) = g(f(3)) = g(6) = 2.
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please help with math .... ok please
Answers
Answer:
A) : 10% = 48
Final result: 432
Step-by-step explanation:
10 * 480 / 100
= 4800 / 100
= 48
480 - 48 = 432 (final result)
Answer:
B) : 54
Final result: 306
Step-by-step explanation:
15 * 360 / 100
= 5400 / 100
= 54
360 - 54 = 306 (final result)
I hope this helps!
*To find the percent, use this formula: part percent * whole number / 100
Kendyl ate 4 pieces of the banana. Adison ate 2
pieces of the banana. They ate the entire
panana. What fraction represents the WHOLE
banana?
Answers
Answer:
Whole banana = 6/6
Step-by-step explanation:
Given information,
→ Kendyl ate 4 pieces.
→ Adison ate 2 pieces.
Now the total number of pieces,
→ 4 + 2
→ 6 banana pieces
Fractional representation is,
→ Kendyl = 4/6
→ Adison = 2/6
→ Whole banana = 6/6 = 1
Hence, the answer is 6/6.
solve the quadratic equation graphically using at least two different approaches when necessary give your solutions to the nearest hundredth. x^2+12x+11=0 a. x=-11 or x=-1 b. x=1 or x=6 c. x=10 or x=-3 d. x=0 or x=-6
Answers
The roots of the quadratic equation are x= -1 and x= -11
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
y = x²+12x+11
Axis of Symmetry is x={-6.00}
Vertex at (x,y) = (-6.00,-25.00)
x -Intercepts (Roots) :
Root 1 at (x,y) = (-11.00, 0.00)
Root 2 at {x,y} = (-1.00, 0.00)
Take some random values for x and find corresponding y values using the equation y = x²+12x+11
Plot the points to get the graph attached
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Triangle DEF is shown below.
How many degrees GREATER is the sum of the measures of angle D and E than the measure of angle f?
Answers
The sum of the measures of angles D and E is (3x + 25)° greater than the measure of angle F. which is the correct answer would be an option (C).
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The given Triangle DEF which has
∠D = 3(x+10)°
∠E = (2x+15)°
∠F = 2(x+10)°
The sum of the measures of angles D and E :
3(x+10)° + (2x+15)°
3x + 30 + 2x + 15
5x + 45
Difference between the sum of the measures of angles D and E and the measure of angle F :
5x + 45 - 2(x+10)
5x + 45 - 2x - 20
3x + 25
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need someone to answer this question please.
Answers
Answer:
56, 265.
Step-by-step explanation:
Since numbers from 0 - 4 turn into a zero and the numbers 5-9 turn into a zero (meaning it cancels) and carry a point to the next number. So for example, the number 38.7 rounded to the nearest ten is 39. Since from the right side, the 7 is higher then 5 that means it cancels and a point goes to the eight turning it into a 9. So 38.7 rounded to the nearest ten is 39.
A-1 Chemical Supply pays Kim Bryant a $1010 monthly salary plus a 12% commission on merchandise she sells each month. Assume Kim's sales were $16,100 for last month.
Answers
Kim's total salary for each month is given as follows:
$2,942.
How to obtain Kim's total salary?Kim's salary is divided into two earnings, as follows:
Fixed salary of $1,010.Commission of 12% on her sales.Kim's sales were $16,100 for last month, hence her commission is found applying the proportion as follows:
0.12 x 16100 = $1,932.
(the proportion is obtained multiplying the decimal equivalent of the percentage by the total amount to obtain the desired amount).
Then, adding to the fixed salary of $1,010, her total salary for the past month is obtained as follows:
1010 + 1932 = $2,942.
Missing InformationThe problem is incomplete, hence we suppose that it asks for Kim's total salary last month.
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For each of the following transformations of the parent function f(x) = x^3, graph both functions on the same set of axes, and evaluate the impact of the transformation on the number and location of the X-and y-intercepts, and on the symmetry of the function.
Answers
The graph of the functions f(x) = (-5x)³ and f(x) = x³ - 4 are drawn below.
How to draw the graph of the function?The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.
The parent function is given below.
f(x) = x³
The function is stretched by 5 units and gets reflected over the y-axis. Then the function is given as,
f(x) = (-5x)³
The function is shifted by 4 units downward then subtract 4 from the function. Then the function is given as,
f(x) = x³ - 4
The graph of the functions f(x) = (-5x)³ and f(x) = x³ - 4 are drawn below.
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which inequalilty corresponds with the graph below
Answers
The inequality which corresponds with the graph below is x + y ≤ 0.
What is inequality?A mathematical expression in which the sides are not equal is referred to as being "inequality." An inequality, in its most basic form, is a comparison of any two values that shows that one value is less than, greater than, or equal to the value on the other side of the equation.
Less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠) are the inequality symbols.
Comparing numbers and identifying the range (or ranges) of values that meet the specifications of a given variable are both done using inequalities.
The equation of the above straight line is
y = −x
or
x + y=0
Now the shading in the above graph is towards the negative part (where x is negative).
Also the line is dark and not dotted. This indicates that the points on the line are part of the inequality.
Thus, the inequality which corresponds with the graph below is x + y ≤ 0.
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Full question:
Which inequality corresponds with the graph below
a. y - x ≤ 0
b. x - y ≤ 0
c. y + x ≤ 0
d. None of the above
Refer to the table on air travel. Suppose a flight that arrived at El Centro is selected at random. What is the probability that the flight did not arrive on time? Express the answer as a fraction, decimal, and percent. Explain your reasoning.
Air Travel
Airport: El Centro (CA) ; Baltimore (MD)
Arrivals (Percent on-time): 80 ; 82
Answers
The expression of the probability that the flight did not arrive on time at El Centro is as follows:
Fraction = 1/5Decimal = 0.2Percentage = 20%.What is the probability?Probability is the chance or likelihood that an expected outcome occurs or does not occur.
Probability describes an occurrence's relative value (ratio) over many possible events.
When the likelihood is 100% certain or uncertain, the probability is 1 or 0, respectively. Otherwise, probability as a fractional value lies between zero and one.
Air Travel
Airport: El Centro (CA) Baltimore (MD)
Arrivals (Percent on-time) 80% 82%
Did not arrive on time:
Percentage = 20% (100 - 80) 18% (100 - 82)
Fraction = 1/5 (20/100) 9/50 (18/100)
Decimal = 0.2 (20/100) 0.18 (18/100)
Thus, the probability that the El Centro flight did not arrive on time is 20%, 1/5, or 0.2.
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Find the sum and express it in simplest form.
(6y³+ y2) + (-4y³ + 2y² + 1)
008
Clear all
Enter the correct answer.
180
?
DONE
Answers
Answer:
[tex]2y^3+3y^2+1[/tex]
Step-by-step explanation:
Given expression:
[tex](6y^3+y^2)+(-4y^3+2y^2+1)[/tex]
Remove the parentheses:
[tex]6y^3+y^2-4y^3+2y^2+1[/tex]
Collect like terms:
[tex]6y^3-4y^3+y^2+2y^2+1[/tex]
Combine like terms:
[tex]2y^3+3y^2+1[/tex]
Determine the truth value of each of the following implications.
a. If 3 + 4 = 12, then 3 + 2 = 6
b. If 3 + 3 = 6, then 3 + 6 = 9
c. If 3 + 3 = 6, then 3 + 4 = 9
d. If Fidel V. Ramos was the twelfth president of the Republic of the Philippines. Then 2 + 3 = 5
Answers
Answer:
Step-by-step explanation:
A: false
B: true
C: true
D: false
a certain college graduate borrows 7506 to buy a car. the lender charges interest at an annual rate of 15%. assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k dollars per year, determine the payment rate that is required to pay off the loan in 2 years. also determine how much interest is paid during the 2-year period
Answers
The payment amount rate required to pay off the loan in 2 years is k = $4,266.67 and the total interest paid during the two-year period is $2,142.66. This is calculated by using the formula for continuous compounding to solve for k and the formula for calculating interest to solve for I.
1. Calculate the payment rate required to pay off the loan in 2 years:
k = P/(1 - e^(-rt))
= 7506/(1 - e^(-0.15*2))
= 7506/(1 - 0.8698)
= 4,266.67
2. Calculate the total interest paid during the two-year period:
I = P(e^(rt) - 1)
= 7506(e^(0.15*2) - 1)
= 7506(1.3302 - 1)
= 2,142.66
Payment rate required to pay off the loan in 2 years: K = $5,062.89. The amount of interest paid during the 2-year period is $1,506.11. The borrower pays back a total of $9,012.89 over the 2-year period. The interest rate of 15% is continuously compounded and the payments are made at a continuous rate of K dollars per year.
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⠀⠀⠀
Solve the quadratic equation graphically using at least two different approaches. When necessary, give your solutions
to the nearest hundredth.
x² + 12x + 11 = 0
a.
b.
x = -11 or x = -1
x = 1 or x = 6
C.
d.
01:41:19
x = 10 or x = -3
x=0 or x = -6
Answers
The solution for the given quadratic equation is x = -11 or x = -1.
What is a quadratic equation?A quadratic equation is an equation of second order. Quad implies the square power, it is also called equation of degree 2.
The standard form of a quadratic equation is ax² + bx + c = 0.
Where a, b and c are constants.
The given quadratic equation is,
x² + 12x + 11 = 0.
The graph of the equation is, plotted below.
From the graph,
The solutions are x = -1 and x = -11
The second approach to find the solution for the given quadratic equation is factorization method,
x² + 12x + 11 = 0
x² + 11x + x + 11 = 0
x(x + 11) + 1(x + 11) = 0
(x + 11) (x + 1) = 0
x = -11 or x = -1
So the required solution is x = -11 or x = -1.
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Allan dreams of being a real estate agent. He has just graduated with a degree in business. When will Allan be ready to start work as a real estate agent?
as soon as a new position becomes available at a local real estate firm
OB.
after he works as an administrative assistant at a real estate firm
O C. after he passes a licensing exam to prove he's qualified to sell real estate
O D. as soon as he job-shadows a successful real estate agent for at least three weeks
A.
Answers
Allan will be ready to start work as a real estate agent; After he passes a licensing exam to prove he's qualified to sell real estate.
What is sell real estate?Selling real estate is the process of transferring ownership of a piece of property from one person or entity to another.
The complex process that involves several steps, includes determining the market value of the property, marketing the property, negotiating with prospective buyers, and finally closing the sale.
This is important to work with an experienced real estate professional who can help guide, through each step in the process and ensure that everything is handled properly.
So the correct option is C.
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Translate this sentence into an equation. 23 more than Delia's height is 56. Use the variable d to represent Delia's height.
Answers
Answer: d + 23 = 56
Step-by-step explanation:
" More than" is another way of saying "added by", so your problem is Delia's height added by 23 is 56. If we replace Delia's height with the variable d, then we get d added by 23 is 56. This is really easy now,
d + 23 = 56
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Which of the following is the best approximation of the volume of the cylinder below?
Answers
The volume of the cylinder is 602.9 cm³
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We need to find the volume of the cylinder whose height is 3 cm and diameter is 16 cm.
Radius =16/2=8 cm.
The volume of a cylinder is equal to the product of the area of the circular base and the height of a cylinder.
V = πr²h
where 'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
As per the given figure,
The radius of a cylinder is 8 cm and the height of the cylinder is 3 cm.
V = 3.14×8²×3
=3.14×64×3
=602.88=602.9 cm³
Hence, the volume of the cylinder is 602.9 cm³
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6. Complete the two-column proof.
Given: 3x + 4 = 10 Prove: x = 2
3x + 4 = 10 __?___
3x = 6 __?___
x = 2 ___?___
Answers
Answer:
see explanation
Step-by-step explanation:
given
3x + 4 = 10 ( subtract 4 from both sides )
3x = 10 - 4 = 6 ( divide both sides by 3 )
x = 6 ÷ 3 = 2
thus x = 2 is proven
3x+4=10 Given
3x=6 Subtraction Property of Equality
x=2 Division Property of Equality
Marcie cooked dinner for herself. The original recipe has a serving size of 2 and requires 2 2/3 pounds of chicken. How many pounds of chicken will be needed for a single serving?
Answers
Answer:The answer is 1 1/3 pounds of chicken.
Step-by-step explanation:
For a single serving of the recipe, you would need half the amount of chicken that is required for a serving size of 2, which is 2 2/3 / 2 = 1 1/3 pounds of chicken.
Elapsed time
Mary rented a movie. She started the movie at 10:29 PM and it ended at 1:49 AM. How long was the movie?
Answers
Answer:3 hours 20 mins
Answer:
3 hours 20 minutes is the length of the movie.
How many three letters code words can be constructed from the first nine letters of the Greek alphabet if no repetition are allowed
Answers
Answer:
504
Step-by-step explanation:
There are 9 choices for the first letter, 8 choices for the second letter, and 7 choices for the third letter, for a total of 987 = 504 three-letter code words that can be constructed from the first nine letters of the Greek alphabet without repetition.
is this problem proportional:
a wood deck quoted at a bulk cost for 25 square ft.
Answers
In the problem, the information is not enough to find whether the problem is proportional or not.
What is proportions?A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given a phrase, a wood deck is quoted at a bulk cost for 25 square ft.
to find the problem proportional or not,
for proportional there must be at least four quantities, whose ratios are to be compared and if their ratios are equal they are said to be in proportion.
for example,
When two ratios are equal, they are said to be in proportion. For instance, the time it takes a train to travel 50 kilometres per hour is equal to the time it needs to travel 250 kilometres in 5 hours. e.g., 250km/5 hours = 50 km/h.
Hence for the given question, the information is not enough.
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factor the exprresion 27+12
Answers
3(13)
